J.M. Marcaide and K.W. Weiler (POSTERS) Cosmic Explosions: On the 10

J.M. Marcaide and K.W. Weiler Cosmic Explosions: On the 10th Anniversary of SN 1993J IAU Colloquium 192 (POSTERS) Springer Berlin Heidelberg NewYork Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo Contents Part I Supernovae: Individual Low Frequency Observations of SN 1993J with the Giant Meterwave Radio Telescope P. Chandra, A. Ray, S. Bhatnagar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Iron Abundance and Density Structure of the Inner Ring Around SN 1987A S.Mattila, P.Lundqvist, P.Meikle, R.Stathakis, R.Cannon . . . . . . . . . . . . . 9 Recent STIS Imaging Spectroscopy of the Hot Spots in SNR 1987A Stephen S. Lawrence, Ben E. K. Sugerman, Arlin P. S. Crotts, the SInS/SAINTS Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 The Formation of the Triple-Ring Nebula Around SN 1987A Thomas Morris and Philipp Podsiadlowski . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Light Echoes from SN 1987A and SN 1993J Ben E. K. Sugerman, Arlin P. S. Crotts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 ESC Observations of SN 2002er around Maximum Light G. Pignata, F. Patat, R. Kotak, P. Meikle, M. Stritzinger, W. Hillebrandt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Distance of the Hypernova SN 2002ap via the Expanding Photosphere Method J.Vinkó, M.Blake, K.Sárneczky, B.Csák, G.Fűrész, Sz.Csizmadia, L.L.Kiss, Gy.M.Szabó, R.Szabó, H.DeBond, M.M.de Robertis, J.R.Thomson, S.W.Mochnacki, S.M.Rucinski . . . . . . . . . . . . . . . . . . . . . . . 39 VI Contents Template Frames of Nearby Galaxies for SN-Photometry: Application to SN 2002bo in NGC 3190 K.Sárneczky, J.Vinkó, Gy.M.Szabó, G.Fűrész, B.Csák, R.Szabó, Sz.Csizmadia, Zs.Bebesi, Zs.Heiner, Sz.Mészáros, B.Sipőcz . . . . . . . . . . . 45 The Late UVOIR Light Curve of SN 2000cx Jesper Sollerman, Cecilia Kozma, Jan Lindahl . . . . . . . . . . . . . . . . . . . . . . 51 The “Central” Source in NGC 2146: a Radio Supernova or a Weak AGN? A. Tarchi, M. A. Garrett, A. Greve, S. T. Garrington . . . . . . . . . . . . . . . . 57 Part II Supernovae: Searches/Statistics StRESS: Southern Intermediate Redshift ESO SN Search, Global SNe Rate Estimate G. Altavilla, M. Riello, M.T. Botticella, S. Valenti, E. Cappellaro . . . . . . 63 The Supernova Program of the Canada-France-HawaiiTelescope Legacy Survey Stéphane Basa, on behalf of the SNLS collaboration . . . . . . . . . . . . . . . . . . 69 Hostless - or Just Very Faint? Lisa M. Germany, L.-G Strolger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 High-Resolution Optical Studies of Nearby Type Ia Supernovae Peter Lundqvist, Seppo Mattila, Jesper Sollerman, E. Baron, Pascale Ehrenfreund, Claes Fransson, Bruno Leibundgut, Ken’ichi Nomoto . . . . 81 Supernova Counts in Deep HST Fields Keren Sharon, Avishay Gal-Yam, Dan Maoz . . . . . . . . . . . . . . . . . . . . . . . . 87 Part III Supernovae: Models Wave Modes in Collapsar Jets Enrique A. Gómez, Philip E. Hardee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Non-radial Instability of Stalled Accretion Shocks: Advective-Acoustic Cycle Thierry Foglizzo, Pascal Galletti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A Self-Similar Problem on Supernova Explosion with an Account of Relativistic Accelerated Particles Yu. V. Petukhov, A. V. Razin, V. A. Razin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Contents VII X-rays from Circumstellar Interaction Tanja K. Nymark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Part IV Supernovae: GRB Connections Search for Correlations BATSE Gamma-Ray Bursts and Supernovae J. Polcar, M. Topinka, G. Pizzichini, V. Hudcová, E. Palazzi, R. Hudec, N. Masetti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Part V Supernovae: Progenitors/Remnants Complex molecules in NGC 2359. The gas chemistry of a core-collapse supernova progenitor J. R. Rizzo, J. Martı́n-Pintado . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Second Epoch Global VLBI Observations of Compact Radio Sources in the M82 Starburst Galaxy J. D. Riley, A. Pedlar, T. W. B. Muxlow, A. R. McDonald, R. J. Beswick, K. A. Wills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Secular Decrease and Random Variations of Cassiopeia A at 151.5 and 927 MHz E. N. Vinyajkin, V. A. Razin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Self-Consistent Model of Ions and Electrons Acceleration at Shock Wave Front in Supernova Remnant G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko . . . . . . . . 147 Development of Turbulent Mixing Semi-Empirical Model for Calculating MHD Parameters of Supernova Remnant G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko . . . . . . . . 155 Magnetohydrodynamic Models for the Structure of Pulsar-Wind Nebulae Stephen P. Reynolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Part VI Cosmology Critique of Tracking Quintessence Sidney Bludman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 VIII Contents Part VII Instruments Observing SNR in VHE γ-rays with the MAGIC Telescope E. Domingo, J. Cortina, A. Robert, V.Vitale, for the MAGIC collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Lobster Eye: Innovative X-Ray Telescopes for Deep Sky Monitoring René Hudec, Adolf Inneman, Ladislav Pı́na, Libor Švéda . . . . . . . . . . . . . 191 SNe and Lobster Eye X-ray Telescopes Libor Švéda, René Hudec, Adolf Inneman, Ladislav Pı́na, Stefan Immler 197 BART Status Martin Jelı́nek, Petr Kubánek, Martin Nekola, René Hudec . . . . . . . . . . . . 203 List of Contributors G. Altavilla INAF - Astronomical Observatory of Padova Vicolo dell’Osservatorio 5 I-35122 Padova, Italy altavilla@pd.astro.it Stéphane Basa Laboratoire d’Astrophysique de Marseille Traverse du Siphon Les Trois Lucs, BP 8 13376 Marseille Cedex 12 France stephane.basa@oamp.fr Sidney Bludman Deutsches Elektronen-Synchrotron DESY Hamburg, Germany, and University of Pennsylvania Philadelphia, PA, USA bludman@mail.desy.de P. Chandra Indian Institute of Science Bangalore, and Tata Institute of Fundamental Research Mumbai India poonam@tifr.res.in G.V. Dolgoleva RFNC-VNIIEF 607190, Sarov Nizhni Novgorod region E. Domingo Institut de Fı́sica d’Altes Energies (IFAE) Universitat Autònoma de Barcelona 08193 Bellaterra, Spain domingo@ifae.es Thierry Foglizzo Service d’Astrophysique CEA/DSM/DAPNIA CE-Saclay, 91191 Gif-sur-Yvette, France Lisa M. Germany European Southern Observatory Casilla 19001 Santiago, Chile lgermany@eso.org Enrique A. Gómez Department of Physics and Astronomy University of Alabama Box 870324 Tuscaloosa, AL 35487-0324 USA enrique.gomez@ua.edu X List of Contributors René Hudec Academy of Sciences of the Czech Republic CZ-251 65 Ondrejov Czech Republic rhudec@asu.cas.cz Yu. V. Petukhov Radiophysical Research Institute (NIRFI) 25 B. Pecherskaya St. Nizhny Novgorod 603950, Russia petukhov@hydro.appl.sci-nnov.ru Martin Jelı́nek Academy of Sciences of the Czech Republic CZ-251 65 Ondrejov Czech Republic G. Pignata European Southern Observatory Karl-Schwarzschild str. 2 D-85748 Garching bei München Germany gpignata@eso.org Stephen S. Lawrence Hofstra University Dept. of Physics Hempstead, NY 11549 USA physsl@hofstra.edu Peter Lundqvist Stockholm Observatory AlbaNova Department of Astronomy, SE-106 91 Stockholm, Sweden peter@astro.su.se S. Mattila Stockholm Observatory AlbaNova Department of Astronomy, SE-106 91 Stockholm, Sweden seppo@astro.su.se J. Polcar Astronomical Institute Ondřejov Czech republic polcar@physics.muni.cz Stephen P. Reynolds North Carolina State University USA steve reynolds@ncsu.edu J.D. Riley Centre for Astrophysics University of Central Lancashire Preston PR1 1JR, UK jdriley@uclan.ac.uk Thomas Morris Department of Astrophysics Oxford University Oxford, OX1 3RH, UK tsm@astro.ox.ac.uk J. R. Rizzo Departamento de Fı́sica Universidad Europea de Madrid Urb. El Bosque E-28670 Villaviciosa de Odon Spain jricardo.rizzo@fis.cie.uem.es Tanja K. Nymark Stockholm Observatory S-106 91 Stockholm Sweden tanja@astro.su.se K. Sárneczky Dept. of Optics University of Szeged Hungary sky@titan.physx.u-szeged.hu List of Contributors Keren Sharon School of Physics and Astronomy Tel Aviv University Israel kerens@wise.tau.ac.il Jesper Sollerman Stockholm Observatory AlbaNova 106 91 Stockholm Sweden jesper@astro.su.se Ben E.K. Sugerman Columbia University Dept. of Astronomy New York, NY 10027 USA ben@astro.columbia.edu Libor Švéda Astronomical Inst. of Charles Univ. XI Prague, Czech Republic woody@sirrah.troja.mff.cuni.cz A. Tarchi Instituto di Radioastronomia CNR Bologna, Italy a.tarchi@ira.cnr.it J.Vinkó Dept. of Optics University of Szeged Hungary vinko@physx.u-szeged.hu E.N. Vinyajkin Radiophysical Research Institute (NIRFI) 25 B. Pecherskaya st. Nizhny Novgorod 603950, Russia evin@nirfi.sci-nnov.ru Part I Supernovae: Individual Low Frequency Observations of SN 1993J with the Giant Meterwave Radio Telescope P. Chandra1 , A. Ray2 , and S. Bhatnagar3 1 2 3 Joint Astronomy Programme-Indian Institute of Science, Bangalore Tata Institute of Fundamental Research, Mumbai, poonam@tifr.res.in Tata Institute of Fundamental Research, Mumbai, akr@tifr.res.in National Radio Astronomy Observatory, New Mexico, sbhatnag@aoc.nrao.edu Summary. In this paper, we discuss the low frequency spectrum of SN 1993J with GMRT. We observed SN 1993J at several epochs in 20cm, 50cm, 90cm and 125cm wavelengths and achieved near simultaneous spectra. We fit synchrotron self absorption (SSA) and free-free models to the data. We compare the size of SN obtained using SSA fits to that of size extrapolated from VLBI measurements at various epochs using public data at earlier epochs. We find that the synchrotron self absorption process is insufficient to reproduce the observed size of the supernova under the assumption of equipartition between magnetic fields and relativistic electrons. We also derive the evolution of spectral index and magnetic field at several epochs. 1 Introduction SN 1993J, a typical type IIb supernova, exploded on March 28, 1993. It was the nearest extragalactic supernova observed (3.63 Mpc away) and due to its high positive declination, it was easily accessible by most of the telescopes for observations for most part of the year. For this reason SN 1993J is the most detailed studied supernova after SN 1987A, in all wavebands. The radio emission in supernovae is due to the synchrotron emission of relativistic electrons in the presence of magnetic field. The radio emission is absorbed in its early phases due to the presence of dense circumstellar medium. It can also be absorbed because of its own highly dense ejecta (synchrotron self absorption). In section 2 we describe the GMRT observations. In section 3, we discuss the spectra, the derived physical parameters from the various fits to the spectra and their physical interpretations. 2 Observations We observed SN 1993J with Giant Meterwave Radio Telescope in 1420, 610, 325 and 235 MHz wave bands. 0834+555 and 1034+565 were used a phase 4 P. Chandra, A. Ray, and S. Bhatnagar PLot file version 13 created 14-APR-2003 12:07:14 BOTH: SN1993J IPOL 232.625 MHZ 1993J 25.REGRD.1 0.0 0.5 1.0 1.5 69 43 30 00 42 30 DECLINATION (J2000) 00 41 30 00 40 30 00 39 30 00 38 30 09 56 15 00 55 45 RIGHT ASCENSION (J2000) Grey scale flux range= 0.000 1.500 JY/BEAM Cont peak flux = 2.1105E+00 JY/BEAM Levs = 2.000E-02 * (-2, -1, 1, 2, 4, 8, 16, 32, 64, 80, 100, 110, 128, 256, 512, 1024, 2048, 4096) PLot file version 4 created 14-APR-2003 11:29:00 BOTH: SN1993J IPOL 232.625 MHZ 1993J 25.REGRD.1 0 50 100 150 30 200 69 05 00 04 30 DECLINATION (J2000) 00 03 30 00 02 30 00 01 30 00 00 30 00 09 55 45 30 15 RIGHT ASCENSION (J2000) Grey scale flux range= 0.0 200.0 MilliJY/BEAM Cont peak flux = 2.1105E+00 JY/BEAM Levs = 1.300E-02 * (-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) 00 Fig. 1. GMRT contour map of FOV of SN 1993J in 243 MHz band (Observed on Mar8,02). Upper panel is M82 and lower panel is M81 (Top left) and SN 1993J (Bottom right). calibrators. 3C48 and 3C147 were used as flux and bandpass calibrators. The data was analyzed using the Astronomy Image Processing Software (AIPS). Figure 1 shows the FOV of SN 1993J at 243 MHz. Right hand upper panel is the zoomed in plot of M82 (neighboring galaxy in FOV) and lower panel is SN (bottom right) and its parent galaxy M81 (top left). The table 1 below gives the details of the observations used in this paper. We plot near simultaneous spectra at 4 epochs (See Figure 2). Since the supernova is 10 years old, we do not expect its flux to change by any significant amount in few days. The flux errors quoted in the table 1 are ((map rms)2 + (10% of the peak flux of SN )2 ) This 10% of the peak flux error takes into account any possible systematic errors in GMRT as well as any little variation in flux in the short time difference due to near simultaneous spectra. 3 Results and Interpretation We have fit the synchrotron self absorption models to the GMRT data and got the best fit radius, magnetic field and spectral index. We fitted the parameters under the assumption of equipartition which seems to be a reasonable approximation [5]. Since in the two cases , we have only 3 datasets for the 100 100 80 80 60 60 Flux in mJy Flux in mJy SN 1993J low frequency spectrum with GMRT 40 20 40 20 0.2 0.4 0.6 0.8 Frequency in GHz 1 1.4 100 100 80 80 60 60 Flux in mJy Flux in mJy 5 40 20 0.2 0.4 0.6 0.8 Frequency in GHz 1 1.4 0.2 0.4 0.6 0.8 Frequency in GHz 1 1.4 40 20 0.2 0.4 0.6 0.8 Frequency in GHz 1 1.4 Fig. 2. Spectrum at four epochs (Clockwise ∼ 8.2, ∼ 8.7, ∼ 9, and ∼ 9.5 years since explosion). Red (solid) line shows the SSA fit and green (dashed) shows the free-free fit. Table 1. Details of observations of near simultaneous spectra of SN 1993J Date of Days since Frequency Time on No. of Flux density rms Observation explosion in GHz Source (Hrs) Antennae mJy mJy Jul 5,01 Aug 24,01 Jun 2,01 3022 3072 2988 0.327 0.616 1.393 2.5 2 3 18 24 28 69.2±15.8 55.8±5.7 32.67±3.3 2.5 0.36 0.19 Dec 31,01 Dec 30,01 Oct 15,01 3199 3198 3123 0.239 0.619 1.396 3 1.7 2 20 20 24 57.8±7.6 47.8±5.5 33.9±3.5 2.5 1.9 0.3 Mar 08,02 Mar 07,02 Mar 08,02 Apr 07,02 3266 3265 3266 3296 0.232 0.325 0.617 1.396 3.3 4.1 3 2.3 17 24 25 25 60.9±10.8 56.2±7.4 44.4±4.5 24.6±3.7 4.1 1.9 0.32 1.0 Sep 16,02 Aug 16,02 Sep 16,02 Sep 21,02 3458 3427 3458 3463 0.240 0.331 0.617 1.397 3.4 2 2.7 2 17 16 15 25 56.7±8.7 62.4±8.8 37.5±3.8 24.3±2.4 4.0 2.7 0.4 0.2 P. Chandra, A. Ray, and S. Bhatnagar SSA Radius in µas 6 1000 1000 VLBI Radius in µas Fig. 3. The fig shows comparison between the VLBI radii of SNe ([1]) and the best fit synchrotron self absorption radius. The straight line is the line where both the radii will be same. Note that best fit SSA radius is much lower than VLBI radii. spectrum, we tried different values of spectral index and get the best χ2 fit. We derived the size of the VLBI supernova from [1] and added 5% error bars to account for any possible error in measurement. Figure 3 shows the plot of best fit synchrotron self absorption radius against VLBI radius at various epochs. For early epochs, we have used VLA public data and data from [4]. The straight line is where both the radii are same. It is noteworthy that the synchrotron self absorption radius is significantly smaller than the VLBI radius at all epochs, contrary to findings of [6]. A combined SSA plus free-free fit also did not improve the results. Figure 4 shows the evolution of spectral index and magnetic field with time. We find that the spectrum of SN becomes flatter with time The magnetic field is also decreasing with time, a reason for decreasing radio flux, because synchrotron emission mechanism becomes less efficient as magnetic field decreases. We also calculate the mass loss rate for Te =7×104 K (assuming a constant temperature at these late epochs [3]). Figure 5 shows the radio mass loss rate curve (green,[7]) overlaid on that of X-ray [2] and red points are mass loss rates obtained from GMRT data. Within error bars they seem to fit well with both radio and X-ray curves. Our derived magnetic field given on the right panel of fig. 5 is marginally consistent with that of Bartel [1] under the assumption of equipartition between magnetic field and relativistic particles. SN 1993J low frequency spectrum with GMRT 7 1.3 0.7 1.2 0.6 Magnetic Field (Gauss) Spectral Index α 1.1 1 0.9 0.8 0.4 0.3 0.2 0.7 0.1 0.6 0.5 0.5 500 1000 1500 2000 2500 Time since explosion (days) 3000 3500 4000 0 0 500 1000 1500 2000 2500 Time since explosion (days) 3000 3500 4000 Fig. 4. The left panel shows the evolution of spectral index α with time. The right panel shows the evolution of the magnetic field. Fig. 5. Left panel is X-ray mass loss rates (black,[2]) and radio mass loss rate (green,[7]). Red pts. are mass loss rates obtained from GMRT. Right panel shows the mag. field derived from GMRT data (square) superimposed on top of Fig. 13 of [1]. Acknowledgement. We thank the staff of GMRT (NCRA-TIFR) that made these observations possible. References 1. 2. 3. 4. 5. 6. 7. Bartel, N., Bietenholz,M.F., Rupen, M.P., et al 2002 ApJ, 581, 404 Immler, S., Aschenbach, B., Wang, D., 2001 ApJ, 561, L107 Fransson, C., Bjornsson, C. 1998 ApJ, 509, 861 Perez-Torres, M.A., Alberdi, A., Marcaide, J.M. 2002 A&A, 394, 71 Scott, M.A., Readhead, A.C.S., 1977 MNRAS, 180, 539 Slysh, V.I. 1990, Sov. Astron. Lett., 16(5), 339 van Dyk, S.D., Weiler, K., Sramek, R. et al, 1994, ApJ, 432, L115 The Iron Abundance and Density Structure of the Inner Ring Around SN 1987A S.Mattila1, P.Lundqvist1 , P.Meikle2 , R.Stathakis3, and R.Cannon3 1 2 3 Stockholm Observatory, AlbaNova, Dept. of Astronomy, Stockholm SE-106 91, Sweden seppo@astro.su.se Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BW, UK Anglo-Australian Observatory, PO Box 296, Epping, NSW 1710, Australia Summary. We present a spectroscopic study of the inner circumstellar ring around SN 1987A. The aim is to determine the elemental abundances and density structure, with particular emphasis on the abundance of iron. We acquired and analyzed optical spectra at the Anglo-Australian Telescope (AAT) between 1400 and 4300 days postexplosion. We also assembled from the literature all available optical/near-IR line fluxes of the inner ring. The observed line light curves were then compared with a photoionization model for the inner ring. This indicates an iron abundance of (0.20±0.08) × solar which is lower than that generally seen in the Large Magellanic Cloud (LMC). 1 Motivation X-ray observations [2] indicate an iron abundance of 0.1 × solar for the circumstellar medium (CSM) of SN 1987A. This is surprisingly low compared to the iron abundances, ranging between ∼0.25 and ∼0.50 × solar, e.g. [7,9,1], generally observed in the LMC. Such a large under-abundance of iron could result from the depletion of iron on dust grains in the red supergiant wind of the progenitor star before the supernova (SN) exploded. 2 The Observed Line Light curves for the Inner Ring 2.1 AAT Observations of SN 1987A Inner Ring Optical spectroscopic observations of SN 1987A were carried out using the Royal Greenwich Observatory (RGO) Spectrograph on the AAT between 1991 and 1998. Data were obtained at four different epochs: 1416, 1680, 1991, and 4309 days post-explosion. At each epoch, the observations comprised a brief, wide slit integration (5-15 min; 5.3”-10.0”), and a longer duration, narrow slit 10 Mattila et al. integration (1-3 hours; 1.5”-2.0”). The SN observations spanned air masses ∼1.5 to ∼3.0 (i.e. zenith distances of 50 to 70 degrees), making accurate flux calibration quite challenging. We therefore carried out the observations with the slit position angle (PA) set to be roughly the same as the line joining Stars 2 and 3. This meant that Star 2 lay well within the broad slit and so could be used to correct for the variable transmission of the atmosphere (for details see [14]). However, an additional problem was that, since the slit PA was generally not at the parallactic angle, when the narrow slit was used, atmospheric refraction could introduce wavelength-dependent vignetting of the ring spectra. Moreover, the magnitude of this effect differed from that experienced by Star 2 since the latter lay nearer the edge of the slit. Consequently, the flux uncertainty introduced could be as large as ±40%. 2.2 Star 3 Contamination Removal Using HST Archival Data The AAT observations suffered from seeing ranging between ∼1” and ∼3” and so the inner ring spectra were always significantly contaminated by light from the two nearby stars. In general, the CSM emission lines could be easily distinguished from the continuum originating from the SN and the two stars. However, Star 3 is a Be star showing strong Hα and Hβ emission together with optical variability of ∼0.5 magnitudes [22]. Consequently, it could affect significantly the observed line fluxes from the inner ring, especially at the later epochs when the ring was fainter. To assess and correct for possible Star 3 contamination, we searched the HST archive for suitable optical spectroscopic (STIS) and photometric (WFPC2) observations. STIS spectra with a large enough slit aperture (52”x2”) and suitable centering and orientation to include Star 3 were selected from the HST archive. These spectra confirm the findings of Wang et al. [22] that there are indeed no forbidden lines present in the Star 3 spectrum (see [14]). The vignetted narrow slit spectra were therefore scaled in flux to match those of the unvignetted broad slit spectra using the brightest forbidden lines present in both the spectra. Deriving line fluxes for the whole inner ring this way assumes homogeneous ring geometry. WFPC2 F502N and F656N images which were contemporary with our AAT spectra were then selected from the HST archive. Average Hα and Hβ fluxes of 44 and 13 × 10−15 erg s−1 cm−2 , respectively, were found for Star 3, with a maximum variability of ∼20% over a 6 year time span. These fluxes were used to correct for Star 3 contamination of the hydrogen line fluxes in the broad slit AAT observations. In addition, the accuracy of the absolute flux of our AAT observations was checked using the HST inner ring data. This indicates that our ground-based fluxes are consistent with the HST measurements to within the estimated errors of ±20-40%. 2.3 The Line Light Curves From the AAT spectra, we measured optical line fluxes at 1416, 1680, 2864 and 4309 days for H, He, N, O, Ne, S, Ar, Ca and Fe (e.g. Fig.1). We also The Inner Ring Around SN 1987A 11 assembled from the literature all available optical/near-IR line fluxes of the inner ring. This includes data from the following sources: [19] (307 days), [20] (511, 552, 586, 678, and 735 days), [15] (574, 668, 695, 734, 840, 958, and 1114 days), [16] (1050 days), [21] (1280 days), [3] (1344 days), [5] (1348, 1469, 1734, 1822, and 2122 days). The resulting dataset (see [14]) spans 300 − 4300 days post-explosion, i.e., from the time when the ring first became visible to the time when the first signs of ejecta/ring collision were seen at these wavelengths. 2.4 Modeling the Line Light Curves of the Inner Ring The latest version of the photoionization code described in [10, 11, 12] was used to model the emission line light curves of the inner ring. In the model the ring is initially ionized by the soft X-ray and UV photons emitted in the SN shock break-out. The SN flash with the temporal and spectral characteristics of the 500full1 model [4] sets up the initial ionization structure of the ring, and the gas then recombines and cools. To model the emission line fluxes of iron, we collected from the literature the latest atomic data for the most abundant ions of iron in the ring (see [14]). Thanks to the Iron Project [8] these atomic data have improved significantly during the last few years and now make such abundance determinations more reliable. 2.5 The Density Structure The mass and density structure of the ionized gas in the inner ring was determined by searching for satisfactory model fits for (1) the absolute line fluxes of Hα and Hβ (Fig.1A-B), and (2) the observed time evolution of the line fluxes of all the other elements (e.g., Fig.1C-D). We found that five density components were needed: 103 , 2 × 103 , 3 × 103 , 2 × 104 , and 4 × 104 atoms cm−3 with masses of ionized gas of 0.4, 1.1, 1.0, 0.8, and 0.5 × 10−2 M , respectively. The low-density components dominate the line light curves at the later times. High resolution (HST) images indicate that this low-density gas is situated, on average, further away from the SN than the gas with a higher density [13]. In reality there is also probably a continuous range of densities within the ring rather than a few discrete density components. 2.6 The Iron Abundance The elemental abundances yielding the observed absolute line fluxes were then determined (Fig.1E-J). This was done by altering the total number of emitting ions relative to hydrogen. However, we have not yet included the effects of these modified abundances on the temperature and ionization structure of the ring. Therefore, the abundances derived for the more abundant elements, e.g. He, N, O, should be considered as only preliminary results (e.g. Fig.1C-D). 12 Mattila et al. Fig. 1. A − J : The observed fluxes of lines of H, N, O, and Fe plotted together with the model fluxes. The observed line fluxes have been dereddened assuming EB−V of 0.05 and 0.15 for the Galaxy and the LMC, respectively. The abundance used for each model fit is given relative to solar. K − L : The observed line fluxes of [Fe II] 7155Å and [Fe III] 4658Å plotted together with the model fluxes for three different metallicities. The Inner Ring Around SN 1987A 13 However, the effect of the modified iron abundance on the temperature and ionization structure is not significant, thus allowing its robust determination. Our estimate of the iron abundance is based on five [Fe II] and one [Fe III] lines (Fig.1E-J). This indicates an average abundance of 0.20 times solar with a dispersion of 35%. In addition, we estimated the effects of the assumed He, N, and O abundances and the overall metallicity on the determined iron abundance. We found that the iron model fluxes are rather insensitive to the He/H and N/O ratios. However, the overall metallicity has a much larger effect on the cooling, and thus on the iron model line light curves (Fig.1KL). We estimate that this introduces an uncertainty of 15% in the average iron abundance. Therefore, from this study, we deduce an iron abundance of (0.20 ± 0.08) times solar (see [14]). This abundance is larger by a factor of two relative to that found by Borkowski, Blondin & McCray [2] from X-ray observations. However, it is at the lower end of the iron abundance range (0.25-0.50 times solar) found for different locations within the LMC. We note that also an inner ring silicon abundance of a factor of ∼2 lower than normal for the LMC was found recently by Lundqvist & Sonneborn [13]. These low abundances are probably due to depletion onto dust grains. The existence of dust in the ring material has been demonstrated by mid-IR observations [17, 6]. Acknowledgement. We thank L. Smith, R. Terlevich, and R. Cumming for helpful discussions. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. Andrievsky S.M. et al.: A&A 367, 605 (2001) Borkowski K.J., Blondin J.M., McCray R.: ApJL 476, L31 (1997) Cumming R.: PhD Thesis, Imperial College, University of London (1994) Ensman L. & Burrows A.: ApJ 393, 742 (1992) Fassia A., Meikle W.P.S., Spyromilio J.: MNRAS 332, 296 (2002) Fischera J., Tuffs R.J., & Völk H. 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Crotts2 , and the SInS/SAINTS Collaboration3 1 2 3 Hofstra University, Dept. of Physics, Hempstead, NY 11549 physsl@hofstra.edu Columbia University, Dept. of Astronomy, 550 W. 120th St., New York, NY 10027 ben@astro.columbia.edu, arlin@astro.columbia.edu http://cfa-www.harvard.edu/cfa/oir/Research/sins.html Summary. We present the latest positions of hot spots in the developing supernova remnant of SN 1987A. We discuss preliminary results from our spectrophotometry of HS 1-029 and a new ER expansion velocity measurement. 1 Introduction With the interaction between the blast wave and the circumstellar equatorial ring (ER) now underway, we are watching SN 1987A turn into a bona fide supernova remnant. As of 2002 October there were 19 “hot spots” where the blast wave is heating the innermost protrusions of the ER. Rapid photometric and spectral evolution of these hot spots provides us with information about the ER and the blast wave on spatial scales smaller than the HST imaging resolution. Strategically planned spectral imaging with the Space Telescope Imaging Spectrograph (STIS) allows us to efficiently isolate the developing hot spot emission from the complex, fading emission of the underlying ER. 2 Observations We present six epochs of HST STIS G750M/6581 data taken between 1997 April and 2002 October. OTFC pipeline-reduced data were downloaded from the archive and dithered frames were used to filter cosmic rays and deviant pixels. Spectral extractions and fits used standard IRAF and STSDAS routines. Spectra were dereddened using an E(B − V ) = 0.16 and the galactic extinction law of Cardelli et al. [1] We have used the 52X2 STIS aperture to maximize our spatial and spectral resolution of the ER. At early times, when the Doppler-broadened profiles of the hot spots in the G750M grating were weak, we centered the slit on the 16 Lawrence et al. Fig. 1. Hot Spot Locations as of 2002 October ER. For the G430L, G750L and later epochs of G750M spectra, we displace the aperture 0. 9 N or S, splitting the ER into two semi-ellipses. By splitting the ER in this fashion, the monochromatic spectral images form ellipsoidal arcs of closely-spaced emission lines which “stack” next to each other with almost no confusion between the spatial and spectral information, even in low resolution G430L and G750L data. 3 Hot Spot Positions and Spectra As of 2002 Oct 30, there were 19 confirmed hot spots, spread fairly uniformly in position angle around the ER [3, 7]. Figure 1 plots their locations; Table 1 lists their precise coordinates and dates of earliest detectability. The substantial time difference between the appearance of HS 1-029 and later spots is mostly due to its location on the largest inward-protruding ER feature, combined with a favorable light travel correction [7]. The hot spots are localized areas of brightening on the inner edge of the ER, which is large, spatially complex, and generally fading with different Hot Spots in SNR 1987A 17 Table 1. Hot Spot Positions Hot Spot ID P.A. (#-PA) (◦ E of N) HS 1-029 HS 2-104 HS 3-126 HS 4-091 HS 5-139 HS 6-229 HS 7-289 HS 10-040 HS 11-355 HS 12-050 HS 13-165 HS 14-249 HS 15-312 HS 16-078 HS 17-268 HS 18-064 HS 19-323 HS 20-188 HS 21-008 28.2±0.75 105.7±0.64 124.6±0.52 91.2±0.90 140.0±1.96 229.0±1.48 291.9±1.28 41.3±1.88 349.7±0.95 51.7±1.20 165.1±1.57 248.2±1.23 314.2±1.42 76.8±0.74 268.6±0.96 63.9±0.95 323.7±0.53 190.7±4 8.1±2 Radius (arcsec) Earliest Detection (d past SN) 0.545±0.005 0.674±0.005 0.612±0.008 0.724±0.013 0.570±0.012 0.658±0.017 0.710±0.016 0.624±0.025 0.529±0.013 0.649±0.010 0.534±0.011 0.752±0.016 0.617±0.019 0.715±0.015 0.752±0.021 0.702±0.015 0.619±0.012 0.524±0.070 0.592±0.025 2931 4282 4335 4335 4439 4439 4439 4725 4816 4816 4861 4861 4861 5012 5141 5400 5400 5561 5624 time scales in each emission line. Great care must be taken when fitting and de-blending these multiple, overlapping components, and these systematics can dominate the errors of even strong lines [5, 6]. Carefully planned and matched observations such as these allow us to register, scale, and subtract each emission line individually, revealing subtle flux differences. Examples of this strategy are displayed in Figure 2. Each column displays a single strong emission line from the G750M grating. Each row contains images from a single epoch, with most recent data at the bottom. North is to the right, East is up. Note that the dispersion direction flips between spring and fall epochs (note the changing position of the bluer [S II] line), due to HST orientation constraints. The last two epochs display only the data from the northern half of the ER. It is easy to trace the evolution of the individual spots in any given line down a single column, with the exception of the [S II] lines, which are collisionally-quenched by the high densities (ne ≈ 106 cm−3 ) in the compressed post-shock gas [4, 6]. In the second column we show the advantages of strategically planned aperture positions such as these. By registering, scaling and subtracting the spot-free [N II] 6583 emission in 1997 April, we were able to create a “hot-spotfree” Hα template. This template was then scaled to spot-free segments in each later epoch, allowing us to subtract the underlying ER. The faint “fringe” of Lawrence et al. [O I] He I [S II] 6583 6300 6678 6731 day 3715 1997 Apr [N II] day 4816 2000 May Hα (spots only) day 4997 2000 Oct 2002 May day 5562 2002 Oct day 5729 2001 Apr Hα 6563 day 5177 18 Fig. 2. STIS 52x2 G750M/6581 spectral images of the ER: 1997–2002 emission to the west of the ER fades much more slowly (presumably due to a much lower density and longer recombination time), so it is progressively oversubtracted. With the complex spatial pattern of the underlying ER emission thus removed, it is much simpler to extract the individual hot spot fluxes. This is particularly true for the latest epochs, where it becomes necessary to de-blend the overlapping spatial profiles of adjacent hot spots. Measurements of the total Hα flux from HS 1-029 with time are presented in Table 2. We plan to apply our ER subtraction algorithm to all cases where extracting weak hot spot flux from atop the ER is difficult, either because the hot Hot Spots in SNR 1987A 19 Table 2. Hα Flux from HS 1-029 Date 1997 Apr 26 2000 May 01 2000 Oct 29 2001 Apr 27 2002 May 16 2002 Oct 30 SN Age Hα Flux GFWHM days 10−16 erg s−1 cm−2 km s−1 3715 4816 4997 5177 5562 5729 48±15 216±36 233±31 322±48 478±86 473±92 273±60 221±26 200±24 214±20 216±13 206±11 spot is young or because the emission lines are naturally weak or suppressed. Examples can be seen in [N II] and [S II] in Figure 2, and there are many other examples in the G430L and G750L spectra (not shown). Of particular interest are the lowest-lying transitions of [O II], [N I] and [S II]. Since these lines are collisionally-quenched in the compressed post-shock gas, we might be able to track the brightening of a second wave of photoionization expected from the high energy radiation produced by the hot spots and the reverse shock. Tentative evidence of this reionization might be present in the “spotonly” Hα image of 2002 Oct. There is diffuse Hα emission between the rows of spot emission, and it is notably asymmetric and exterior to the ER. But removal of the underlying ER was challenging in this epoch, and a registration or under-scaling error could be to blame. Another epoch of data was taken in May 2003, so the reality of this emission will be tested soon. The alternation of the dispersion direction relative to the spatial orientation of the ER allows us to make a clear, spatially-resolved measurement of the maximum radial velocity difference between the ends of the minor axis. The observed minor axis width (W ) of the spectral images will be different than that of an undispersed direct image (W ), due to the total Doppler shift (δWDopp ) between the receding and approaching sides. This factor δWDopp will change signs every six months as the slit (anti-)parallels the major axis. By fitting the spatial profiles of spot-free ER emission along the minor axis we can recover both W and δWDopp : + WApr )/2, W = (WOct δWDopp = (WOct − WApr )/2 (1) Fits to early, spot-free Hα and [N II] images are in excellent agreement with other sources. The minor axis is W = 1. 194±0.003 [7]. Assuming that the ER is circular and inclined at an angle of 43.78◦[7], the measured radial expansion velocity of the ER is 12.8±1.5 km s−1 , in good agreement with prior, marginally-resolved ground-based studies [2]. Acknowledgement. This research was supported by NASA grant NAG5-3502 and STIS grants GO 8806 and GO 8872. 20 Lawrence et al. References 1. 2. 3. 4. 5. 6. 7. J. Cardelli, G. Clayton, J. Mathis: ApJ, 345, 245 (1989) A. Crotts, S. Heathcote: ApJ, 528, 426 (2000) S. Lawrence et al: ApJ, 537, L123 (2000) S. Maran et al: ApJ, 545, 390 (2000) E. Michael et al: ApJ, 542, L53 (2000) C. Pun et al: ApJ, 572, 906 (2002) B. Sugerman et al: ApJ, 572, 209 (2002) The Formation of the Triple-Ring Nebula Around SN 1987A Thomas Morris and Philipp Podsiadlowski Department of Astrophysics, Oxford University, Oxford, OX1 3RH, UK tsm@astro.ox.ac.uk, podsi@astro.ox.ac.uk Summary. We present preliminary 3-dimensional hydrodynamical simulations, using the SPH code GADGET, to illustrate the formation of the outer rings in the triple-ring nebula surrounding SN 1987A. We show that this matter is likely to have been ejected during the merger phase of two massive stars ∼ 20, 000 years before the explosion. Because of the rotational flattening of the merged envelope, mass loss occurs preferentially at an intermediate latitude (at least initially). This provides the basic seed anisotropy in the mass outflow, which is subsequently shaped into a well-defined truncated double-cone, terminated by the outer rings, by the action of photoionization-driven shocks in the final blue-supergiant phase. This model explains the main observed features of the outer ring nebula, its orientation and velocity structure. It also accounts for the observed diffuse emission in the region between the two rings, as seen in the HST image. We briefly outline the future work which will help to improve the model further. 1 Introduction The enigmatic nebula around SN1987A, a peculiar supernova in the LMC and the brightest since Kepler’s star, is still not completely understood. The favored explanation of both the triple-ring structure (Fig. 1) and the other anomalous features of SN1987A is the merger of a massive binary about 20,000 years before the SN event [2, 5, 9, 14]. Recent hydrodynamical calculations of such a slow merger [6, 13] explain the main chemical anomalies (e.g., the helium abundance which is twice solar) and the blue-supergiant progenitor of SN1987A. The inner ring is relatively easy to understand [3, 10] as a rotationally enforced outflow [4] caused by the contraction of a rapidly rotating red supergiant. Following the merger and associated mass loss, the red supergiant contains almost all the angular momentum of the original binary system, which must be lost during the transition to the blue, most likely in a slow equatorial outflow. 22 Thomas Morris and Philipp Podsiadlowski Fig. 1. HST image of the triple-ring nebula [1]. The outer rings do not constitute the limb-brightened surface of an hourglass nebula but form two almost co-planar rings with their dynamical center close to the plane of the inner ring but significantly displaced from the SN remnant [1, 11, 15]. While various wind-interaction models have been proposed [3, 7, 11, 16], we show here that an arguably more natural explanation connects the formation of the outer rings with mass ejection during the merger event. 2 The Model One-dimensional simulations of the merger process have already demonstrated that significant mass loss can occur even in cases when most of the envelope remains bound [12] and that this mass loss can be highly anisotropic due to the energy dissipation close to the orbital plane [19] and the rotational flattening of the envelope. All of the angular momentum of the binary, Eq. 1, will be transferred to the envelope of the primary and will significantly change its structure (see also Table 1). 2 −1 J = 6.60 × 10 g cm s 54 A 2500R 12 M1 15M M2 5M M1 + M2 20M −1/2 (1) The rate of gravitational energy release increases rapidly as the cores approach each other during the spiral-in phase, which drives mass loss first from mid-latitudes (see Fig. 2) since the large mass concentration close to the equatorial plane initially prevents ejection in the equatorial plane. Subsequently mass may be ejected from the equatorial region but only if the energy deposition exceeds some threshold. This threshold increases as the envelope becomes more oblate. Fig. 2 shows this anisotropic mass ejection for different amounts of spin-up of the envelope and different amounts of energy deposited in the core region. Since these anisotropies provide the seed structures for the ring nebula, the E = 0.4, L = 0.817 model is a likely precursor of the outer rings, The Formation of the Triple-Ring Nebula Around SN 1987A 23 Fig. 2. Anisotropic mass loss after 5 dynamical timescales for T/W = 0.117 (left column), and T/W = 0.151 (right column); the energy deposition as a fraction of the envelope binding energy (see Table 1) increases from top to bottom. The histograms show the amount of mass ejected as a function of the cosine of the angle from the orbital plane. The blue curves (median and upper, lower quartiles) indicate the range of velocities at infinity. while one of the E = 0.5 models may also explain the inner ring as the result of mass loss during the merger. Following the merger, the single rapidly rotating star will become a blue supergiant after a transition period lasting a few thousand years. The strong flux at 912 Å will then begin to photoionize the illuminated part of the ejecta and induce hydrodynamical motions which sweep the anisotropies into welldefined structures (the importance of these photoionization-driven shocks was 24 Thomas Morris and Philipp Podsiadlowski Table 1. Properties of the three rotating envelopes immediately before the energy deposition. T/W 0.039 0.117 0.151 54 2 −1 Angular momentum 10 g cm s Mean angular velocity 10−8 s−1 Flattening Req /Rpolar Rotation velocity (km/s) Binding energy (1047 ergs) 2.3 3.7 1.7 42 −6.2 5.7 2.2 4.3 21 −5.4 8.0 1.1 6.8 15 −4.5 first emphasized by Meyer [8]). An example of the resulting structures is shown in Fig. 3 for a case in which little mass is ejected in the equatorial plane. 3 Technical Aspects We use the 3-dimensional smoothed particle hydrodynamics (SPH) code GADGET [17] for all the simulations. Initially the star is represented by 105 particles distributed according to the density profile of a 20 M polytrope (index γ = 5/3) with a 8 M core. The radius is taken as R0 = 1500 R, typical for a RSG during late He shell burning; this value is used in all calculations quoted in cgs units. The spiral in and merger processes are modeled as a continuous injection of angular momentum into the envelope (see Table 1) over a period of about 6 years, followed by an instantaneous deposition of energy in the core region (R/R0 = 2/15) where the magnitude is taken as some fraction of the binding energy of the envelope. Fig. 2 shows the angular distribution of the ejected material after 5 dynamical timescales (about 4 years). After 8 years the ejecta is freely coasting on radial trajectories; we then integrate the particle trajectories ballistically for 8,000 years before the photoionization is switched on. The density distribution of the ejected material is averaged about the spin axis and resampled with 5 × 105 particles; this becomes the initial model for a second SPH calculation. The effect of photoionization is approximated by bursts of ionizing photons, between which the ionized material may recombine and cool. Outside this region material is adiabatic below 104 K and cools radiatively above 104 K, according to the tables of Sutherland and Dopita [18]. 4 Results The plots in Fig. 3 illustrate the nebula 8, 000 + 22, 000 years after the merger event. The outer rings are 0.6 pc from the symmetry axis, contain The Formation of the Triple-Ring Nebula Around SN 1987A 25 Fig. 3. Left: Simulated emission measure of the triple-ring nebula after the SNflash photoionization. Note in particular the extended emission near the outer ring overlap region, where the double-cone structure is nearly aligned to the line of sight. Right: Illustration of the final density structure in a cylindrical projection (i.e. z versus ρ). 0.03 solar masses and are expanding at about 35 km s−1 . We resampled the E = 0.4, L = 0.817 model and used an ionizing flux of φ = 8.4 × 1046 s−1 , consistent with the immediate B3 I supernova progenitor. The opening angle is very close to the observed value of 45◦ . Future work includes parameter studies (dependence on photoionizing flux, angular momentum and energy deposition) and an improved code in which we solve the equations of ionization rate and one-dimensional radiative transfer exactly. Also we plan to investigate: • The formation of the inner ring: is it associated with the post-merger mass loss or is it ejected simultaneously with the outer rings? • The role of the energetic blue supergiant wind and the possible formation of the Napolean’s hat nebula. • The displacement of the dynamical center of the outer rings from the supernova (and the inner ring), perhaps due to a small kick (∼ 1 − 2 km s−1 ) of the post-merger system relative to the pre-merger binary due to anisotropic mass ejection. References 1. C. Burrows et al. : Astrophys. J. 452, 680 (1995) 2. R.A. Chevalier, N. Soker: Astrophys. J. 341, 867 (1989) 3. T.J.B. Collins, A. Frank, J.E. Bjorkman, M. Livio: Astrophys. J. 512, 322 (1999) 26 Thomas Morris and Philipp Podsiadlowski 4. A. Heger, N. Langer: Astron. Astrophys. 334, 210 (1998) 5. W. Hillebrandt, F. Meyer: Astron. Astrophys. 219, L3 (1989) 6. N. Ivanova, Ph. Podsiadlowski: In: From Twilight to Highlight: The Physics of Supernovae, ed. W. Hillebrandt, B. Leibundgut (Springer: Berlin, 2002) p. 19 7. H.M. Lloyd, T.J. O’Brien, F.D. Kahn: Mon. Not. R. Astron. Soc. 173, L19 (1995) 8. F. Meyer: Mon. Not. R. Astron. Soc. 285, L11 (1997) 9. Ph. Podsiadlowski, P.C. Joss, S. Rappaport: Astron. Astrophys. 227, L9 (1990) 10. Ph. Podsiadlowski: Nature 350, 654 (1991) 11. Ph. Podsiadlowski, A.C. Fabian, I.R. Stevens: Nature 354, 43 (1991) 12. Ph. Podsiadlowski: In: Evolution of Binary and Multiple Star Systems, ed. Ph. Podsiadlowski, S. Rappaport, A.R. King, F. D’Antona, L. Burderi (PASP: San Francisco, 2001) p. 239 13. Ph. Podsiadlowski, N. Ivanova: In: From Twilight to Highlight: The Physics of Supernovae, ed. W. Hillebrandt, B. Leibundgut (Springer: Berlin, 2002) p. 13 14. Ph. Podsiadlowski: In: SN1987A: Ten Years Later, ed. M.M. Phillips, N.B. Suntzeff, in press 15. Ph. Podsiadlowski, R.J. Cumming: preprint (1994) 16. N. Soker: Mon. Not. R. Astron. Soc. 383, 611 (1999) 17. V. Springel, N. Yoshida, S.D.M. White: New Astron. 6, 51 (2001) 18. R.S. Sutherland, M.A. Dopita: Astrophys. J. Suppl. 88, 253 (1993) 19. R.E. Taam, E.L. Sandquist: Ann. Rev. Astron. Astrophys. 38, 113 (2000) Light Echoes from SN 1987A and SN 1993J Ben E. K. Sugerman1 and Arlin P. S. Crotts1 Columbia University Dept. of Astronomy, New York, NY 10027 ben,arlin@astro.columbia.edu Summary. Light echoes are an extremely powerful tool for precision three-dimensional mapping of dust in circumstellar (CSE) and interstellar (ISE) environments. We present light echoes discovered around two supernovae: SN 1993J in M81 and SN 1987A in the LMC. We have discovered at least two interstellar light-echo structures around SN 1993J, arising from sheets of material roughly 81 and 220 pc in front of the supernova. We model these echoes and find that they likely arise from dust similar to that of our own Galaxy. Echoes from 9 years of imaging of SN 1987A reveal the fossil record of the progenitor’s mass-loss history. The CSE is a richlystructured bipolar nebula, with an outer, double-lobed “peanut” extending 28 ly along the poles and 11 ly near the equator, but pinched to 6 ly at the waist, while interior, a cylindrical hourglass, 1 ly in radius and 4 ly long, connects to the peanut by a thick equatorial disk. The nebulae have a total mass of ∼ 1.7 M , suggesting a red-supergiant mass loss of 5 × 10−6 M yr−1 . 1 Introduction Scattered-light echoes occur when the light pulse from some varying object (e.g. a SN) is scattered by dust into the line of sight. An echo observed a given time after the pulse must lie on the locus of points equidistant in light travel from the source and observer, i.e. an ellipsoid with known foci. This simple geometry directly yields the three-dimensional position of an echo, uncertain only by the assumed distance to the source. As the spectrum of an echo is determined by the scattering properties of the dust, light echoes further constrain the grain-size distribution, density, and composition of the dust. We summarize the results of two studies of light echoes around recent SNe: SN 1993J in M81, and SN 1987A in the LMC. In both cases, echoes are identified using PSF-matched difference image photometry [10]. The line-ofsight positions z of echoes are computed from their projected distance ρ from the SN and the time t of observation using 28 Ben E. K. Sugerman and Arlin P. S. Crotts z= ρ2 ct − . 2ct 2 (1) Dust properties are inferred from the scattering model of [6]. 2 SN 1993J Using archival WFPC2 images from 1995 and 2001, we [8] find up to three light echoes from SN 1993J (compared to only one echo reported by [4]). Shown in figure 1, these echoes define two structures: SW770, lying 770 ly in front of the SN, and roughly parallel to the disk of the host galaxy M81; and NE260, lying 260 ly in front of the SN. The geometry of these echoes is shown schematically in figure 2, as viewed far to the north. Overall, these echoes are consistent with dust of a Galactic size-distribution and chemical composition. Gas densities of order 10 cm−3 are required to produce the observed echoes. Fig. 1. Direct (a) and difference (b–d) WFPC2 images of echoes around SN 1993J. SW770 is visible between PA 160–280. The fainter, inner echo NE260 is apparent from PA 10–60 at a radius of ∼ 1 in (b) and (c). A faint negative region around PA 190–260, r = 0.85 appears in panels (b) and (d), suggestive of an echo in the 1995 integration. 3 SN 1987A SN 1987A in the LMC is surrounded by a complicated 3-ring nebula. Formation scenarios generally invoke interacting fast (blue supergiant or BSG) and slow (red supergiant or RSG) winds. Fossil remnants of these interactions have been illuminated by the SN light pulse, as reported previously by [2, 3]. We have reanalyzed ground-based data from Dec. 1988 to Jan. 1996 taken in specially-chosen continuum filters centered at 470, 612, 688 and 809Å. We have also found echoes in archival WFPC2 imaging from 1994–1997. Full details of this analysis are presented in [7]. Light Echoes from SN 1987A and SN 1993J 29 Fig. 2. Geometry of M81 and the light echoes. Echo parabolae from 1995 and 2001 are drawn with dotted lines. Echoes are marked as follows: (a) SW770 in 2001, (b) NE260 in 2001, and (c) SW770 in 1995. Gray scale indicates height of the echoing material above (below) the page, with darker (lighter) shades indicating greater northern (southern) position. The light echoes trace out three known structures, a circumstellar (CS, [3]) hourglass, Napoleon’s Hat (NH, [11]), and a large-distance contact discontinuity (CD, [1]) between the RSG and main-sequence winds, all in significantly greater detail and over a much larger volume than previously reported. Additionally, we discover a significant volume of circumstellar material that was, until now, only suggested from previous studies, as well as a previouslyundiscovered southern counterpart to the Napoleon’s Hat material. In total, over 2500 ly3 of space surrounding SN 1987A was probed. Each structure has an inclination close to 40◦south and 8◦ east of the line of sight. Assuming all echoes lie on a surface of revolution, we revolve their positions about the inclination axis and reflect about the equator to produce the rendered structures shown in figures 3. The cross-section through these structures is schematized in figure 4. At the largest scale is a bipolar “peanut”, much of which is well-fit by a prolate ellipsoid with axes of 11 and 23 ly, but severely pinched at the waist (to 6 ly) and extended at the poles (to 28 ly). Material is present interior to the peanut along the poles and in “spurs” above/below the equator, outside the peanut. At the waist is a thick (2–4 ly) equatorial plane that ends at the inner hourglass, which is fairly cylindrical with a radius of 1 ly. The inside of the peanut is filled with diffuse material, but little is found outside of it. Application of the dust-scattering model suggests the following. (1) dust density decreases with increasing distance from the SN. Relative densities are indicated in figure 4 by gray scale shading. (2) Echoes from dust at large distance are better modeled with LMC dust (carbonaceous and silicate) abundances, while the innermost dust is mostly silicate. This suggests the progenitor’s envelope was more oxygen-enriched in its final stages than when creating the peanut. (3) The total mass of gas and dust is ∼ 1.7 M with 70% of the 30 Ben E. K. Sugerman and Arlin P. S. Crotts Fig. 3. Rendered views from the east of the complete structures traced by light echoes. Major ticks mark 2 ly and the SN is marked by a black dot. (a) NH (green) and the CD (other colors) trace a prolate bipolar “peanut” that is highly extended at the poles and pinched at the waist. (b) Echoes interior to NH reveal an equatorial over density (blue and cyan) and an hourglass (red, cyan, gold) the interior of which is evacuated. The inner hourglass is also shown in (c). It is pinched at the waist, but fairly cylindrical in profile. mass in the CD. For a RSG lifetime of ∼ 3 × 105 yr, this implies an average mass-loss rate of Ṁ ∼ 5 × 10−6 M yr−1 . y z Fig. 4. Cartoon showing the cross-section of the CSE. Gray scale indicates relative density, which increases with darkness. The orientation arrows indicate 10 ly. 3.1 Implications for Formation Scenarios Most formation scenarios for the three ring nebula invoke the interaction of an isotropic, fast BSG wind with an equatorial over density created by the slow, dense RSG material. The result is an evacuated, bipolar bubble. The light echoes show that such an evacuated, hourglass-shaped cavity is present, Light Echoes from SN 1987A and SN 1993J 31 as is the required equatorial plane of dense gas. Furthermore, this hourglass passes through the projected positions of the outer rings, and is consistent with the inferred size and orientation of the equatorial ring. Requiring the outer rings to lie along the hourglass, the north and south rings are located 1.4 and 1.1 ly from the SN, respectively. The inner hourglass is offset to the west of the SN and is slightly elliptical, consistent with the findings of [9]. Requiring the equatorial ring to have the hourglass orientation, we find it has an orientation 41◦ south and 8◦ east of the line of sight, ellipticity of b/a = 0.98, major axis of 0.82 rotated 9◦ north of east, and centroid shifted 20 mas west of the SN. Most interacting-winds models (e.g. [5]) predict the lobes of this hourglass will be round and mushroom-shaped, which is not found. Rather, the shape of the outer, bipolar peanut is similar to that predicted from hydrodynamic models. One possible explanation is that the progenitor experienced two blueloops, in which the first BSG phase was long and created the large peanut, after which the star evolved back first to a RSG, then a BSG, during which the thick equatorial plane and cylindrical hourglass were formed. We anxiously await the results of new hydrodynamic models that aim to reproduce the full extent of the CSE presented here. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Chevalier, R. A. & Emmering, R. T., 1989, ApJL, 342, L75 Crotts, A. P. S. & Kunkel, W. E. 1991, ApJL, 366, L73 Crotts, A. P. S., Kunkel, W. E. & Heathcote, S. R. 1995, ApJ, 438, 724 J.-F. Liu, J. N. Bregman & P. Seitzer: ApJ, 582, 919 (2002) C. L. Martin, D. Arnett: ApJ, 447, 378 (1995) B. E. K. Sugerman: AJ, in press (2003) B. E. K. Sugerman: A Tail of Two Sightings, New Observational Constraints of the Mass-Loss History of SN 1987A, Ph.D. Thesis, Columbia University, New York (2003) B. E. K. Sugerman & A. P. S. Crotts: ApJL, 581, L97 (2002) B. E.K. Sugerman et al: ApJ, 572, 209 A. Tomaney, & A. P. S. Crotts: AJ, 112, 2872 (1996) Wampler, E. J. & Richici, A. 1989, A&A, 275, 883 ESC Observations of SN 2002er around Maximum Light G. Pignata1 , F. Patat1 , R. Kotak2 , P. Meikle2 , M. Stritzinger3 , W. Hillebrandt3 1 2 3 European Southern Observatory, Karl-Schwarzschild str. 2, D-85748 Garching bei München, Germany. gpignata@eso.org Imperial College London, Prince Consort Road, London SW7 2BZ, United Kingdom. Max-Planck-Institute für Astrophysik, Karl-Schwarzschild str. 1, D-85741 Garching bei München, Germany. Summary. We present preliminary results of the observational campaign on SN 2002er carried out by the European Supernova Collaboration (ESC). For this supernova the optical coverage from epochs −11 days to +50 days is excellent, both in imaging and spectroscopy. The extinction deduced from the photometry is E(B − V ) = 0.35, while ∆m15 = 1.31. In general SN 2002er behaves like a “normal” type Ia supernova, very similar to SN 1996X. 1 Introduction In order to carry out a comprehensive study of the physics of Type Ia Supernovae (SNeIa), all the major European institutes working in this field have formed the European Supernova Collaboration (ESC). This is partially supported as an EU European Research Training Network, commencing operation in 2002. The ESC has already carried out detailed monitoring of a number of nearby SNe Ia using a large number of telescopes and instruments. In this poster we present preliminary results for SN 2002er in UGC 10743, one of the first targets followed by the ESC. SN 2002er (α = 17h 11m 29s .88, δ = +7◦ 59 44 .8, J2000) was discovered on August 23.2, IAU 7959[3]. On the basis of a low resolution spectrum taken at La Palma with the INT on August 26.9 UT, the SN candidate was classified by some of the ESC members as a type Ia, approximately 10 days before maximum brightness [9]. 34 G. Pignata, F. Patat, R. Kotak, P. Meikle, M. Stritzinger, W. Hillebrandt 2 Interstellar Extinction In order to estimate the intrinsic luminosity of the SN, it is crucial to estimate an accurate value for the reddening and to correct for this effect. To compute E(B − V ), we have used different methods. Using the Lira locus [5] in the tail phase, we get 0.44 ± 0.08. If we compare our observed B − V color around B maximum with that given by Phillips [5], we obtain 0.31 ± 0.05. Finally considering the results of CMAGIC method [13] we get 0.28 ± 0.04. Independent estimates of E(B − V ) will be provided by spectral modeling of the spectroscopic data. For our purposes, here we adopt the weighted mean of the above mentioned values of reddening, i.e. E(B − V )=0.35. 3 U BV RI Light Curves The U BV RI light curves of SN 2002er are shown in Fig. 1. The ∆m15 of SN 2002er is 1.31 (Table 1). For comparison, the light curves of other Type Ia SNe with similar values of ∆m15 are also sketched. As can be clearly seen from the figure, the best match is with SN 1996X. This object resembles SN 2002er even in the I band, where the differences between SNe are usually more pronounced. The main photometric parameters of SN 2002er, are summarized in the Table 1. The extinction corrected colors, decline rates, light curve shape and time offsets between maxima in different passbands are typical of “normal” SNe. Table 1. Main photometric parameters of SN 2002er. Filter mag. first max phase ∆m15 mag. second max phase (days) (days) U 14.69 -0.4 B 14.88 0.0 1.31 V 14.62 2.1 R 14.42 1.7 I 14.45 -0.2 14.93 25.5 (U − B)0 =−0.63 , (B − V )0 =−0.10, (V − I)0 =−0.27 4 Absolute Magnitude and Bolometric Light Curves We can derive the absolute magnitude of SN 2002er in two ways: In the first case we assume H0 =71 km s−1 Mpc−1 [10] and, from the radial velocity corrected for LG infall onto Virgo (vr =2694 km s−1 ), we derive a distance modulus µ=32.9±0.3 for host galaxy. Then, taking into account the estimated ESC Observations of SN 2002er around Maximum Light 35 Fig. 1. U BV RI light curves of SN 2002er, The ordinate scale refers to the B-band, The other bands are shifted by the amount shown in the plot. Different symbols refer to different instruments with which the SN was observed. The dashed lines and dashed-dotted lines represent the U BV RI light curve of 1994D (∆m15 = 1.32), [4] and SN 1992A (∆m15 = 1.47) [11]. The solid lines refer to the BV RI light curve of SN 1996X (∆m15 = 1.31) [7]. AB = 4.315 × E(B − V ) = 1.47 [8] we obtain MBmax = −19.5±0.3. Alternatively, we can use the relation between MBmax and ∆m15 found by Hamuy [2] This empirical law, applied to the case of SN 2002er, gives MBmax = −19.1± 0.3. We note that the two values agree to within the errors, although the associated errors are rather large. With our well sampled U BV RI data of SN 2002er we are able to construct a U V OIR light curve and obtain a reliable estimate of the total luminosity at maximum light. The U V OIR light curve, computed using the method described in Vacca & Leibundgut [12], is presented in Fig. 2. For comparison we have overplotted the corresponding curve for SN 1996X [7, 6], which has a similar ∆m15 (1.31). Distance moduli were computed assuming H0 as in the previous section. For extinction to SN 2002er we have used the value discussed above, while for SN 1996X we have adopted the estimates available in the literature µ=32.7, E(B − V )=0.08. Using Arnett’s rule [1], we obtain Nickel masses of 0.41 M and 0.77 M for SN 2002er and SN 1996X respectively. The similarity in the shape of the U V OIR light curves during early epochs 36 G. Pignata, F. Patat, R. Kotak, P. Meikle, M. Stritzinger, W. Hillebrandt Fig. 2. Bolometric light curves of SN 2002er (red line) and SN 1996X (green line). to beyond the ∼28-day feature is remarkable considering that the difference in maximum luminosity among normal SNe Ia is of the order a factor of 2. 5 Spectral analysis The spectral evolution of SN 2002er from −10d to +35d is shown in Fig. 3 which presents just a subset of the entire dataset. The evolution is very similar to that of other normal type Ia supernovae like SN 1994D. The dominant features are due to the Fe-group and intermediate mass elements (notably Si, Ca, Mg). The lines exhibit the characteristic P-Cygni profiles, and the minima of the absorption components shift to redder wavelengths (i.e. lower expansion velocities) with time. This is most apparent in the SiII 6150 Å feature. The blue edge of the SiII feature at −10d corresponds to a velocity of ∼20500 km s−1 which is comparable to that found for SN 1994D at a similar epoch (∼21600 km s−1 , [4] see Fig. 4). Note that the spectra in Fig 3. have not been de-reddened. Acknowledgement. This work was supported by the EC through contract HPRNCT-2002-00303. ESC Observations of SN 2002er around Maximum Light 37 Fig. 3. Spectral evolution of SN 2002er. Fig. 4. Comparison of the spectra of SN 2002er and SN 1994D at two different epochs. 38 G. Pignata, F. Patat, R. Kotak, P. Meikle, M. Stritzinger, W. Hillebrandt References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. D. Arnett et al. : Nature 314, 337 (1985) M. Hamuy et al. : Astron. J. 112, 2391 (1996) W.D. Li, B. Swift, M. Ganeshalingam: IAUC 7959 (2002) F. Patat et al. : Mon. Not. R. Astron. Soc. 278, 111 (1996) M.M. Phillips et al. : Astron. J. 118, 1766 (1999) A.G. Riess et al. : Astron. J. 117, 707 (1999) M.E. Salvo et al. : Mon. Not. R. Astron. Soc. 321, 254 (2001) D.J. Schlegel et al. : Astrophys. J. 500, 525 (1998) S. Smartt et al. : IAUC 7961 (2002) D.N. Spergel et al. : astro-ph 0302209 (2003) N.B. Suntzeff: In:IAU Colloq. 145, ed. R. McCray W.D. Vacca, B. Leibundgut: Astron. J. 116, 2431 (1996) L. Wang et al. : astro-ph 0302341 (2003) Distance of the Hypernova SN 2002ap via the Expanding Photosphere Method J.Vinkó1, M.Blake2 , K.Sárneczky1 , B.Csák3 , G.Fűrész3,4 , Sz.Csizmadia4 , L.L.Kiss3 , Gy.M.Szabó3, R.Szabó4 , H.DeBond2 , M.M.de Robertis2 , J.R.Thomson2, S.W.Mochnacki2, and S.M.Rucinski2 1 2 3 4 Dept. of Optics, University of Szeged, Hungary vinko@physx.u-szeged.hu David Dunlap Observatory, University of Toronto, Canada Dept. of Experimental Physics, University of Szeged Konkoly Observatory, Budapest, Hungary Summary. We present optical spectra of SN 2002ap obtained around maximum, and BVRI light curves up to +300 days. Photospheric velocity curves are determined from the minimum of the 6355 Si II line. The light and velocity curves are combined together applying the Expanding Photosphere Method for the data around maximum, when the atmosphere was optically thick. This resulted in a new distance estimate of 6.7 ± 1 Mpc for M74, the host galaxy. 1 Introduction The Type Ic supernova (SN) 2002ap occured in the nearby spiral galaxy M74 (d ≈ 8 Mpc) received considerable attention, both observationally and theoretically. It is one of the closest extragalactic SNe observed ever, and before maximum it showed very broad spectral features characteristics of a “hypernova”, similar to SN 1998bw and SN 1997ef. Although, unlike SN 1998bw, it was not associated with a GRB, it could be detected from X-ray ([13]) to radio bands ([1]). Optical spectropolarimetry ([5]) suggested an asymmetric (about 10 percent) explosion. From spectral modeling Mazzali et al. ([7]) estimated Ekin ≈ 4 − 10 1051 erg kinetic energy and MNi ≈ 0.07 M nickel mass. The progenitor was not detected by deep INT- and KPNO-frames ([11]). 1.1 Basic observational data of SN 2002ap Host Galaxy: M 74 (NGC 628), cz = 657 kms−1 Discovery: January 29th, 2002 (JD 2452303.7), Y. Hirose, R.Kushida, W. Li B-maximum: JD. 2452311 Peak brightness (mag): B = 13.10 ± 0.05, V = 12.35 ± 0.05, R = 12.24 ± 0.04, I = 12.25 ± 0.10 40 J.Vinkó et al. 2 Observations (B-V) We made CCD-observations of SN 2002ap through Johnson-Cousins BVRI(V-R) + 1.5 filters from t = (V-I) −4+ 2 to +291 days using telescopes at Konkoly and Szeged Observatory. The SN magnitudes were measured with aperture photometry, and the data were transformed to the standard system using field comparison stars calibrated via Landolt standards. 10 12 SN 2002ap 13 I-2 R-1 14 V 16 15 Ni -> Co 16 17 Co -> Fe 18 B+1 18 SN 2002ap 14 mbol (mag) Magnitude 12 19 20 250 300 350 400 450 500 Time (JD) 550 600 650 20 250 300 350 400 450 500 Time (JD) 550 600 650 Fig. 1. Light curves of SN 2002ap (left panel: BV RI, right panel: bolometric). The bolometric light curve has been determined by combining our photometry with the optical and near IR-data by Gal-Yam et al. ([4]), Cook et al. ([3]), Borisov et al. ([2]), Pandey et al ([8]) and Yoshii et al. ([15]). The bolometric decline rate of the late light curve is 0.0170 ± 0.0005 mag/day, considerably steeper than 0.0098 mag/day as expected from the 56 Co - 56 Fe decay with full gamma-ray trapping (see also [8]). This behavior is similar to the case of SN 1998bw ([9]), indicating significant escape of gamma-rays from optically thin, transparent ejecta. Low-resolution optical spectra were obtained at DDO on 7 nights with the Cassegrain spectrograph attached to the 74” telescope (Fig.2). The radial velocity curve (Fig.3) of the expanding atmosphere was determined from the Doppler-shift of the Si II (λ6355Å) line. The decline of the velocity curve is steeper than in other hypernovae SN 1998bw ([9]) and SN 1997ef ([7]). 3 Analysis In order to estimate the distance of the SN, the Expanding Photosphere Method (EPM, [6]) has been applied. Although this method is suited for Type II SNe with optically thick atmospheres, it may be applicable to hypernovae, at least at the early phases. Assuming free expansion of the ejecta, the relation between the elapsed time t and the angular radius of the photosphere θ is Distance of the Hypernova SN 2002ap 41 1.4e-13 SN 2002ap 1.2e-13 -7 d 1e-13 Flux (erg/s/cm2/A) -5 d 8e-14 -4 d 0d 6e-14 +2 d +7 d 4e-14 +8 d +11 d +14 d +17 d 2e-14 +18 d 0 -2e-14 +20 d 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 Wavelength (A) Fig. 2. Spectral evolution of SN 2002ap (red: DDO spectra, green: Wise Obs. spectra ([4]). 35000 30000 V_Si II (km/s) 25000 20000 15000 SN 1998bw 10000 5000 0 300 SN 1997ef SN 2002ap 310 320 330 340 JD - 2452000 350 360 370 Fig. 3. The velocity curves of hypernovae (black: SN 2002ap, blue: SN 1998bw, red: SN 1997ef). t = t0 + d θ= θ vphot fbol 4 σ Teff (1) (2) where fbol is the observed bolometric surface brightness (in Wm−2), vphot is the photospheric velocity, t0 is the moment of explosion and d is the distance. At each epoch, the effective temperature was estimated from the dereddened (B − V ) color index (E(B − V ) = 0.09 was applied, [14]) using hyper- 42 J.Vinkó et al. nova model atmospheres by Mazzali et al. ([7]). Then, the angular radius of the photosphere was calculated via Eq.2. 0.0125 40 0.012 35 t0 = 304.3 30 D = 6.7 Mpc 0.011 25 0.0105 t-t0 Ang.diam. (mas) 0.0115 0.01 0.0095 15 0.009 10 0.0085 5 0.008 0.0075 305 20 310 315 320 JD - 2452000 325 330 335 0 0 1 2 3 4 5 6 K*Theta/V_phot Fig. 4. Left: the calculated angular radius of the photosphere as a function of time. The expanding phase are marked with blue symbols. Only the blue points have been used for the EPM-analysis. Right:the fitting of Eq.1 to the expanding phase. The slope yields a distance of 6.7 ± 1 Mpc. 4 Results The results of this study are summarized in Table 1 below. Table 1. Inferred parameters of SN 2002ap. max max Distance MB MVmax MR MImax Bol.decline rate (Mpc) (mag) (mag) (mag) (mag) (mag/day) 6.7 ± 1 −16.44 −17.05 −17.14 −17.07 0.017 ± 0.0005 The EPM-distance agrees well with previous distance estimates of M74 based on the brightness of blue supergiant stars (d ≈ 8 Mpc, [10, 12]). Acknowledgement. This work has been supported by Hungarian OTKA Grant T034615 and the Bolyai Janos Research Scholarship to JV. References 1. Berger, E., Kulkarni, S.R., Chevalier, R.A.: ApJ 577, L5 (2002) 2. Borisov G., Dimitrov, D., Semkov, E. et al.: IBVS 5264 (2002) 3. Cook,L.M., Katkova,E.V., Sokolov,N.A., Guseva,I.S.: IBVS 5283 (2002) Distance of the Hypernova SN 2002ap 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Gal-Yam, A., Ofek, E., Shemmer, O.: MNRAS 332, L73 (2002) Kawabata, K.S., Jeffery, D.J., Iye, M. et al.: ApJ 580, 39 (2002) Kirshner, R.P., Kwan, J.: ApJ 193, 27 (1974) Mazzali, P.A., Iwamoto, K., Nomoto, K.: ApJ 545, 407 (2000) Pandey, S.B., Anupama, G.C., Sagar, R. et al.: MNRAS 340, 375 (2003) Patat, F., Capellaro, E., Danziger, J. et al.: ApJ 555, 900 (2001) Sharina, M.E., Karachentsev, I.D., Tikhonov, N.A.: A&AS 119, 499 (1996) Smartt, S.J., Vreeswijk, P.M., Ramirez-Ruiz, E. et al.: ApJ 572, 147 (2002) Sohn, Y.J., Davidge, T.J.: AJ 111 2280 (1996) Sutaria, F.K., Chandra, P., Bhatnagar, S., Ray, A.: A&A 397, 1011 (2003) Takada-Hidai, M., Aoki, W. Zhao, G.: PASJ 54, 899 (2003) Yoshii, Y., Tomita, H., Kobayashi, Y. et al.: astro-ph/0304010 (2003) 43 Template Frames of Nearby Galaxies for SN-Photometry: Application to SN 2002bo in NGC 3190 K.Sárneczky1 , J.Vinkó1 , Gy.M.Szabó3, G.Fűrész3,4 , B.Csák3 , R.Szabó4 , Sz.Csizmadia4, Zs.Bebesi2 , Zs.Heiner1 , Sz.Mészáros2 , and B.Sipőcz 1 2 3 Dept. of Optics, University of Szeged, Hungary sky@titan.physx.u-szeged.hu Dept. of Experimental Physics, University of Szeged Konkoly Observatory, Budapest, Hungary Summary. We present a progress report of collecting CCD frames of nearby galaxies to be used as template frames for image subtraction. Our purpose is to set up a collection of CCD frames of the closest, brightest northern galaxies, that may produce potentially bright SNe in the future. We demonstrate the usefulness of the template images with the current Type Ia SN 2002bo in NGC 3190. 1 Introduction Supernovae often occur close to bright HII-regions and/or dust lanes of their host galaxies, where the background is bright and strongly varies in position. Photometry of these SNe is reliable only if the contamination of the background can be removed somehow from the CCD frame. It is usually done with a subtraction of a template frame that does not contain the SN. However, if the template frame must be obtained after the discovery of the SN, it often takes at least 1-2 years to capture such a frame of a particular galaxy, because the SN (and sometimes its light echo) must fade away entirely. The aim of our project is to obtain a set of CCD frames of a selected sample of galaxies that are potential hosts of bright SNe. The selection criteria were the followings: • declination is higher than −10◦) • distance is less than 30 Mpc • included in New General Catalogue The parameters of the galaxies were collected from the catalogue of Tully (1988). In addition, we have included NGC 664 and NGC 3690, because these showed more than 2 SNe earlier. 46 K.Sárneczky et al. 2 Current status We have applied the 60/90 cm Schmidt telescope at Piszkéstető Station of Konkoly Observatory, Hungary, equipped with a Photometrics AT-200 CCD camera. The frames have 1536 x 1024 pixel dimensions, the plate scale is 1.02 arcsec/pixel, the total field of view is 26.1 x 17.4 arcmin. The frames were exposed through standard Johnson BV RI - filters. The exposure times were fixed as 5 minutes for V RI frames and 10 minutes for B frames. The saturation level for stars was about 13 mag on R and I frames. Currently we have full set of BV RI-frames for 162 program galaxies and 29 additional ones imaged through at least one filter. The images are registered using WCSTools ([6]). Some frames (combined into color images) are shown below as examples. The total number of program galaxies is 645. Fig. 1. NGC 891 3 Application: SN 2002bo SN 2002bo has been discovered in the spiral galaxy NGC 3190 by P.Cacella and Y.Hirose on Mar.9, 2002 (cf. [2]). The first spectroscopic observations ([1, 4]) revealed that this is a type Ia SN discovered well before maximum. Matheson et al. ([5]) and Chornock et al. ([3]) reported that the spectrum shows strong Si II line at 5850 Å ( characteristics of an underluminous, fastdecliner SN, similar to SN 1999by), but lacks other strong Ti II features, indicating a peculiar type Ia SN. We have obtained frames on NGC 3190 on March 4, just before the discovery of SN 2002bo ([8]). These frames are used as templates for image subtraction during the photometric monitoring of the SN. We could follow SN 2002bo Template frames of Nearby Galaxies 47 Fig. 2. NGC 3031 Fig. 3. NGC 2403 on 11 nights between t = −6 days and t = 78 days. The strong background contamination of the host galaxy could be nicely removed using our template frames. The magnitude of the SN was calculated with aperture photometry on the subtracted image (see below). Later, the field was calibrated via Landolt standards. The resulted light curve has been analyzed with the MLCS-method ([7]). This resulted in D ≈ 30 Mpc distance, and AV ≈ 1 mag interstellar absorption. The most interesting result is that the MLCS-analysis gave ∆ = −0.2 mag, meaning an overluminous, rather than underluminous SN. This result 48 K.Sárneczky et al. Fig. 4. Distribution of program galaxies on the sky. Red symbols denote galaxies with completed BV RI-frames, blue dots mark objects observed with at least one filter. Fig. 5. CCD-images of SN 2002bo in V RI-filters (from top to bottom) before (left panel) and after the subtraction of the template frame (right panel). Template frames of Nearby Galaxies 49 is in contrast with the reported spectroscopic properties, further strengthening the peculiarity of SN 2002bo. A more detailed analysis based on larger datasets would be desirable. 10 11 SN 2002bo T0 = 356.0 E(B-V) = 0.31 mu_0 = 32.34 Delta = -0.20 Mag 12 13 I-2 14 R-1 15 V 16 17 340 360 380 400 420 440 460 JD - 2452000 Fig. 6. The observed and fitted light curves of SN 2002bo. The resulted parameters are also shown. Acknowledgement. This work has been supported by Hungarian OTKA Grant T034615 and the Bolyai Janos Research Scholarship to JV. References 1. Benetti, S., Altavilla, G., Pastorello, A., Riello, M., Turatto, M., Cappellaro, E., Tomov, T., Mikolajewski, M: IAU Circular 7848, 3 (2002) 2. Cacella, P., Hirose, Y., Nakano, S., Kushida, Y., Kushida, R., Li, W.D.: IAU Circular 7847, 1 (2002) 3. Chornock, R., Li, W.D., Filippenko, A.V: IAU Circular 7851, 3 (2002) 4. Kawakita, H., Kinugasa, K., Ayani, K., Yamaoka, H: IAU Circular 7848, 2 (2002) 5. Matheson, T., Jha, S., Challis, P., Kirshner, R., Hradecky, V.: IAU Circular 7849, 2 (2002) 6. Mink, D.J. in: Astronomical Data Analysis Software and Systems VIII, ASP Conf. Ser., Vol. 172 (1999) eds: D. Mehringer, R.Plante, D. Roberts, p. 498 7. Riess , A.G., Filippenko, A.V., Challis, P. et al. : AJ 116, 1009 (1998) 8. Sárneczky, K., Bebesi, Z.: IAU Circular 7863, 3 (2002) 9. Tully, R.B. Nearby Galaxies Catalogue (Cambridge Univ. Press, 1998) The Late UVOIR Light Curve of SN 2000cx Jesper Sollerman1 , Cecilia Kozma1 , and Jan Lindahl1,2 1 2 Stockholm Observatory, AlbaNova, 106 91 Stockholm, Sweden jesper@astro.su.se Onsala Space Observatory, 439 92 Onsala, Sweden Summary. We present preliminary data and modeling of the late time light curve of the Type Ia supernova SN 2000cx. Optical and near-infrared data obtained with the VLT at 360 to 480 days past maximum light show the increasing importance of the near-infrared regime. Detailed multi-band modeling based on W7 also show this effect. Conclusions on positron escape in this phase may therefore require more detailed observations and modeling than hitherto appreciated. 1 Introduction Type Ia supernovae (SNe Ia) are believed to be the destructive thermonuclear explosions of white dwarfs. Their light curves are during the first couple of years powered by the radioactive decay of freshly synthesized 56 Ni, releasing γrays and positrons in the ejecta. At phases later than about 200 days, virtually all γ-rays escape freely from the ejecta, and the luminosity is then provided by the kinetic energy deposited by the positrons. Whether or not the positrons are able to slip out of the ejecta depends on the strength and geometry of the magnetic field (e.g., [5, 6, 8]). While a weak and radially combed magnetic field might allow positron escape, thus providing a steep light curve, a strong, tangled magnetic field would efficiently trap all the positrons, and drive the light curve to the radioactive decay rate. As a first step to investigate whether or not observations of the positron phase can establish conclusions about positron escape, we have conducted a photometric study at late phases of the SN Ia 2000cx, and modeled its light curve in detail. Here we present some preliminary results from that study. The final analysis will be reported elsewhere. 2 Observations of SN 2000cx SN 2000cx was discovered on 17.5 July 2000 [10] far from the nucleus of the S0 galaxy NGC 524, and became the brightest supernova observed that year. 52 Jesper Sollerman, Cecilia Kozma, and Jan Lindahl This made it a very good target for late time photometry. The early evolution has been extremely well covered [1, 4]. We have observed the field of SN 2000cx in the optical, (U)BVRI, regime during four epochs between 360 and 480 days past maximum light. These observations were obtained with the FORS instruments at the ESO VLT. The data were reduced in a standard way using IRAF. Near-infrared observations were obtained using the ISAAC instrument at the VLT. Data were obtained in the J and H (and K) bands at three epochs close to the optical observations. The data were reduced within Eclipse and IRAF. Magnitudes were measured using aperture photometry and zero points in the standard system were obtained by observations of standard stars. A detailed description of the observations and the data reductions will be given elsewhere. Very late observations using the HST will be included in a future study. 3 Modeling We have performed detailed modeling of the emission from SNe Ia in the nebular phase, 100 − 1000 days after explosion, in order to interpret our observations of SN 2000cx. The code is an updated version of the code described by Kozma & Fransson [3]. The decay of 56 Co dominates the energy input at the epochs we are modeling. The γ-rays emitted in the decays give rise to fast electrons which deposit their energy by heating, ionizing, or exciting the ejecta. In our calculations we assume full and immediate positron deposition within the regions containing the newly synthesized iron. As input to our calculations we use the density structure, abundances and velocity structure from model W7 [7, 9]. UV-scattering is not included and as it may be important for the ionization structure we have made model calculations with and without including photoionization. 4 Results In Fig. 1 the light curves for the B- to H-bands are shown for both observations and models. We find a general good agreement between observations and models, with a steeper slope in the BV R- (V band declines 1.4 mag. per 100 days) and virtually constant light curves in the JH-bands. The curves for the model without photoionization (dotted) drops quickly after 400-600 days. This is due to a lower temperature in the ejecta for this model. For the BV RI-bands the model including photoionization (dasheddotted) appears to give a better fit to the observations. However, since the differences in the light curves are mainly a temperature effect, other processes The Late UVOIR Light Curve of SN 2000cx 53 might give the same result. For example, clumping of the ejecta would allow low density regions to be hotter, keeping the light curves from dropping. 18 18 B 20 20 22 22 24 24 26 26 200 400 600 V 200 Time (days past B-maximum) 400 600 Time (days past B-maximum) 16 18 R I 18 20 20 22 22 24 24 26 26 200 400 600 200 Time (days past B-maximum) 18 16 J 20 18 22 20 24 22 26 24 200 400 400 600 Time (days past B-maximum) 600 Time (days past B-maximum) H 200 400 600 Time (days past B-maximum) Fig. 1. Late light curves of SN 2000cx. The error bars fall within the circles. 4.1 Bolometric luminosity The wide coverage of broad band magnitudes allows an attempt to construct a uvoir “bolometric” lightcurve. We estimated the bolometric lightcurve by simply integrating the flux from (U)B to H(K) at all epochs. The result is shown in Fig. 2. 54 Jesper Sollerman, Cecilia Kozma, and Jan Lindahl Fig. 2. Upper panel: The full curve shows the modeled bolometric luminosity and the others show the V-band for the two models (see Fig. 1). The curves are matched to the same value at 100 days. Lower panel: The full curve shows the observed integrated luminosity in the (U)BVRIJH(K) bands, while the dashed curve is the observed luminosity in the V-band. For both models and observations the slope of the “bolometric” light curve diverges from the V-band light curve at later epochs. 5 Discussion As the trapping of the γ-rays decreases, the kinetic energy of the positrons will start to dominate the energy input to the ejecta. Our model assumes full trapping of the positrons. In this case the bolometric light curve should flatten out and approach the decay rate of 56 Co in the positron dominated phase. However, late observations of SNe Ia in different pass bands indicate that the light curve continues to fall more rapidly also at epochs later than 250 days. This has been interpreted as due to positron escape [2, 5, 6, 8]. However, since the observations of late light curves are sparse, in particular in the near-IR, it is generally not possible to construct true bolometric light curves. For example, Cappellaro et al. [2] had to assume that the late bolometric light curve follows the V-band. This assumption is not necessarily The Late UVOIR Light Curve of SN 2000cx 55 valid. As the input heating decreases and the ejecta expands the temperatures will decrease, and color evolution could mimic the effect of positron escape. In Fig. 2 we compare the bolometric light curve to the V-band light curve for our two model calculations. Even with full positron trapping we find an increasing deviation between the bolometric and V-band light curve with time. Especially for the model without photoionization the drop in the V-band is rapid around 400-500 days. The emission in the various bands behave quite differently, due to the evolution of temperature and ionization structure within the ejecta. This makes it a hazard to assume that any particular band reflects the true bolometric luminosity. Also in the observations do we find that the slope of the bolometric and V-band light curves differs (Fig. 2 lower panel). A comparison to a true bolometric light curve would increase this effect. We therefore find it difficult to draw any conclusions about the degree of positron escape in SNe Ia without having a detailed and consistent knowledge of the temperature and ionization evolution of the ejecta. Time dependent bolometric corrections can instead be a likely explanation for these observations. Acknowledgement. We are grateful to K. Nomoto for providing the W7 model, and to S. Nahar for iron recombination rates. We thank B. Leibundgut, C. Fransson, P. Lundqvist, N. Suntzeff and the SINS team, as well as P. Milne for discussions on this project. The observations are based on observations collected at the European Southern Observatory (67.D-0134 and 68.D-0114). JS trip to Valencia was paid by Wallenbergsstiftelsens jubileumsfond. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. P. Candia, K. Krisciunas, N. B. Suntzeff et al.: PASP 115, 227 (2003) E. Cappellaro, P. A. Mazzali, S. Benetti et al.: A&A 328, 203 (1997) C. Kozma, C. Fransson: ApJ 496, 946 (1998) W. Li, A. F. Filippenko, E. Gates et al.: PASP 113, 1178 (2001) P. A. Milne, L. S. The, D. Leising: ApJS 124, 503 (1999) P. A. Milne, L. S. The, D. Leising: ApJ 559, 1019 (2001) K. Nomoto, F.-K., Thielemann, K. Yokoi: ApJ 286, 644 (1984) P. Ruiz-Lapuente, H. Spruit: ApJ 500, 360 (1998) F.-K., Thielemann, K. Nomoto, K. Yokoi: A&A 158, 17 (1986) C. Yu, M. Modjaz, W. Li: IAUC 7458 (2000) The “Central” Source in NGC 2146: a Radio Supernova or a Weak AGN? A. Tarchi1,2, M. A. Garrett3 , A. Greve4 , and S. T. Garrington5 1 2 3 4 5 Instituto di Radioastronomia, CNR, Bologna, Italy a.tarchi@ira.cnr.it Osservatorio Astronomico di Cagliari, Capoterra (CA), Italy JIVE, Postbus 2, 7990 AA, Dwingeloo, the Netherlands IRAM, 300, St. Martin d’Hères, France Jodrell Bank Observatory, Macclesfield, Cheshire, UK Summary. We present a two-frequency radio continuum VLBI study of the strongest compact radio source in the starburst galaxy NGC 2146. Its largely negative spectral index, consistent with optically thin synchrotron emission, together with its high brightness temperature suggest that the object is a radio supernova. On the other hand the location of the source, very close to the dynamic center of the galaxy, its extreme compactness (< 0.3 pc), and a faint jet-like feature associated with the source may hint in favor of an alternative nature. The source could in fact be a weak active core pinpointing, for the first time, the undiscovered true nucleus of the galaxy. Implications for the two different options are discussed and possible follow-up studies to help determining the nature of the source are also addressed. 1 Introduction NGC 2146 is a nearby starburst galaxy (D = 14.5 Mpc; [1]). The strongest star formation activity is concentrated in the central two kiloparsecs of the galaxy. Because of optical obscuration by dust, radio observations are the most suitable to observe the inner hundredths parsecs. In the central kiloparsec a dozen of compact sources has been detected at radio wavelengths with MERLIN and the VLA, and they have been identified with supernova remnants (SNRs), radio supernovae (RSNe), and compact Hii regions [2]. In the following we report on a study, using MERLIN and VLBI observations, of the compact sources in NGC 2146, with particular interest for the strong source 37.6 + 24.2 close to the dynamical center of the galaxy, which presents peculiar features hinting at a possible weak-AGN nature. 58 A. Tarchi et al. 2 Observations MERLIN – NGC 2146 was observed in the L-Band with MERLIN (6 antennas, including the Lovell telescope) in May 1997 and April 1999, for a total period of 24 h. The observing frequency was 1.658 GHz (λ = 18 cm), with a bandwidth of 15 MHz in both circular polarizations. VLBA – NGC 2146 was observed with the VLBA (10 antennas) for 5.5 hours at 1.6 GHz in January 2000 and for 11 hours at 5 GHz in March 2002. In order to maximize the sensitivity of the observations we used the 256-8-2 mode (64 MHz overall bandwidth). Because of weakness of the “central” source in NGC 2146 a phase referencing observation was necessary. EVN – NGC 2146 has been also observed for 11 hours with the European VLBI Network (EVN; 7 antennas: Effelsberg, Mark2, Westerbork, Medicina, Noto, Onsala, Torun) at 5 GHz in June 2000. 3 Discussion and Conclusions The compact radio source 37.6+24.2 found in NGC 2146 has been proposed to be a RSN or a young SNR by Tarchi et al. (2000; hereafter TNG), because of its negative spectral index, consistent with optically thin synchrotron emission, and its brightness temperature, too high to be due to free-free emission from ionized gas. This source has been detected also in the MERLIN 5 GHz uniformly weighted map with a resolution of 0.04. The source was still unresolved at this resolution indicating a strong and compact object, with a diameter smaller than 3 pc [3]. Interestingly enough at the lower resolution of our 1.6 GHz MERLIN map (res ≈ 0.12) the source seems to be slightly resolved, though only at a weak level. Furthermore, a “500−λtapered” 1.6 GHz MERLIN image of this source (res. = 0. 45) shows a weak jet-like feature starting from the central source in the direction SE (Fig. 1). This feature, if real, and together with the relative vicinity with the dynamical nucleus of the galaxy (position offset ∼ 1.15), may suggest that the source is associated with an active core, in analogy to a similar jet-like feature in M 82 [4]. Furthermore, because of the compactness of the source and according to the Σ−D relation, the source 37.6+24.2 should be young, and hence, having a rapid decay in flux. From a comparison between our recent data and previous available VLA ones (e.g. [5]), we derived a relatively constant flux density over more than two decades. Our 1.6 and 5 GHz VLBA images of 37.6+24.2 (Fig. 2) and the derived quantities (Table 1) suggest that the source: • is very compact (< 0.2 pc) • has a high brightness temperature (> 2 · 107 K at 1.6 GHz) • has a flatter radio spectral index (∼ − 0.4) than previously derived, but still consistent with optically thin synchrotron emission The “Central” Source in NGC 2146 59 • does not show a clear evidence of an elongated structure. In the 1.6 GHz map the source shows an elongated structure extending both NW and SE, but we think that this is due to the strongly elliptical shape of the beam (bottom-right corner in Fig. 1). This suspect is confirmed by the 5 GHz EVN map of the source where no elongated shape has been detected. These preliminary results support the hypothesis by TNG that the source 37.6+24.2 is either a RSN or a SNR. In particular, because of the flatter spectral index found by us w.r.t. that reported in TNG, we tend in favor of the latter option. However, it has still to be explained the relative constancy in the radio flux density over several years, especially when related to the very high brightness temperature and compactness of the object. A comparison between our radio images of NGC 2146 and those at X-ray frequencies produced by Chandra is planned. This should help to locate the undiscovered true nucleus of the galaxy, in order to correlate its position with that of 37.6+24.2 and confidently determine the nature of this source. Acknowledgement. We would like to acknowledge E. Ros, A. Peck, and D. Gabuzda for their cheerful help. Part of this work was supported by the European Community under its Access to Research Infrastructure action of the Improving Human Potential Programme, contract number HPRI-CT-1999-00045. References 1. P. Benvenuti, M. Capaccioli, & S. D’Odorico: A&A 41, 91 (1975) 2. A. Tarchi, N. Neininger, A. Greve, et al: A&A 358, 95 (2000); TNG 3. A. Tarchi: Radio observations of starburst galaxies: the case of NGC 2146. Ph. D Thesis, Bonn University, Bonn (2001) 4. K.A. Wills, M.P. Redman, T.W.B. Muxlow T.W.B., et al: MNRAS 309, 395 (1999) 5. P.P. Kronberg, & P. Biermann: ApJ, 243, 89 (1981) Table 1. Observed quantities of the compact radio source 37.6+24.2 in NGC 2146: integrated flux densities at 1.6 and 5 GHz, spectral index (after convolution to the same beam), and brightness temperature at 1.6 GHz. The errors of the observed quantities are reported in parentheses. Source S1.6 (mJy) S5 (mJy) α51.6 Tb (K) 37.6+24.2 2.39 (0.13) 1.62 (0.11) − 0.36 (0.08) > 2 · 107 60 A. Tarchi et al. Fig. 1. MERLIN 1.6 GHz tapered map of the central source and the region around it at 300 mas resolution. The peak flux density is 3.9 mJy/beam and the first contour and the contour interval are 0.04 mJy/beam. The contours are drawn up to 50 % of the peak flux. 78 21 24.32 1.6 GHz 78 21 24.32 24.30 24.29 24.28 24.27 06 18 37.600 37.598 37.596 37.594 37.592 37.590 37.588 37.586 37.584 37.582 RIGHT ASCENSION (J2000) DECLINATION (J2000) DECLINATION (J2000) 24.31 5 GHz 24.31 24.30 24.29 24.28 24.27 06 18 37.600 37.598 37.596 37.594 37.592 37.590 37.588 37.586 37.584 37.582 RIGHT ASCENSION (J2000) Fig. 2. Left panel: uniformly weighted 1.6 GHz VLBA image (res. = 7.6 × 3.5 mas) of the source 37.6+24.2 in NGC 2146. The first contour and the contour interval are 0.1 mJy/beam. Right panel: naturally weighted 5 GHz VLBA image (res. = 2.7 × 2.3 mas) of the source 37.6+24.2 in NGC 2146. The first contour and the contour interval are 0.08 mJy/beam. Part II Supernovae: Searches/Statistics StRESS: Southern Intermediate Redshift ESO SN Search, Global SNe Rate Estimate G. Altavilla1,2, M. Riello1,2, M.T. Botticella3 , S. Valenti3, and E. Cappellaro3 1 2 3 INAF - Astronomical Observatory of Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy (altavilla, riello)@pd.astro.it Department of Astronomy, University of Padova, Vicolo dell’Osservatorio 2, I-35122 Padova, Italy INAF - Astronomical Observatory of Capodimonte, Via Moiarello 16, I-80131 Napoli, Italy (botticella, valenti, cappellaro)@pd.astro.it Summary. We present the preliminary results of our Supernova Search. We monitored several fields, surveying about two square degrees in each run at the MPG/ESO2.2 m, and we checked our supernova candidates by spectroscopic observations at VLT. From the beginning of the search we discovered 21 Supernovae (SNe), with redshift out to z ∼ 0.6. We found both Thermonuclear SNe (type Ia) and Core Collapse SNe (CCSNe: type II-Ib/c), almost in equal proportions (10 type II, 9 type Ia, 1 type IIn and 1 type Ic). We analyzed the global SN rate using a subsample of the collected data and, under reasonable assumptions for type Ia SN rate, we found evidences of a significant increase for CCSNe rate at z ∼ 0.3, which turns out to be a factor 3 greater than the local Universe value. 1 Introduction One of the main goal of SN searches is to measure the supernova rate (SNR) at different redshifts. The SNR is strongly linked to the star formation rate (SFR): the rate of Core Collapse SNe (CCSNe) is correlated with the instantaneous SFR because of the short lifetime of their massive progenitors (M > 8M ), while the rate of type Ia SNe, originating in evolved binary system, can give information about the long term star formation history. The comparison of SNRs measured at different redshifts therefore can provide important information on the SNR history with cosmic age and thus on galaxy evolution. In recent years, many authors have published predictions of the expected SN rate as a function of redshift, based on SN progenitor scenarios and modeling of the cosmic star formation evolution [1, 2, 3, 4, 5, 6]. But, while the local SNR for different SN classes and morphological galaxy 64 G. Altavilla et al. Table 1. SNe spectroscopically confirmed SN 1999ey 1999gt 1999gu 2000fc 2000fp 2001bc 2001bd type z IIn Ia II Ia II II II 0.09 0.27 0.15 0.42 0.30 0.19 0.10 IAUC SN 7310 7346 7346 7537 7549 7615 7615 2001be 2001ge 2001gf 2001gg 2001gh 2001gi 2001gj type z Ia Ia Ia II II Ia II 0.24 0.22 0.10 0.61 0.16 0.20 0.27 IAUC SN 7615 7762 7762 7762 7762 7762 7762 2001io 2001ip 2002cl 2002cm 2002cn 2002co 2002du type z IAUC Ia Ia Ic II Ia II II 0.19 0.54 0.07 0.09 0.30 0.32 0.21 7780 7780 7885 7885 7885 7885 7929 types is reasonably well known [7], at present there are few observational estimates of the frequencies of SNe at high redshift. Two pioneering works [8, 9] were based on three and four SNe respectively, whereas a more recent study Pain et al. 2002[10] present more statistically significant results based on a sample of 38 SNe, all of type Ia. Indeed, so far the observational estimates of the SN rates at high redshift have been based on the SN searches aimed to use SN Ia as cosmological probes [8, 10] and were therefore strongly biased1 . Because of this situation, some years ago we decided to start a SN search especially designed to estimate the rate of SNe of all types at intermediate redshift. We present here the first estimate of the global SN rate at z ∼ 0.3. 2 Observational data The search was performed using the MPG/ESO 2.2 m telescope equipped with the Wide Field Imager; because of the faint magnitude of the candidates the spectroscopic classification and follow up was performed with ESO VLT + FORS1/2. We surveyed 21 fields and the effective searched area is ∼ 5.1 square degrees. We detected about 100 SN candidates but, because of the limited VLT time allocated, we could obtain spectroscopic confirmation only for 21 supernovae (9 type Ia, 10 type II, 1 type IIn and 1 type Ic), with redshift up to z = 0.6 (Table 1) and V magnitude at discovery ranging in the interval 20–24 (Fig.1a). We found CCSNe and SNe Ia in almost equal proportion but, as expected, due to the brighter absolute magnitude the latter are on average at higher redshift than the former ones (Fig.1b). 1 e.g. the candidates had to be not coincident with the host galaxy nucleus, not too much fainter than host galaxy (to make accurate photometry) and blue (to avoid uncertain reddening correction). StRESS, Global SN Rate Estimate 65 Fig. 1. a) V magnitude distribution and b) redshift distribution of the 21 SNe spectroscopically confirmed. Upper panels: SNe Ia+CCSNe; middle panels: SNe Ia; lower panels: CCSNe 3 SNe rates In order to make a sound and direct comparison of our SN rate estimates at intermediate redshift with the values for the local Universe [7], we follow the same method used to estimate the local SN rates. The rest-frame SNR (in SNu2 ) at a given redshift z is thus defined in the following way: NSN (z) rSN (z) = N (z) (1 + z) gal LBi ∆t(z) i=1 (1) where NSN (z) is the observed number of SNe occurred per redshift interval, Ngal (z) is the number of galaxies with rest-frame LBi luminosity per redshift interval (in unit of solar B luminosity) and ∆t(z) is the time interval (control time), z corrected, during which a supernova of a given type at redshift z is brighter than the detection limiting magnitude. As shown by eq. 1, to estimate the SNR we need to: - define a distance limited sample of galaxies with known integrated B luminosity; - estimate the control times of the galaxies; - count the SNe exploded in the sample. 2 1SN u = 1SN (100yr)−1 (1010 LB )−1 66 G. Altavilla et al. Fig. 2. Left: Redshift distribution of the SN candidates (both type Ia and CCSNe) (solid line); expected distribution obtained assuming the SN rates to be constant and equal to the values found for the local Universe (long dashed line); expected distribution obtained assuming the SN Ia rate to be 1.5× the local value and the CCSN rate 3× the local value (short dashed line). Right: SN Ia rate per comoving volume determined by [8, 10] (circles at z ∼ 0.4, z ∼ 0.55), by [7] (filled diamond at z ∼ 0.01) and [9] (open diamond at z ∼ 0.1). The interpolated value at z = 0.3, equal to 1.5× the local value, is also shown. Theoretical predictions for two Star Formation History (SFH) scenarios and two delay times are shown for comparison. Figure adapted from [10]. In this work we have considered a subsample of the collected data, consisting in 5 of the 21 fields monitored in our campaign (corresponding to ∼ 1.2 square degree). In order to detect the faintest galaxies, we produced B, V , R deep images combining the frames obtained in different epochs, provided that the seeing was better than ∼ 1.0. Compared with the images obtained in a single epoch, the limiting magnitude is significantly improved: in a typical search image V 24.5 while in the deep stacked image V 26. We then built the object catalogs for each deep field by SExtractor [12]. Using the Hyper-z software [13], we derived the photometric redshift and B luminosity for each galaxy of our subsample. For each field we then estimated the overall control time per redshift bin, for four SN types (Ia, IIP, IIL, Ib/c). The light curve templates were redshifted, time dilated and K-corrected according to the redshift bin considered. In order to compare directly our results to the local SN rate, we adopted the light curve templates and cosmological parameters used by [14]. In the subsample analyzed in this work, we detected ∼ 50 reliable3 SN candidates but, because of the limited VLT time available, we could not confirm spectroscopically all of them. In order to determine the true number of SNe occurred in the selected fields, we proceeded as follows. In addition to the spectroscopically confirmed SNe, we assumed to be true SNe all the candidates 3 according to their variability history StRESS, Global SN Rate Estimate 67 far from the host galaxy nuclei. For what concern the other candidates located in the nuclear region of the host galaxy, there is a significant chance that they are AGN. Only ∼ 40% of them were counted as real SNe, according to our experience gained with the candidates during the follow-up observations. Since we have not enough data to discriminate between different SN types, we compared the redshift distribution of all the “true” SN candidates, whose mean redshift is < z > 0.3 (Fig. 2, left panel), with the expected distribution for a constant SN rate rSN given by NSN exp(z) = Ngal (z) rSN LBi ∆t(z) 1 + z i=1 (2) Firstly we assumed the SN rates for CCSNe and SNe Ia to be constant and equal to the values found for the local Universe4 : rIa = 0.14 SNu, rCCSNe = 0.30 SNu (H0 = 75 km s−1 Mpc−1 ) [7]. The comparison shows a deficit of the expected distribution. Pain et al. (2002) [10] suggested that the rate of type Ia SNe at z ∼ 0.55 is about a factor 2 greater than the local one. Even taking into account this effect and assuming the SNe rate at z ∼ 0.3 to be a factor 1.5 greater than the local value (see Fig. 2, right panel), we do not obtain a reasonable match between the expected and the observed distributions. The only assumption we can adjust is the rate of CCSNe: indeed if we allow the CCSNe rate at z ∼ 0.3 to be greater than the local value by a factor ∼ 3, we obtain a good agreement between the two distributions (short dashed line). The result obtained is in concordance with the SFR evolution with redshift derived by [15], which shows the same ratio between the local SFR and the value derived at z = 0.24. This confirm the goodness of our assumptions about the SN rates. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 4 P. Madau, M della Valle, N. Panagia: MNRAS 297, 17 (1999) R. Sadat, A. Blanchard, B. Guiderdoni, J. Silk: A&A 331, 69 (1998) T. Dahlén, C. Fransson: A&A 350, 349 (1999) L. R. Yungelson, M. Livio: ApJ 528, 108 (2000) C. Kobayashi, T. Tsujimoto, K. Nomoto: ApJ 539, 26 (2000) M. Sullivan, R. Ellis, P. Nugent, I. Smail, P. Madau: MNRAS 319, 549 (2000) E. Cappellaro, R. Evans, M. Turatto: A&A 351, 459 (1999) R. Pain et al.: ApJ 473, 356 (1996) D. Hardin et al.: A&A 362, 419 (2000) R. Pain et al.: ApJ 577, 120 (2002) The extinction correction was not applied because of the difficulties in determining the effects of absorption at high z. Thus reference has been made to the local SN rate values and the light curve templates not corrected for absorption. 68 G. Altavilla et al. 11. E. Cappellaro, M. Turatto, D. Y. Tsvetkov, O. S Bartunov, C. Pollas, R. Evans M. Hamuy: A&A 322, 431 (1997) 12. E. Bertin, S. Arnouts: A&AS 117, 393 (1996) 13. M. Bolzonella, J. M. Miralles, R. Pelló: A&A 363, 476 (2000) 14. E. Cappellaro, M. Turatto, S. Benetti, D. Y Tsvetkov, O. S. Bartunov, I. N. Makarova: A&A 268, 472 (1993) 15. S. S. Fujita et al.: ApJL 586, 115 (2003) The Supernova Program of the Canada-France-Hawaii-Telescope Legacy Survey Stéphane Basa, on behalf of the SNLS collaboration Laboratoire d’Astrophysique de Marseille, Traverse du Siphon, Les Trois Lucs, BP 8, 13376 Marseille Cedex 12, France, and Centre de Physique des Particules de Marseille, 163 Avenue de Luminy, Case 907, 13288 Marseille Cedex 09, France stephane.basa@oamp.fr Summary. The CFHT Legacy Survey (CFHTLS) is a large-scale multi-component program intended to operate for 5 years. Started in August 2003, the deep survey of the CFHTLS will cover a total of 4 square degrees in four fields. It will detect and monitor as many as 1200 supernovae up to a redshift of about 0.9. This unprecedented supernova data set will provide a precise measurement of the cosmological parameters including a first measurement of the pressure-energy density ratio, w, as described in section 2. Before giving more details on this program, a panorama of the present scientific context is presented in section 1. 1 Scientific Rationale 1.1 Motivation The Cosmological Model that is now emerging describes the present Universe as flat and the energy component that dilutes with the expansion, i.e. matter, amounts only to one third of the total energy content today. The remainder, often called Dark Energy, appears not to dilute with expansion: its density decreases slowly or not at all as time goes on. Rather than the acceleration itself, the characterization of the Dark Energy equation of state is of primary importance due to its profound relation to fundamental physics and to the universal geometry. The pressure and the energy density are linked via the parameter w by a simple equation: w = pρΛΛ , which also defines the expansion rate of this component: ρΛ ∼ a−3(1+w) , where a is the scale factor. Friedman’s equation relates the acceleration and w via the equation: aä = − 4πG 3 (ρM + ρΛ (1 + 3w)). Current constraints on w [4, 8], are consistent with a very wide range of Dark Energy models. Among them, the historical cosmological constant 70 Stéphane Basa, on behalf of the SNLS collaboration (w = −1) remains 10120 to 1060 smaller than plausible vacuum energies of fundamental particle theories. It also cannot explain why matter and Dark Energy have comparable densities today. These challenges have teased the imagination of theorists and many “dynamical Λ” models have been proposed (quintessence, k-essence, ...) based on speculative field models, and some predict w values above -0.8, significantly different from -1. Among available experimental approaches, the Hubble diagram of type Ia supernovae remains the most sensitive to the Dark Energy component of the Universe. This method which was used in 1998 by two independent teams, has been the first one to measure a non-zero cosmological constant ([8, 10]). However, it is important to note that type Ia supernovae cannot be really qualified as standard candles, but can be “standardized” by using a luminosity-decline rate relation [9]. 1.2 Second generation type Ia supernova experiments To separate the cosmological constant from dynamical Dark Energies, second generation supernova experiments are now starting. All of them aims at beating down statistical errors to a marginal level to have a better handling of the systematics errors. To reach their goals, new type Ia supernovae experiments aim at: • Improving the knowledge of the type Ia supernova phenomenom by studying large samples of nearby objects (i.e. more than 100). These nearby supernovae are also mandatory to anchor the low redshift part of the Hubble diagram. No compelling estimate of cosmological parameters can be obtained without them. • Characterizing the Dark Energy equation of state by increasing by a factor ten the supernova sample (i.e. more than 500) at high redshift (typically between 0.2 and 1.0 where the measurement of w is the most sensitive). This sample has to be of excellent quality in order to allow precise comparisons from redshift to redshift and with nearby samples. Observation strategy is different between nearby supernovae for which a wild field survey is required and high redshift supernovae for which a deep survey is required. This leads to a natural classification of the second generation type Ia supernova experiments as a function of the redshift and of their scientific motivation. At low redshift (study of type Ia supernova phenomenom): The Lick Observatory Supernova Search, LOSS, has discovered and followed-up more than 200 supernovae since 1998 [5]. The program is still under way. The Supernova Nexus program at CfA has already obtained spectra of about 100 supernovae [6]. This program which has started in 1996 is also underway. Finally, the Supernova Factory project aims at obtaining spectrophotometric series of about 300 supernovae at 0.02 < z < 0.08 [11]. This program will start at the end of 2003 and run for 3 years. The supernova program of the CFHTLS 71 At high redshift (characterization of the Dark Energy equation of state): The ESSENCE project, “Equation of State: SupErNovae trace Cosmic Expansion ”, is an observing program started in October 2002 for a planned duration of 5 years [3]. This program proposes to find and follow ∼200 type Ia supernovae in the redshift range 0.15 < z < 0.75. The supernova program of the CFHTLS aims primarily at detecting and monitoring as many as 1200 supernovae up to a redshift of about 0.9, [2]. It has started in 2003 for a planned duration of 5 years This CFHTLS program is probably one of the most ambitious projects at high redshift. It will be described in details in the following section. 2 The Supernova Program of the CFHTLS 2.1 General description The program is composed of a large imaging survey at CFHT for the photometric detection and follow-up of the supernovae and a large spectroscopic survey on 8-meter-class telescopes to identify the type and to measure the redshift. It has been designed to improve very significantly the data quality. Its main advantages are the following: • Time sampling: a given field is observed every 2-3 nights as long as it remains visible (“rolling search” mode). The light curve can then be continuously monitored during at least a time interval of [-10 days, +15 days] in the rest frame. • Multi-band photometry: light curves are measured in g’, r’, i’ and z’ bands. It allows the measurement of the color excess E(B-V) and then the extinction correction. • Multiplexing and data homogeneity: discovery and photometric follow-up are always carried out with the same imager, MegaCam. Both operations are also performed on the same image thanks to the wide field of the imager (one square degree). • Low detection threshold: the detection of objects uses a light curve rather than a single difference. • Spectroscopic trigger: the “rolling search” strategy allows one to monitor the rise of the object and trigger spectroscopy at maximum light. It minimizes the time required to acquire a spectrum. • Low background: repeating observations of the same fields over and over again allows the identification of long term varying objects such as AGN’s and variable stars. 2.2 Imaging survey Started officially in August 2003, the imaging survey is a part of the deep survey of the CFHT Legacy Survey which is performed with the new one 72 Stéphane Basa, on behalf of the SNLS collaboration Table 1. Fields selected for the deep survey of the CFHTLS. Deep 1 Deep 2 Deep 3 Deep 4 RA 02h 26m 00s 10h 00m 29s 14h 17m 54s 22h 15m 32s DEC -04d 30m 00s 02d 12m 21s +52d 30m 31s -17d 44m 6s square degree imager, MegaCam [2]. The CFHTLS represents a total amount of 474 nights over 5 years. It consists of 3 surveys: a very wide shallow survey (1300 square degrees), a wide survey (123 square degrees) and a deep survey (4 square degrees). The 4 square degrees of the deep survey are spread over four fields of one square degree evenly distributed in RA (table 1). Observations will be sequenced at an average rate of 2-3 nights, a dark run for 5 runs in a row each year on each field, for a total amount of 202 nights allocated in service mode. Each 1 square degree field is then observed every 2-3 nights in 4 colors for 5 months. The individual exposure length and limiting Vega magnitudes are: g’(900s:26.0), r’(1800s, 25.5), i’(3600s, 25.2), z’(1800s, 23.4). Detection is performed by subtracting an image to a reference one computed by stacking previous images of the same field. An algorithm due to Alard and Lupton is applied to match the two images [1]. Follow up of already detected supernovae is performed on the same image. The achieved precision on the magnitude measured at the maximum is then dominated by intrinsic dispersion, about 0.15 mag. 2.3 Spectroscopic survey Primary goal of the spectroscopic survey is to identify supernova type and to measure the redshift of the host galaxy. Observations are performed in long slit with an orientation such that the slit goes through both supernova and its host galaxy. Supernova identification is then based on a comparison of the spectroscopic features with template spectra. The host galaxy redshift is measured by using the emission or absorption lines when the host galaxy is bright enough to be acquired or by fitting template spectra on the supernova spectrum when the host galaxy is too faint. Thanks to the regular time sampling of the imaging survey, it is possible to estimate in advance the moment of maximum luminosity and spectrum can be acquired as near as possible to the maximum in order to minimize the exposure time. In spite of this advantage, supernova spectroscopy requires a very large amount of observing time and observations have to be carried out over several telescopes: Keck, Gemini North and South and VLT (a Large Programme has been allocated on FORS1, 240 hours spread over 4 semesters). It is important to note that the spectroscopy survey defines the fiducial volume of the final supernova sample. Even if the imaging survey is able to detect type Ia supernovae beyond a redshift of 0.9, spectroscopy of distant The supernova program of the CFHTLS 73 w -0.5 CFHTLS alone no prior -0.55 -0.6 CFHTLS with σ(ΩM)=0.03 CFHTLS with σ(ΩM)=0.015 -0.65 -0.7 -0.75 -0.8 -0.85 -0.9 -0.95 -1 0 0.2 0.4 ΩM 0 0.2 0.4 ΩM 0 0.2 0.4 ΩM Fig. 1. One, two and three σ(ΩM , w) joint contours (39, 86 and 99% CL) for: Left The full 5 years CFHT Legacy Survey statistics plus 200 nearby objects with no prior on ΩM ; Center With a prior on ΩM of 0.03; Right With a prior on ΩM of 0.015. The values assumed for the cosmological parameters are ΩM = 0.3, w = 1 and a flat Universe. Table 2. Expected number of supernovae in the four 1 square degree fields of the CFHTLS, in five years of observation. Unlike distant type Ia rates which are now known within about ∼20% precision, core collapse supernova rates are very uncertain and likely to increase with redshift. Redshift 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Total Number of SN Ia - 45 65 80 100 110 120 125 645 Number of SN Ib/c+SN II 50 110 150 180 - 490 objects is very time consuming and it is necessary to limit the sample to a redshift of about 0.9. 2.4 Achievable precision Recent measurements indicate a total explosion rate of about 100 type Ia supernovae per square degree per year, up to z = 1.0 [7]. For core collapse type supernovae, current observations show that about 1 type II or Ib/c supernova is detected for 10 type Ia supernovae. This is mostly due to the fact that although core collapse supernovae are about 5 times more numerous, they are much fainter than type Ia and usually embedded in their host galaxy with a lower contrast. Table 2 gives the expected number of monitored supernovae, including observational setup and quality cuts. About 700 type Ia supernovae will be entered in the Hubble diagram after the 5 years of the survey. The accessible constraints in the space of cosmological parameters are displayed in Fig. 1: w can be measured with a precision of about 0.1 if ΩM is known to 0.03 (i.e. 10 %). Thanks to the high statistics, statistical errors will be small and it will be possible to better understand systematic errors. For example, it will become 74 Stéphane Basa, on behalf of the SNLS collaboration possible to gather on average 100 objects per redshift bin of 0.1. This allows the study of samples in redshift bins, by populating the brightness, declinerate and color 3-dimensional parameter space, in order to detect possible drifts in “type Ia demography” and to avoid biases of the average distance in each bin. The size of the sample even allows the correlation of photometric and spectroscopic features and may lead to an improvement of the distance estimator. 3 CFHTLS pre-survey and conclusion During the engineering pre-survey of the CFHTLS which was organized between March and July 2003, it has been possible to test in real conditions the overall system: photometric discovery, spectroscopic identification and photometric follow-up. Several supernovae have been discovered and announced to the community (8147, 8148 and 8149 IAU circulars). The measured rates are within the expectations. Results are accessible from the collaboration web page [12]. The supernova program of the CFHT will produce an unprecedented sample of well measured supernova light curves, on a single and well monitored instrument. It will measure the parameter w of the Dark Energy equation of state with a precision of about 10% and allow a better understanding of the systematic uncertainties. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Alard C. and Lupton R.H., 1998, ApJ 325, 503. CFHTLS home page: http://www.cfht.hawaii.edu/Science/CFHLS/ ESSENCE home page: http://www.ctio.noao.edu/essence/ Garnavich et al., 1998, ApJ 509, 74. LOSS home page: http://astron.berkeley.edu/ bait/kait.html NEXUS: home page:http://cfa-www.harvard.edu/cfa/oir/Research/supernova.html Pain, R. et al. 2002, ApJ 577, 120. Perlmutter.S et al., 1999, ApJ 517, 565. Riess A.G. et al., 1996, ApJ 88, 473. Riess A.G. et al., 1998, ApJ 116, 1009. SNIF home page: http://snfactory.in2p3.fr/ SNLS home page: http://snls.in2p3.fr/ Hostless - or Just Very Faint? Lisa M. Germany1 and L.-G Strolger2 1 2 European Southern Observatory, Casilla 19001, Santiago, Chile lgermany@eso.org Space Telescope Science Institute, 3700 San Martin Drive, Baltimore MD 21218 strolger@stsci.edu Summary. Is it possible to have a supernova explode outside of a galaxy? There is some evidence that suggests this could happen. Here we present the results of a deep VLT imaging project to discover the underlying galaxies of selected “hostless” SNe. 1 Introduction There have been several supernovae (SNe) discovered during the course of nearby surveys, for which a host galaxy was not visible down to the search detection limits. In many cases, the underlying host galaxy does exist, but is an intrinsically faint dwarf galaxy whose compact central region can be as faint as MRc ≥ −14. This being said, it is still possible that truly “hostless” SNe do exist, in particular in cluster environments as a result of the tidal disruption of cluster galaxies. Gal-Yam et al. [1] have presented convincing evidence for two such SNe, discovered while searching rich, northern Abell Clusters. Discovery of these and other hostless SNe may be used to confirm and provide information on intergalactic stellar populations. In 2002 we undertook a deep imaging project with the VLT to recover the host galaxies of a sample of nearby (z ≤ 0.1) SNe reported as having faint or absent hosts. These SNe came from both cluster and field environments. In all cases except that of SN 2000cd (see Section 4), we recovered a host galaxy. Here we present the three most interesting SNe in our sample. 2 SN 1998bt Discovered by the Mount Stromlo Abell Cluster Supernova Search [4], deep VLT imaging revealed a faint host galaxy with MR = −12.6 ± 0.9. If we assume this SN is at the redshift of the targeted Abell Cluster (we did not manage to get a spectrum of the SN), it had a peak magnitude and light curve 76 Lisa M. Germany and L.-G Strolger morphology similar to that of SN 1987A [5]. Figure 1 shows a preliminary comparison of the light curves of these two SNe. To unequivocally decide whether the light curves of SN 1998bt and SN 1987A are similar, we need to obtain a spectrum of this faint host galaxy in order to accurately determine its redshift. This would be the first port of call for further research into this particular SN. SN 1998bt SN 1987A Fig. 1. Preliminary comparison suggests that SN 1998bt could be similar to SN 1987A, if indeed it falls at the redshift of the targeted cluster. 3 SN 1999aw Discovered as part of the Nearby Galaxies Supernova Search (NGSS), SN 1999aw was a luminous, slow-declining, type Ia SN with no visible host galaxy [6]. Subsequent deep imaging with Magellan and VLT did reveal a low luminosity host with MB = −12.2 ± 0.2 MV = −12.5 ± 0.2 MR = −12.6 ± 0.2 Hostless - or Just Very Faint? 77 MI = −12.2 ± 0.9 This makes the host galaxy fairly blue in comparison to dwarf galaxies in the local group and supports the studies of Ivanov, Hamuy & Pinto [3] and Hamuy et al. [2] which show that • late type galaxies tend to produce bright, slow-declining SNIa • bright SNIa occur more frequently in bluer environments • bright SNIa occur more frequently in less luminous galaxies However, as they point out, it is difficult to disentangle how these colorluminosity correlations relate to age and metallicity effects. 16.5 17 17 17.5 18 18 18.5 19 19 R (Vega) 19.5 20 20 20 40 60 80 100 120 140 160 180 200 16.6 21 16.8 17 22 17.2 17.4 23 24 17.6 SN 2000cd Type II-L Template Type II-P Template 1 17.8 10 100 Log (days) 1000 18 5 10 15 20 25 Days Fig. 2. Comparison of the evolution of SN 2000cd R-band light curve, and those of normal Type II SNe. 4 SN 2000cd SN 2000cd was an apparently hostless, narrow line type II SN (SNII-n) also discovered as part of the NGSS. Deep VLT imaging of the SN field 2 years 30 35 40 78 Lisa M. Germany and L.-G Strolger after the event did not reveal a host galaxy, but rather the SN itself! This imaging has still not uncovered an obvious host galaxy, although it has shown that there are several faint galaxies within a ∼ 10 − 20 arcsecond radius. We currently estimate an upper limit of MR < −14 for the host galaxy, if one exists. 17 18 R (Vega) 19 20 21 22 23 24 SN 2000cd SN 1988Z Fit 1 10 100 1000 Log (days) Fig. 3. R-band points for SN 2000cd and SN 1988Z shifted to match the end of their respective plateau phases. The SN is still clearly visible in recent images, 3 years after explosion, and light curve fitting has shown that it is ∼ 2 − 3 magnitudes brighter than expected for a ”typical” type II SN (Plateau or Linear) at its current epoch (Figure 2). This behavior is reminiscent of another SNII-n, SN 1988Z. Figure 3 plots the R-band light curves of SN 1988Z shifted by 200+ days from its discovery, and SN 2000cd. The best-fit light curve supports the idea that SN 2000cd is a SN 1988Z-like SN discovered ∼ 200 days prior to the end of its long plateau phase in the R-band. This is also supported by comparing the spectra of the two SNe. Early spectra of SN 2000cd and SN 1988Z are dominated by a multi-component Hα emission on a nearly featureless continuum. Recent spectra of SN 2000cd continue to be dominated by this Hα emission while the continuum remains featureless, indicating that although it has been 1000+ days since discovery, SN 2000cd has not yet begun its nebular phase. Hostless - or Just Very Faint? 79 Based on observations of other SNII-n, we expect SN 2000cd to soon enter its nebular phase, and have been awarded VLT time for another epoch of observations in March 2004. If the SN is no longer visible at this time, we may yet be able to uncover an underlying host galaxy. 5 Summary Although there is compelling evidence for the existence of hostless SNe in clusters, this project to investigate the environments of apparently hostless SNe has detected an obvious underlying galaxy in all cases except one. In this particular case, the SN itself is still visible and is potentially swamping any light we might get from a faint host galaxy. Alternatively, the SN may be associated with any one of a number of faint galaxies within a radius of few arcminutes. Although we did not find more examples of truly hostless SNe, the existence of low luminosity host galaxies is interesting in its own right, since it is not clear how such a low density environment can produce a massive progenitor star. It is only with further photometric investigation of these lowluminosity hosts that we will better understand the star formation histories of dwarf galaxies and the progenitors of SNe. References 1. 2. 3. 4. 5. 6. A. Gal-Yam et al: AJ 125, 1087 (2003) M. Hamuy et al: AJ 120, 1479 (2000) V. Ivanov, M. Hamuy & P. Pinto: ApJ 542, 588 (2000) D. Reiss et al: AJ 115, 26 (1998) D. Reiss et al: in preparation L. Strolger et al: AJ 124, 2907 (2002) High-Resolution Optical Studies of Nearby Type Ia Supernovae Peter Lundqvist1 , Seppo Mattila1 , Jesper Sollerman1 , E. Baron2 , Pascale Ehrenfreund3 , Claes Fransson1 , Bruno Leibundgut4 , and Ken’ichi Nomoto5 1 2 3 4 5 Stockholm Observatory, AlbaNova, Department of Astronomy, SE-106 91 Stockholm, Sweden peter@astro.su.se Department of Physics and Astronomy, University of Oklahoma, Norman OK 73019-0225, USA Leiden Observatory, P.O. Box 9513, 2300 RA Leiden, Netherlands European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching bei München, Germany Department of Astronomy and the Research Center for the Early Universe, University of Tokyo, Tokyo 113-0033, Japan Summary. Since April 2000, a program using the ESO/VLT/UVES6 to search for early circumstellar signatures from nearby supernovae has been conducted.7 Until now, two Type Ia supernovae have been observed, SNe 2000cx and 2001el. Here we report on preliminary results for SNe 2001el, and we discuss how the observations can be used together with detailed modeling to derive an upper limit on the putative wind from the progenitor system. For a hydrogen-rich wind with velocity 10 km s−1 , −5 −1 the mass loss rate for the progenitor system of SN 2001el is Ṁ < ∼ 1 × 10 M yr . 1 Introduction The origin of Type Ia supernovae (SNe Ia) is still unclear. Branch et al. [3] list possible types of systems, and argue that the most likely system is a C-O white dwarf which accretes matter from the companion, either through Roche lobe overflow, or as a merger with another C-O white dwarf. We need methods to discriminate between the possible progenitor scenarios. In nonmerging scenarios a wind from the companion star is expected. If the wind is ionized and dense enough, it could reveal itself in the form of narrow lines before being overtaken by the supernova blast wave, just as in narrow-line core-collapse supernovae, SNe IIn. For a hydrogen-rich wind, Hα would be 6 7 Based on observations collected at the European Southern Observatory, Paranal, Chile. Program ID 67.D-0227(A). See http://www.astro.su.se/∼peter/sntoo.html. In collaboration with the SN Ia RTN team (PI: W. Hillebrandt), see http://www.mpa-garching.mpg.de/∼rtn 82 P. Lundqvist et al. emitted, and if helium dominates He I λλ5876, 10830 and He II λ4686 may be prominent. A pioneering observational and theoretical study of circumstellar line emission in SNe Ia was that of SN 1994D [6, 10]. The spectrum was obtained ∼ 6.5 days after explosion with a spectral resolution of ∼ 30 km s−1 , and covered Hα. The analysis of the non-detection involved full time-dependent photoionization calculations to estimate the narrow Hα emission from the tentative wind. The analysis in [10] gave an upper limit on the mass loss from the −5 −1 progenitor system of Ṁ < ∼ 2.5 × 10 M yr , assuming cosmic abundances for the wind, and a wind speed of vw = 10 km s−1 . More recently, Lundqvist et al. [12] studied SN 2000cx with the Ultraviolet and Visual Echelle Spectrograph (UVES) on ESO’s Very Large Telescope (VLT). The spectral resolution of UVES is ≈ 50, 000, i.e., 6 km s−1 in the region of Na I D and Hα. The preliminary upper limit on the mass loss rate from the progenitor system is −6 −1 −1 Ṁ < ∼ 9 × 10 M yr for vw = 10 km s . Here we report on the second of our SNe Ia observed with VLT/UVES, SN 2001el. 2 Observations and Results SN 2001el was discovered on September 17.1 2001 [13]. It was situated 9” west and 15” north of the nucleus of the nearby (recession velocity vrec = 1164 km s−1 ) galaxy NGC 1448. SN 2001el was observed as part of our VLT/UVES Target-of-Opportunity (ToO) program on September 21. This spectrum had a complete wavelength coverage between 3260 − 10600 Å and allowed a classification of the supernova as a Type Ia observed well before maximum [15]. SN 2001el was also observed on September 26, and then revisited for the last time on September 28. Our UVES observations were thus obtained 9, 4 and 2 days before the supernova B-band maximum light [8]. The lines expected from a hydrogen- or helium-rich companion wind were sought for in the SN spectra at the three epochs of observation at the expected range of wavelengths assuming vrec = (1180 ± 300) km s−1 for the supernova. No such lines were detected, and therefore upper limits for the emission line fluxes and absorption line equivalent widths were derived. This was done by fitting Gaussian profiles with fixed FWHMs at fixed positions within the expected range of wavelengths in the unbinned spectra. The 1σ levels for the emission line fluxes and absorption line equivalent widths were then obtained by requiring 68.3 % of the measured line fluxes (or equivalent widths) to be below this level. Adopting an extinction of AV = 0.83, a distance of d = 18 Mpc for SN 2001el and assuming that the line has a FWHM of 10 km s−1 (see Mattila et al. in prep.), we obtain an upper limit for the Hα narrow line-luminosity of LHα = 3.2 × 1036 ergs s−1 in our third epoch (Sep 28.3 UT) spectrum. To reach this limit, we performed a careful background subtraction of the host galaxy emission. This was done manually outside the UVES pipeline. High-Resolution Optical Studies of Nearby Type Ia Supernovae 83 Fig. 1. Normalized third epoch (Sep 28.3 UT) spectrum of SN 2001el showing the region around the expected wavelength range of Hα (marked with a horizontal dashed line). The lower and uppermost plots, respectively, show the SN spectrum before and after including simulated 3σ features with a Gaussian profile and FWHM of 6 km s−1 . The locations of these features at 6584.6 Å (emission), 6590.2 Å (absorption), 6593.0 Å (emission), and 6594.7 Å (absorption) are marked with vertical lines. The spectra have been rebinned by a factor of 2, and thus have a pixel size of ∼1.6 km s−1 . The uppermost spectrum has been moved upward for clarity. Figure 1 shows examples of artificially introduced unresolved emission and absorption lines at the 3σ level. These lines with FWHM = 6 km s−1 were simulated at the expected wavelength range of Hα in the unbinned third epoch UVES spectrum. The spectrum was then rebinned by a factor of 2 resulting in a pixel size of ∼ 14 × FWHM in the rebinned spectrum. The simulation parameter for the line peak was selected for each line such that the measured apparent flux of the line corresponds to the 3σ level. No features with fluxes (or equivalent widths for the absorption lines) as high as the ones of the simulated lines are apparent in the real data. 3 Modeling and Discussion We have modeled the line emission in a way similar to what was done in [6, 10, 12]. We assume that the supernova ejecta have a density profile of ρej ∝ r −7 , and that the ejecta interact with the wind of a binary companion which has a density profile of ρw ∝ r −2 . The power-law density distributions makes it possible to use similarity solutions for the expansion and structure of the interaction region [4]. Calculations are started at t0 = 1.0 day, and at this 84 P. Lundqvist et al. Fig. 2. Hα luminosity at 18 days after the explosion as a function of mass loss rate, assuming vw = 10 km s−1 and cosmic abundances. Triangles show models for which ionizing radiation is only produced by the reverse shock, while in models marked by squares we have also included the photospheric emission from the model w7jzl155.ph [2]. Filled symbols are for temperature equipartition between electrons and ions behind the reverse shock, whereas for open symbols the electron temperature is 12 × the reverse shock temperature. The observed limit for SN 2001el, ‘18 Mpc, AV = 0.83’, is also shown. epoch we assume that the maximum velocity of the ejecta is Vej = 4.5 × 104 km s−1 . At 1 day, the velocities of the circumstellar shock and the reverse shock going into the ejecta are Vs ∼ 4.5 × 104 km s−1 and Vrev ∼ 1.1 × 104 km s−1 , respectively. The ionizing radiation from the interaction region consists of free-free emission from the shocked ejecta and circumstellar gas, and photospheric radiation [1, 2, 12] Comptonized by hot electrons in the shocked gas. To model the time dependent ionization and temperature structure of the unshocked circumstellar gas we use an updated version of the code used in [6, 11, 12]. Models were made for values of Ṁ in the range (1 − 300) × 10−7 M yr−1 , assuming vw = 10 km s−1 . For low mass loss rates, the photospheric radiation dominates the ionization, and its soft photons heat the wind to temperatures −6 −1 in the range (0.5−5)×104 K, whereas for Ṁ > ∼ 5×10 M yr , the ionizing radiation from the reverse shock becomes more important, heating the wind 4 close to the shock to > ∼ 7 × 10 K. Figure 2 shows the line emission produced in models with different wind densities. Using our derived limits on the Hα luminosity for SN 2001el at the third epoch, we obtain (for cosmic abundances and vw = 10 km s−1 ) a wind density described by Ṁ ∼ 1×10−5 M yr−1 , i.e., High-Resolution Optical Studies of Nearby Type Ia Supernovae 85 similar to our limit for SN 2000cx [12]. Such a low limit for the circumstellar gas, as well as other similar limits in the radio and X-rays for other SNe Ia (cf. Ref. [12]), contrasts the recently reported strong Balmer line emission from the SN Ia 2002ic by Hamuy et al. [7]. The observations of SN 2002ic have been used both in favor [9] and against [5] a merger scenario. While the true nature of SN 2002ic is still under debate, detection of early, faint circumstellar line emission in a SN Ia, with temporal variation in the line profiles, would be stronger evidence for a non-merger scenario. Finally, we note that the mass loss rate in symbiotic systems is in the range 10−7 − 2 × 10−5 M yr−1 [14]. Our results do not support that systems at the upper end of this interval are progenitors of normal SNe Ia. Acknowledgement. This work was supported by the Swedish Research Council, the Swedish Space Board, the Royal Swedish Academy of Sciences, and the EU RTN program RTN2-2001-00037. PL is a Research Fellow at the Royal Swedish Academy supported by a grant from the Wallenberg Foundation. References 1. S.I. Blinnikov, E. Sorokina: A&A 356, L30 (2000) 2. S.I. Blinnikov, E.I. Sorokina: ‘Prospects of investigations of thermonuclear supernovae in far UV’ (in Russian). 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Lundqvist, J. Sollerman, E. Baron, et al.: ‘Constraining Circumstellar Matter in SN Ia - High-Resolution Optical Studies with VLT/UVES’. In: From Twilight to Highlight: The Physics of Supernovae, ed. by W. Hillebrandt, B. Leibundgut (Berlin, Springer 2003) pp. 309–314 13. A.G. Monard: IAU Circ., 7721 (2001) 14. E.R. Seaquist, M. Krogulec, A.R. Taylor: ApJ 419, 260 (1993) 15. J. Sollerman, B. Leibundgut, P. Lundqvist: IAU Circ., 7723 (2001) Supernova Counts in Deep HST Fields Keren Sharon, Avishay Gal-Yam and Dan Maoz1 School of Physics and Astronomy, Tel Aviv University, Israel kerens@wise.tau.ac.il Summary. We have searched for high-redshift supernova candidates in multiple, deep Hubble Space Telescope (HST) archival images of nine galaxy clusters, and in the Groth Survey Strip (GSS). We detect ten apparent SNe, with 21.6 ≤ I814 ≤ 28.4 mag, in a total area of ∼ 270 arcmin2 . Of the six SNe discovered in the galaxycluster sample, two are associated with cluster galaxies (at redshifts z = 0.18 and z = 0.83), three are probably in galaxies not in the clusters (at z = 0.49, z = 0.60, and z = 0.98), and one is at unknown z. Three of the four SN candidates discovered in the GSS are also at unknown redshifts, and one is possibly at z = 1.45. After accounting for observational efficiencies and uncertainties (statistical and systematic) we compare our observed counts of field SNe (i.e., non-cluster SNe of all types) to recent model predictions. The observed field count is N ≤ 3 SN with I814 ≤ 26 mag, and 5 ≤ N ≤ 7 SNe with I814 ≤ 27 mag. These counts rule out one model, and are only marginally consistent with another. Since the counts at these magnitudes are likely dominated by type-II SNe, our observations suggest obscuration of distant SNe-II, or a SN-II luminosity distribution devoid of a large high-luminosity tail. 1 Data acquisition and analysis We have searched the HST archive for duplicate WFPC2 observations. For two WFPC2 observations to be considered duplicates, we required that the images had been obtained through the same filter, with angular distance of less than 75 arcsec between field centers, minimal time separation of 30 days, and total exposure times of at least 2000 s. We also required that at least one of the duplicate data sets consist of at least three sub-exposures, in order to facilitate reasonable rejection of cosmic rays and hot pixels. When both duplicate data sets had three or more sub-exposures, we searched for candidate variable objects in both. In cases where only one of the data sets was suitably split, the other set was used only as a reference, since the possibility of cosmic ray events mimicking transient objects could not be ruled out. 88 K. Sharon et al. Sets of WFPC2 images at a given epoch were combined, registered, scaled and subtracted, forming a difference image. The stable HST point-spread function (PSF) allows for good cancelation of almost all non-variable objects. The difference images were methodically scanned by eye, and all residual objects checked and classified. For a candidate to be considered secure, we required that it have a stellar PSF, and appear in at least three independent subsets of the data, each consisting of the sum of individual exposures in which its location is not obviously affected by cosmic rays, with non-variable flux levels, to within errors. In practice, all but one of the transient sources we found can be identified on each individual exposure, and not only in summed subsets. We have carried out simulations in order to estimate our SN detection efficiencies. Several tens of artificial point sources (“fake” SNe) with known flux and the proper amount of Poisson noise were blindly added to the data for each field. The simulated data were reduced and searched for SNe, like the real data, and the fraction of recovered objects noted. The flux limit at each epoch depends on the length of the exposures and the filter used, and therefore varies between our sample fields, but in all sets the limit for > 50 per cent detection is better than I814 = 26 mag. 2 Results We have detected four SN candidates in the GSS data, and six apparent SNe in the cluster fields, including the rediscovery of SN 1996cl, which was previously known. For each SN, Table 1 lists the details, and Fig. 1 shows a section of the GSS images at two epochs (for a figure of the six SNe detected in the galaxy-cluster survey, see Fig. 1 of [3] in this volume). Among the ten SNe, eight are projected within 2.5 half-light radii of galaxies that are likely their hosts, while two have no obvious host. We have been able to determine the redshift and types of the host galaxies of five or six events from the literature. Two events in the cluster sample are associated with cluster galaxies. 3 Comparison with theoretical predictions We compare the numbers and magnitudes of the non-cluster (i.e., background or foreground) SNe we have found to predictions of field-SN number counts, published by Sullivan et al. [4] (hereafter S2000), and by Dahlén & Fransson [1] (hereafter DF), in order to provide some initial constraints on these models. Given a predicted SN surface density on the sky ([4], [1]), we can calculate the expected number of SNe in our observed sample. The predicted SN count per magnitude interval, dm, per observed field is the surface density per magnitude interval, np (m)dm, times the effective area, times the search efficiency η(m), with the latter modified by a color term for data sets that were not Supernova Counts in Deep HST Fields 89 Table 1. Apparent Supernovae SN Field Magnitude Host z 1999gv 1996cl 1996cq 1996cp 1995bf 1994ao 1994 2001 2001 1994 Abell 2218 MS1054.4−0321 MS1054.4−0321 MS1054.4−0321 CL1604+4304 CL1604+4304 GSS GSS GSS GSS V606 = 21.64 ± 0.03 I814 = 23.71 ± 0.04 I814 = 25.61 ± 0.05 I814 = 26.7 ± 0.2 I814 = 26.14 ± 0.06 I814 = 28.4 ± 0.5 V606 = 24.57 ± 0.05 V606 = 25.5 ± 0.1 V606 = 26.5 ± 0.2 V606 = 26.7 ± 0.2 0.175, cluster event 0.827, cluster event ? 0.596a 0.985 0.496 1.45(?)b Notes: a Other host galaxies possible, see [2] b Photometric redshift Fig. 1. Sections of the images, at two epochs, for each of the four apparent SN candidates in the GSS. The scales shown in the upper-left-hand corners correspond to 1 . See Fig. 1 of [3] in this volume, for a figure of six SNe detected in the galaxycluster survey. observed in the I band: n(m)dm = np (m) × S × η(m, band) dm. The total SN counts expected per field to a given limiting magnitude can be obtained by integrating this equation over m. The cumulative number of SNe predicted to a limiting magnitude, is plotted in Fig. 2. The counts predicted by S2000 are significantly higher than the observed values, and can be ruled out. However, the predictions of DF are marginally consistent with the observations. We note that some of the events we counted as field events in the cluster sample (SNe 1996cp and 1996cq, for which the 90 K. Sharon et al. 30 Predicted(S2000) Predicted(DF) Found Cumulative no. of SNe 25 20 15 10 5 99% CL 95% CL 90% CL 0 23 23.5 24 24.5 25 25.5 Magnitude 26 26.5 27 27.5 28 Fig. 2. Cumulative number of SNe to limiting magnitude. Predictions of DF and S2000 are plotted in dashed line and squares respectively. The shaded areas represent 90%, 95% and 99% confidence levels of the observed numbers of SNe (solid line). redshift is uncertain), may have been cluster events after all. In this case, the difference between the prediction of DF and the data becomes statistically significant as well. Finally, our adopted efficiency values are likely underestimates, leading to too-low predictions. The bulk of the discrepancy between the predictions of S2000 and DF stems from two subtle differences in the treatment of type-II SNe, for which S2000 predict ∼ 2 times more counts than DF. First, S2000 use a larger value for the dispersion of peak absolute magnitudes of type II-L SNe (σ = 1.3 mag), which results in a high-luminosity tail of type II-L SNe, a large number of which will be visible in a flux-limited SN search. Second, S2000 adopted a constant dust extinction value for all type-II SNe, of AV = 0.45 mag, equivalent to AB = 0.66 mag. DF used a minimum extinction value of AB = 0.32 mag, but modified it according to a random orientation of the host galaxy. This produced a large extinction for nearly edge-on hosts. This again, makes DF’s SNe fainter than those of S2000, and the total predicted numbers lower. Returning to our observational results, it appears that the combined assumptions of DF for the type-II SN peak magnitudes, dispersions, and dust Supernova Counts in Deep HST Fields 91 extinctions are definitely a better description of the high−z SN population than those used by S2000. Of course, other variations on these assumptions can be devised, which may better fit the observed counts. Furthermore, some of the assumptions that are common to the models of both DF and S2000 could also be wrong, but counterbalanced by wrong SN-II parameters. With improved knowledge of the relative fraction of different SN types, their luminosity functions, and their spectra, the observed SN counts will be able to constrain some of the other parameters, such as the extinction of core-collapse SNe at high redshift. 4 Future work This work shows that useful limits on high-z SN counts can be derived from repeated, deep HST imaging, even without any follow-up observations. Obviously, similar analyses of larger datasets such as the GOODS HST Treasury program, would yield SN counts with higher precision. We will analyze this and other new datasets in order to extend and improve the results obtained in the present work. Planned observations (rather than an archival search) would enable followup work that would reduce the systematic errors, and enable accurate determination of the SN types. In light of the discrepancy between recent models and our observations, it is desirable to re-calculate the theoretical predictions using additional information on the parameters that has recently become available. It would also be interesting to test the effects of varying these parameters (e.g., the relative fractions and lightcurve distribution of sub-types of SNe within the SN population, the amount of obscuration by dust at high redshifts) that are currently unknown, in order to constrain them by observations. References 1. Dahlén, T. & Fransson, C. 1999, A&A, 350, 349 (DF) 2. Gal-Yam, A., Maoz, D., & Sharon, K. 2002, MNRAS, 332, 37 3. Gal-Yam, A., Maoz, D., Sharon, K., Prada, F., Guhathakurta, P., & Filippenko, A. V.: In: These proceedings. 4. Sullivan, M., Ellis, R., Nugent, P., Smail, I., & Madau, P. 2000, MNRAS, 319, 549 (S2000) Part III Supernovae: Models Wave Modes in Collapsar Jets Enrique A. Gómez and Philip E. Hardee Department of Physics and Astronomy University of Alabama Box 870324, Tuscaloosa, AL 35487-0324. USA. enrique.gomez@ua.edu, hardee@athena.astr.ua.edu Summary. Collapsars may be a source for the “long” Gamma Ray Bursts (GRBs) in the BATSE catalog. Collapsars may radiate gamma rays anisotropically by beamed jet emission close to the observer’s line of sight. These jets must penetrate the radiation-dominated medium of their collapsar progenitor and break through its atmosphere in order to produce a GRB. We present a study of previously published, axisymmetric, collapsar jet simulations. Here we use the linearized, relativistic fluid equations to find the Kelvin-Helmholtz modes that are triggered by recollimnation shocks within the jet. The modes will grow as they propagate with the jet. These are of interest since the light curves of GRBs show evidence of a variable flow from the GRB engine. We also evaluate effects of grid scaling in the numerical simulation and show that short wavelength modes are suppressed by grid scaling before the jet breaks out of the Helium shell. 1 Introduction The close association between GRB030329 and SN2003dh proves that a subset of “long” GRBs is associated with core collapse supernovae [1,2]. The light curve of GRB030329 steepens over time. Price et al. [3] interpret this as a broadening of a jet-like outflow from the GRB source. Multiwavelength observations by Uemura et al. [4] along with those from GRB021004 [5] strengthen the case for a variable jet outflow from the central engine. These observations support the prompt (Type I) collapsar model of GRBs [6,7]. In this model, a progenitor star with mass > 30 M fails to eject its envelope after the core collapses into a black hole. Accretion of free falling material may drive a relativistic jet of gas that may break through the stellar envelope. At issue is whether hydrodynamic instabilities within the jet will grow so that the radial profile of jet velocity becomes time and space dependent. Such information could offer insight into the production of gamma rays as well as prompt optical afterglows of GRBs. 96 Enrique A. Gómez and Philip E. Hardee 2 Dispersion Relations for Collapsar Jets Analyses of collapsar jet models have shown that the jet is unstable as it propagates through its progenitors atmosphere. Axisymmetric, relativistic hydrodynamic simulations by Aloy et al. (2000) [8] show evidence of pinch-body modes triggered by recollimnation shocks. We studied the simulations that Aloy et al. (2000) [8] made using the author’s GENESIS code. In the radial direction, the energy deposition region extends from the inner grid boundary located at 200 km to a radius of 600 km (2-6 x 107 cm) . We studied two of their jets with constant energy deposition rates of dE/dt = 1050 (C50) and 1051 ergs s−1 (C51). Our approach to analyzing the space-dependent structures is to use the linearized relativistic fluid equations to find the Kelvin-Helmholtz modes that may be triggered by recollimnation shocks within the jet. Space-dependent perturbations propagate with a dispersion relation given in the appendix of Hardee, Clarke & Rosen (1997) [9]. This dispersion relation assumes uniform conditions inside and outside a jet with sharp discontinuity at the jet surface. The jets in the simulations have velocity profiles in the transverse direction. In order to identify modes in the simulation we must determine typical sound speeds in the jet and the external medium. To calculate the value of the relevant parameters in the jet and the external medium, we define the jet ∗ ∗ radius Rj wherever Γ vr /c = 0.5Γ vr /c. Here vr is the radial velocity, Γ = 2 2 1/ 1 − vr /c is the Lorentz factor, vr∗ is the maximum value for the jet velocity at a given cross section and Γ ∗ the corresponding Lorentz value. Figure 1 shows the angular cross sections of pressure, density and velocity for the jet C50 near its base and near the head of the jet. We calculate the weighted average for jet speed and sound speed in the region R ≤ Rj and sound speed in the interval Rj ≤ R ≤ 3Rj . The local sound speed for a relativistic gas is defined by as ≡ p γ ρ + [ γ /( γ − 1)]p/c2 12 (1) where γ is the adiabatic index (4/3 for a relativistic gas), p is the pressure, ρ is the density, and c is the speed of light. From the average of the jet speed typical values of Γ range from 1-5; however, the C51 jet late in the evolution near the jet head reaches a Γ ∼ 20. 3 The Stages of Jet Evolution We identify two distinct stages of jet evolution: downstream from the inlet and upstream from the breakout. The inlet region corresponds to where the jet is Wave Modes in Collapsar Jets model 50 3.35s r = 6.5 x 108 cm 1024 1022 model 50 3.35s r = 1.3 x 1010 cm 1020 1020 1019 ρ x 1018 1018 1022 1021 P P 97 ρ x 10 1018 18 1016 1017 1016 5 1014 4 Γvr/c 3 4 Γvr/c 2 3 vr/c 1 2 vr/c as/c 0 1 as/c -1 0 5 10 degrees 15 20 2 4 degrees 6 8 0 10 Fig. 1. Cross sections for pressure P, density ρ, velocity vr , and sound speed as for the C50 jet at t=3.35s for cuts near the base and the jet head. Black vertical lines identify the defined jet radius, Rj . injected. In the C50 jet simulation at time t=3.35 s, we can study the stability downstream from the inlet near its base (r ∼ 108 cm). Breakout through the Helium shell of the progenitor occurs at r ∼ 1011 cm. Here the stability can be studied in the region immediately upstream from the jet head (r ∼ 1010cm). The dynamics of these two regions are comparable to the same jet at a later time and for the C51 simulation. Figure 2 shows the result of our stability analysis for these two regions with our calculated values for normalized wavelength and frequency for the fundamental, 1st, 2nd, and 3rd pinch body modes. Once the jet has penetrated the He shell, it enters a hydrogen medium where it will be over pressured. The jet will √expand adiabatically in the perpendicular direction to the jet axis at c/ 3 in the reference frame of the fluid [10,11]. Recollimnation shocks below the He-H boundary shell destroy all upstream perturbations. At the same time they can trigger pinch modes downstream. We are most interested in perturbations just upstream of the jet head after it has crossed the He layer at 1011 cm. It is at this point that the jet becomes a causally disconnected wind where density and velocity perturbations “freeze” in the base of the wind. 98 Enrique A. Gómez and Philip E. Hardee model C50 3.35s 2.0 10.00 (p/p0 ) (p/p0 ) 1.5 1.0 1.00 0.5 0.10 0.01 0.05 0.0 0.05 vθ/c 0.00 -0.05 -0.05 -0.10 -0.15 5 4 3 2 1 0 -0.15 15 Γvr/c -0.10 Γvr/c vθ/c 0.00 2•108 1.000 0.100 4•108 6•108 8•108 x (cm) 1•109 Pinch Modes 5 0 1.000 B2 re B1 re B2 im B3 im SO re B1 im 0.010 0.001 0.01 10 10.000 C50 3.35s, r=6e8 cm B3 re kRj 10.000 kRj model C50 3.35s 1000.00 100.00 ωRj/u 1.00 1.0•1010 x (cm) 10.00 0.001 0.01 1.5•1010 2.0•1010 Pinch Modes C50 3.35s, r=1.3e10 cm B3 re B2 re B1 re B2 im SO re B1 im B3 im SO im 0.010 SO im 0.10 0.100 5.0•109 0.10 ωRj/u 1.00 10.00 Fig. 2. Top row diagram shows cuts for the C50 jet at t=3.35 seconds for the jet close to the base (6.5 x 108 cm) and for the jet close to the head (1.3 x 1010 cm). Cuts are for the angles 0.25◦ , 1.125◦ , 2.25◦ and 3.25◦ (solid, long dash, short dash, and dash-dot, correspondingly). On the bottom row diagrams show the fundamental (SO), 1st, 2nd, and 3rd pinch body modes (B1, B2, B3). These are the real and imaginary solutions for these regions. 4 Conclusion We solved the dispersion relations in Hardee, Clarke, & Rosen 1997 [9] for k(ω) with the appropriate parameters from each cut of the jets. We found the solutions for the fundamental and the first three body modes for both jets. Figure 2 shows the solutions for C50 just downstream from the inlet and upstream from breakout at t=3.35s. We compute the wavelengths at ∗ ∗ the maximum growth rate λ∗ = 2πvw /ω∗ (where vw and ω∗ are the wave speed and frequency at maximum growth) and the minimum growth length ∗ = (kI∗ )−1 (where kI∗ is the imaginary wave number). The growth time τ = /vw for any given solution is calculated from, vw = ωkR + kI2 2 kR (2) Wave Modes in Collapsar Jets 99 where kR is the real wave number. We find that our solutions depend on the distance from the inlet r. The range for maximum growth wavelength λ∗ for the body modes near the jet inlet is 0.1r to r, and the range upstream from breakout is 0.06r to 0.6r. The range for the growth length ∗ is 0.5r to r near the inlet, and for near breakout the range is 0.2r to 2r. Near breakout the growth time τ ranges from 0.3 r/c to 3 r/c or 1 to 10 seconds at the distance of the He shell. Our numerical analysis of jet stability assumes a sharp lateral boundary between the jet and the external medium. The analytical approach of Aloy et al. (2002) [12] for the same jet assumes an extended shear layer. For Lorentz factors of order 10, they predict a growth time τ ∼ 0.01r/c which is one order of magnitude smaller than our method; however, the characteristic order of λ∗ ∼ 0.1r − 0.5r is also what we predict. One objective of our study was to find if there were wave modes that would not show up in the simulation because their length scale would be smaller than the computational grid scale. Aloy et al. (2000) use a logarithmic grid scaling so that the jet is better resolved at the base than at the head of the jet [8]. For the jet downstream from the inlet, grid scaling is ∼ 0.1 Rj and this is sufficient to resolve wave modes. Near the jet head the grid scaling is ∼ Rj and this can suppress the pinch body modes numerically. Since this region will be the most relevant to the evolution of the jet flow at breakout, simulations with greater grid resolution need to be done. Acknowledgement. E. A. G. wishes to acknowledge the funding of this study through the Alabama Space Grant Consortium project. The authors would like to thank Miguel Angel Aloy for his generosity in sharing his simulation results and his comments. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. J. Hjorth et al: Nature 423, 847 (2003) K. Z. Stanek et al: astro-ph/0304173, (2003) P. A. Price et al: Nature 423, 844 (2003) M. Uemura et al: Nature 423, 843 (2003) D. W. Fox et al: Nature 422, 284 (2003) S. E. Woosley: ApJ 405, 273 (1993) A. I. MacFadyen, & S. E. Woosley: ApJ 524, 262 (1999) M. A. Aloy et al: ApJ 531, L119 (2000) P. E. Hardee, D. A. Clarke, & A. Rosen: ApJ 485, 533 (1997) J. Granot et al: astro-ph/0103038 (2001) P. Mészáros, & M. J. Rees et al: ApJ 556, L37 (2001) M. A. Aloy et al: A&A 396, 693 (2002) Non-radial Instability of Stalled Accretion Shocks: Advective-Acoustic Cycle Thierry Foglizzo and Pascal Galletti Service d’Astrophysique, CEA/DSM/DAPNIA, CE-Saclay, 91191 Gif-sur-Yvette, France Summary. The linear stability of stalled accretion shocks is investigated in the context of core collapse of type II supernovae. We focus on a particular instability mechanism based on the coupling of acoustic perturbations with advected ones (vorticity, entropy). This advective-acoustic cycle takes place between the shock and the nascent neutron star. Both adiabatic and non-adiabatic processes may contribute to this coupling, but only adiabatic ones are considered in this first approach. The growth time of the adiabatic instability scales like the advection time, and is dominated by low degree modes l=0,1,2. Non radial modes (l=1,2) found unstable by Blondin et al. [1] can be related to this mechanism. 1 Introduction Shocked accretion onto the surface of a compact star is known to be unstable in the context of magnetized white dwarfs, leading to shock oscillations (from [2] to [3]). Houck & Chevalier [4] made a linear stability analysis of shocked accretion onto a neutron star, and found an instability reminiscent of the instability found by Langer et al. [2]. They showed specific cases where the cooling occurs mostly in a thin layer at the surface of the neutron star, while the flow is essentially adiabatic above it. The mechanism of the instability was described by Langer et al. and subsequent authors as a kind of thermal instability: if the shock surface is moving outwards, the higher incident velocity in the frame of the shock produces a higher temperature blob, which pushes the shock further out if the increased cooling time exceeds the increased advection time. This cycle, however, resembles the unstable adiabatic cycle described in the context of shocked spherical accretion onto a black hole ([5, 6, 7]). In this case the acoustic feedback is purely adiabatic and is due to the advection of vortical/entropic perturbations from the shock to the accretor. A similar coupling must also take place if the accretor is a neutron star. Is the instability found in [4] due to a cooling process, in the spirit of [2], or is there a significant contribution of the adiabatic coupling between vortical/entropic 102 Thierry Foglizzo and Pascal Galletti and acoustic perturbations ? The recent work of Blondin et al. [1] seems to support this second hypothesis. However, is the acoustic feedback identified in [1] linear or due to turbulence ? Understanding the physical mechanism underlying this instability could prove useful in order to evaluate its role when realistic non-adiabatic processes are taken into account. 2 The Perturbed Adiabatic Flow Viewed as a Forced Oscillator In order to distinguish between adiabatic processes and non adiabatic ones, the flow structure between the shock rsh and the surface of the nascent neutron star r is schematized as an adiabatic flow above a cooling layer rcool. The present study focuses on the stability of the adiabatic part of the flow rcool < r < rsh . The entropy and vorticity equations can be integrated explicitly as in [6]. The Rankine-Hugoniot conditions at the shock impose that entropy and vorticity perturbations δS, δw are simply related through: (δwr , δwθ , δwϕ) = 0, − c2 ∂δS c2 ∂δS , γrv sin θ ∂ϕ γrv ∂θ . (1) The differential system satisfied by perturbations is the same as in [6] (Eqs. (B18-B19)), only the functions M, v, c describing the stationary flow are different. Pressure perturbations satisfy a differential equation with a source term due to entropy/vorticity perturbations (Eq. (4) in [6]) : ∂2 ∂ + a1 + a0 ∂r 2 ∂r δp = b0 δS. p (2) The source term b0 (Eq. (B23) in [6]) characterizes the “excitator,” whereas the left hand side of Eq. (2) characterizes the ”oscillator”. The local strength of the excitator depends on the value of the ratio ωr/v: ωr 1 iωr ∂ log c2 1 ∼ 2 , v r v ∂ log r ωr 2 ∂ log c2 ∂ log M b0 1 ∼− 2 if l = 0, v r ∂ log r ∂ log r 2 ∂ log M ∂ log v if l ≥ 1. ∼ 2 r ∂ log r ∂ log r c2 r b0 (3) (4) (5) In view of Eqs. (3) to (5) and the advective-acoustic cycles described in [6, 7], two physical processes couple advected perturbations to the acoustic field: Title Suppressed Due to Excessive Length 103 (i) The gradient of temperature characteristic of the entropic-acoustic cycle is essential for spherical perturbations l = 0 (Eq. (4) and [5]) and high frequency perturbations (Eq. (3) and [6]). (ii) Even in a isothermal flow (i.e., ∂c2 /∂r = 0), non radial perturbations can excite acoustic waves in a vortical-acoustic cycle at low frequency (Eq. (5) and [7]). The simple estimate in Eqs. (3) to (5) shows that the strength of the excitator is comparable for radial and non radial perturbations, and that its amplitude is highest near the lower boundary. An efficient coupling between the excitator and the oscillator requires not only a strong amplitude of the excitator, but also a good matching of their spatial length scales. The wavelength of the excitator (∼ 2πv/ω) is approximately a factor M smaller than the wavelength of the oscillator (∼ 2π(c ± v)/ω). This contrasts with the simpler case of black hole accretion, in which case the excitator and oscillator have comparable wavelengths near the sonic radius (M → 1). The numerous oscillations of the excitator per acoustic wavelength should thus lead to a weak efficiency of the advective acoustic coupling in the inner regions where M 1. The inner regions, however, are precisely the place where the amplitude of the excitator is highest, because the adiabatic gradients are strongest there. What is the net effect ? The choice of the lower boundary condition is crucial in answering this question. 3 Boundary Condition at rcool In order to separate the adiabatic effects from the non adiabatic ones, we choose to estimate the contribution of the adiabatic region by neglecting the acoustic feedback from the cooling layer as much as possible. The following assumptions are made at the lower boundary rcool: (i) acoustic perturbations propagating downward are perfectly reflected out (ω ccool /rcool), (ii) entropy and vorticity perturbations are freely advected below rcool in the cooling region, where their coupling to acoustic waves is ignored. Condition (ii) is equivalent to imposing that below rcool, entropy and vorticity perturbations cease to be source terms of the acoustic equation. The source term in Eq. (2) is thus artificially damped by multiplying it by a smooth transition function Φλ . The transition is assumed to take place over a length λ, comparable to the cooling length. This damping of the source term can either be viewed as an ad-hoc damping of the entropy perturbation itself, independent of its frequency, or as a smoothing of the flow gradient responsible for the coupling. The equations corresponding to these assumptions are obtained by matching the pressure perturbation δp for r ≥ rcool with the homogeneous solution δp00 associated to Eq. (2) for r < rcool . 104 Thierry Foglizzo and Pascal Galletti 4 Eigenmodes of Shocked Accretion The Rankine-Hugoniot jump conditions are used to compute the perturbed quantities after the shock. These calculations are similar to those of [8] (chapter 90) extended to the case of a non uniform flow, or [9] extended to non radial perturbations. For a perturbed shock velocity ∆v in the strong shock limit, δvr 2 γ 5 − 3γ iωrsh ∆v = + , (6) vsh γ+1 vsh 2 γ − 1 iωrsh δρ γ 5 − 3γ ∆v =− , (7) ρsh γ + 1 γ − 1 iωrsh δvΩ 2 ∂ ∆v =− , (8) vsh γ − 1 ∂Ω iωrsh δp ∆v γ − 1 iωrsh 5 − 3γ γ 2 + 1 = −2 + . (9) psh γ + 1 vsh 4 (γ − 1)2 iωrsh The boundary value problem was solved numerically for l = 0, 1. A broad range of unstable modes grow on a timescale comparable to a fraction of the advection timescale. The radial mode is always the most unstable, closely followed by the non radial mode l = 1. 5 Evidence for the Advective-Acoustic Cycle Following the same method as [7], the discrete spectrum obtained in the boundary value problem is checked by computing, in two steps, the efficiency Qadv of sound production by the advection of an entropy/vorticity perturbation (without a shock), and the efficiency Qsh of entropy/vorticity production by an outgoing acoustic wave reaching a shock. The efficiency Qsh is obtained through a WKB approximation at high frequency. The global efficiency Q ≡ |Qadv Qsh | of the advective-acoustic cycle leads to a first estimate of the growth rate at high frequency: ωi = 1 log Q, τtot (10) where τtot is the total duration of the cycle (advection + acoustic). The exact resolution of the discrete eigenfrequencies was successfully compared to the continuous WKB estimate (10). 6 Comparison with BMD03 Our stability analysis in an adiabatic flow should apply directly to the numerical simulations of [1]. The authors recognized the existence of an advectiveacoustic cycle similar to the one occuring in the vortical-acoustic instability Title Suppressed Due to Excessive Length 105 [7]. Our linear study seems to agree qualitatively with their results concerning the mode l = 1. Nevertheless, the mode l = 0 is stable in their simulations, whereas it is the most unstable one according to our calculations, as well as in [4]. This important difference may come from the ”leaky” lower boundary condition in [1], which is different from ours even in the linear regime. 7 Conclusion The temperature and velocity gradients in the subsonic flow between the shock and the accretor is responsible for an efficient linear coupling between entropy/vorticity and acoustic perturbations. Most of the sound comes from the region close to the lower boundary of the adiabatic region, despite the fact that the wavelength of advected perturbations is much smaller than acoustic ones. The acoustic waves reaching the shock produce new entropy/vorticity perturbations, in an unstable cycle. The growth time is comparable to the advection time. The most unstable modes correspond to l = 0, 1 perturbations. The identification of the advective-acoustic cycle as the mechanism responsible for the instability was checked numerically through the calculation of Qadv and Qsh . Since the region contributing most efficiently to the instability is the vicinity of the lower boundary rcool, the role of cooling processes is at least crucial in determining the growth rate of the instability. The principle of a cycle between propagating and advected perturbations could be useful in interpreting the stability analysis of non adiabatic flows. Whether non adiabatic processes are partially stabilizing or even more destabilizing remains to be determined. The difficulties of 1-D numerical models in reaching an explosion (e.g., [10]) suggests that cooling processes are indeed important enough to significantly stabilize the entropic-acoustic cycle at work for radial perturbations. Acknowledgement. The authors are grateful to T. Janka for his initial suggestion to study the effects of advective-acoustic cycles in the problem of core-collapse, and his permanent encouragements since then. Useful discussions with J. Blondin, A. Burrows and R. Chevalier are acknowledged. References 1. 2. 3. 4. 5. 6. 7. J. Blondin, A. Mezzacappa, C. DeMarino: ApJ 584, 971 (2003) S.H. Langer, G. Chanmugam, G. Shaviv: ApJ 245, L23 (1981) C.J. Saxton, K. Wu: MNRAS 324, 659 (2001) J.C. Houck, R.A. Chevalier: ApJ 395, 592 (1992) T. Foglizzo, M. Tagger: A&A 363, 174 (2000) T. Foglizzo: A&A 368, 311 (2001) T. Foglizzo: A&A 392, 353 (2002) 106 Thierry Foglizzo and Pascal Galletti 8. L. Landau, E. Lifshitz: Fluid Mechanics 6, Pergamon Press (1987) 9. K. Nakayama: MNRAS 259, 259 (1992) 10. R. Buras, M. Rampp, H.-T. Janka, K. Kifonidis: astro-ph/0303171 (2003) A Self-Similar Problem on Supernova Explosion with an Account of Relativistic Accelerated Particles Yu. V. Petukhov, A. V. Razin, V. A. Razin Radiophysical Research Institute (NIRFI), 25 B. Pecherskaya st., Nizhny Novgorod, 603950, Russia petukhov@hydro.appl.sci-nnov.ru razav@inbox.ru razin@nirfi.sci-nnov.ru Summary. A self-similar problem has been considered on supernova explosion in a radially inhomogeneous medium taking into account generation of relativistic accelerated particles. An initial density of the medium decreases with the distance from the center of the explosion according to the power law. A two-fluid approach is used for the description of relativistic particles. The analysis of numerical results leads to the following conclusions. Processes of acceleration of cosmic rays show the most considerable influence on the formation of supernova shell (making it thinner) in the approximation of the uniform circumstellar medium. A typical circumstellar matter density decay with a distance from an explosion center causes a decrease of effects of shock accelerated particles on the shell formation, making the shell more thick and less dense. As concentration of relativistic accelerated particles increases, the influence of circumstellar matter inhomogeneity on the gas velocity profile becomes weaker. 1 Introduction It is now widely accepted that particle acceleration by shock waves from supernova explosions plays a considerable role in cosmic ray generation [1, 2]. The acceleration of charged particles is caused by repeated crossings of a shock front. Accelerated particles act back on a shock front and cause considerable variations of parameters of a shock [2]. A solution of a self-consistent problem is very much complicated, so, a two-fluid approximation [3–5] is widely used for a description of shock wave propagation in a presence of relativistic accelerated particles in a circumstellar medium. Such an approach allowed to investigate effects of accelerated particles on a process of shell formation by supernova explosion [6, 7]. In papers [6, 7] an approximation of homogeneous circumstellar medium was used. The aim of the present report is to treat the general case and to study the combined influence of a background medium 108 Yu. V. Petukhov, A. V. Razin, V. A. Razin regular inhomogeneity and relativistic accelerated particles on a supernova explosion formatted shell. 2 Statement of the problem and the basic equations Consider a radially inhomogeneous medium, in which a density decreases with distance r from a symmetry center according to a power law: ρ0 = A , rω where ω is a positive quantity. At a moment t = 0 at a symmetry center r = 0 a strong point explosion occurs and an energy E releases. Following [7] we neglect the equilibrium pressure in the background medium in comparison with the pressure at the shock front and behind it. We also ignore a fine diffusive structure of the shock front and assume that an effective diffusion coefficient is equal to zero. In other words, we accept that the thickness of the shock front is small as compared with its radius. We emphasize that the last condition is necessary for efficient particles acceleration [1, 2]. Finally, we assume that the ratio of the relativistic particles pressure to the background gas pressure is constant at the shock front. The equations of gas dynamics written down in spherical coordinates in Eulerian form in the two-fluid approximation are the following: ∂ρ ∂(ρv) 2ρv + + = 0, ∂t ∂r r ∂v ∂v 1 ∂pg 1 ∂pc +v + + = 0, ∂t ∂r ρ ∂r ρ ∂r γg ∂ρ 1 ∂pg γg ∂ρ 1 ∂pg − +v − = 0, pg ∂t ρ ∂t pg ∂r ρ ∂r (1) (2) (3) ∂pc ∂v 2γc ∂pc (4) +v + γc pc + pc v = 0. ∂t ∂r ∂r r Here t is time, ρ, v, pg , and pc denote the background gas density, the flow velocity, the gas and the relativistic accelerated particles pressure, respectively, γg = 5/4 and γc = 4/3 are Poisson’s adiabatic indexes of the gas and of the relativistic accelerated particles. Introduce a shock radius [8] Rs (t) = β Et2 A 1 5−ω , where β is a dimensionless constant, which may be calculated using the condition of equality of total background gas and relativistic accelerated particles energy to the explosion energy E. To find the self-similar solutions, we set Self-Similar Problem s= ρ(r, t) = r r = Rs (t) β A G(s), rω pg (r, t) = pc (r, t) = A Et2 v(r, t) = 4r 2 (5 2 − ω) t2 γg 4r 2 (5 2 − ω) t2 γc 109 1 5−ω , 2 r V (s), 5−ω t A G(s) Z(s), rω A G(s) Y (s), rω where s, G(s), V (s), Y (s) and Z(s) are dimensionless quantities. Equations (1)–(4) then reduce to ordinary differential equations in which s is the only independent variable: d ln G 1 dV = + (3 − ω)V , (5) d ln s 1 − V d ln s 3V (Y + Z) − 3(Y /γc + Z/γg ) − V (1 − V ) 52 − V − ω2 dV = , (6) 2 d ln s (1 − V ) − Y − Z d ln Y γc − 1 dV (3γc − 1)V − 5 + ω = + , d ln s 1 − V d ln s 1−V (7) d ln Z γg − 1 dV (3γg − 1)V − 5 + ω = + . (8) d ln s 1 − V d ln s 1−V Boundary conditions for these dimensionless equations must be derived from principles of conservation of mass, momentum and energy fluxes through the shock surface (s = 1). According to the two-fluid approximation the relative compression of the medium at the shock front must be set as an external parameter [7]: G(1) = σ, (9) where σ ≥ σg = γg + 1 = 4. γg − 1 The boundary conditions are the following (see [7]): V (1) = 1 − 1 , σ ηγc Y (1) = , σ γg 1 Z(1) = 1− −η , σ σ where (10) (11) (12) 110 Yu. V. Petukhov, A. V. Razin, V. A. Razin η= γc − 1 γg − γc (γg − 1)σ γg + 1 − γg + . 2 2σ The set of equations (5)–(8) have been integrated numerically subject to boundary conditions (9)–(12). After that, ratios have been calculated of the corresponding gas dynamics quantities to their values at the shock front (these values are denoted by the subscript s): Π(s) = G(s) ρ = s−ω , ρs G(1) U (s) = V (s) v =s , vs V (1) P (s) = p G(s) γc Z(s) + γg Y (s) = s2−ω , ps G(1) γc Z(1) + γg Y (1) Pg (s) = G(s) pg γc Z(s) = s2−ω , ps G(1) γc Z(1) + γg Y (1) Pc (s) = G(s) pc γg Y (s) = s2−ω . ps G(1) γc Z(1) + γg Y (1) Here the total pressure in the medium is introduced: p = pg + pc. 3 Numerical results and conclusions Fig. 1. Normalized density profiles for ω = 0 (solid lines) and ω = 2 (dashed lines) compared for differ-me ent values of relative compression σ (given near each curve) Representative results of numerical calculations are demonstrated in Fig. 1– 3. Figure 1 illustrates the plots of quantity Π versus s for different values of ω and σ. The density profiles are shown to be considerably sensitive to ω and σ variations. As the parameter ω increases from ω = 0 to ω = 2, a supernova shell becomes more thick and less dense. As relative compression σ grows for given ω, the shell becomes thinner and denser. Figure 2 shows dependencies on s of ratios Π(s, σ = σ1 ) δ(σ1 , σ2) = Π(s, σ = σ2 ) Self-Similar Problem Fig. 2. Dependencies of the quantity δ on parameter s. 111 Fig. 3. Normalized velocity profiles for ω = 0 (solid lines) and ω = 2 (dashed lines) compared for different values of relative compression σ (given near each curve.) compared for ω = 0 and ω = 2. Figure 3 presents velocity profiles. These profiles exhibit small changes due to ω and σ variations. The analysis of numerical results leads to the following conclusions. Processes of acceleration of cosmic rays show the most considerable influence on the formation of supernova shell (making it thinner) in the approximation of the uniform circumstellar medium. A typical circumstellar matter density decay with a distance from an explosion center causes a decrease of effects of shock accelerated particles on the shell formation, making the shell more thick and less dense. As concentration of relativistic accelerated particles increases, the influence of circumstellar matter inhomogeneity on the gas velocity profile becomes weaker. Acknowledgement. We are grateful to professor Stephen P. Reynolds for information on paper [6]. This research was supported by the International Science and Technology Center (Project No. 729). References 1. E. G. Berezhko, G. F. Krymskii: Soviet Phys.- Uspekhi 31, 27 (1988) 2. E. G. Berezhko, V. K. Elshin, L. T. Ksenofontov: J. Exp. Theor. Phys. 82, 1 (1996) 3. L. O.’ C. Drury, H. J. Volk: Astrophys. J. 248, 344 (1981) 4. P. A. Becker, D Kazanas: Astrophys. J. 546, 429 (2001) 5. L. O.’ C. Drury, H. J. Volk, W. J. Markiewicz: Astron. Astrophys. 236, 487 (1990) 6. R. A. Chevalier: Astrophys. J. 272, 765 (1983) 7. I. N. Toptygin: Pis’ma v Astronomichesky Zhurnal 26, 421 (2000) (in Russian) 112 Yu. V. Petukhov, A. V. Razin, V. A. Razin 8. L. Sedov: Similarity and Dimensional Methods in Mechanics, (New York: Academic Press, 1959) X-rays from circumstellar interaction Tanja K. Nymark Stockholm Observatory, S-106 91 Stockholm, Sweden tanja@astro.su.se Summary. We present a model for the emission from the cooling region behind the reverse shock created by the interaction between the supernova ejecta and the circumstellar medium. Applications to X-ray emission from the interaction region between supernova ejecta and pre-supernova wind are discussed. 1 Circumstellar interaction For supernovae with sufficiently dense circumstellar medium the interaction between the ejecta and the circumstellar gas creates a strongly emitting region of shocked gas. The interaction region consists of two distinct shells which are separated by a contact discontinuity. The outer shell consists of shocked circumstellar gas with temperatures of the order of 109 K, which emits mainly hard X-rays from free-free interactions. The inner shell is created by the reverse shock which moves backward into the ejecta, and consists of shocked ejecta with temperatures up to 107 K. This region emits soft X-rays and due to the lower temperature line emission is strong. The energy loss caused by the strong line emission causes the region to collapse, forming a dense, cool shell close to the contact discontinuity. At early stages the cool gas absorbs the line emission and soft X-rays, but as the shell expands the optical depth drops and more of the reverse shock emission emerges. Eventually it comes to dominate the X-ray spectrum from the supernova. 2 Shock structure For the radiative reverse shock, where the cooling time is short compared with the expansion time, we may assume that the post-shock region is thin compared to the size of the ejecta. We describe the region behind the shock as a steady state flow, for which the input parameters are given by a self-similar solution. The post-shock region is divided into a fine grid with a constant 114 Tanja K. Nymark density step between the zones, and the steady state equations are solved in each zone. In this way we determine the density structure of the shocked ejecta as well as the temperature and velocity at each grid point. From figure 1 we see that the size of the region is of the order of 1012 cm. Since a typical size of the supernova is 1015 cm, the assumption of a thin shell clearly holds. Fig. 1. The structure of the shocked ejecta behind the reverse shock. The lower right plot shows the emission behind the shock, most of which comes from the thin, cool shell close to the contact discontinuity, which also absorbs a significant amount of the emitted radiation. 3 Spectral code Once the temperature and density of each zone is known, the ionization structure can be computed. Assuming steady state also here, we obtain the ionization state of each element in each zone. We then solve the full multi-level equations for most ions, yielding the populations of a number of levels [1]. From the level populations we obtain the emission in each line, which is given by Pij = ni Eij Aij , where ni is the population of level i, Eij is the energy difference between levels i and j (i > j) and Aij is the probability that this Circumstellar Interaction 115 transition will take place. The continuum emission is computed by the method of Mewe et al [4]. 4 One temperature versus many The reverse shock is often modeled with a single temperature. While this is a good approximation for an adiabatic shock, it is not sufficient for reproducing the emission from a radiative shock. The total emission will be overestimated, and many lines from low-temperature regions will not be present in the synthetic spectrum. By combining hydrodynamic calculations with an emission code, our model traces the cooling region better (figure 2). Fig. 2. Spectrum created by our model (upper) and by a single temperature model of T= 107 K (lower). 5 Composition effects Since the gas behind the reverse shock consists of shocked ejecta, the composition of this gas is determined by the composition of the ejecta at the position 116 Tanja K. Nymark of the shock. This in turn reflects the composition of the outer layers of the progenitor star as well as the explosion physics. As the reverse shock moves backward into the ejecta it passes through regions abundant in elements which are rare in the circumstellar medium, resulting in quite distinct spectra, which change over time as the shock moves on (figure 3). Fig. 3. Effects of varying composition in the reverse shock. The upper panel shows the emitted spectrum from a single-temperature model if the composition of the shock is solar, while the middle and lower panels show the spectrum from the reverse shock when the shock is in the helium zone and oxygen zone respectively. 6 Absorption in the cool shell At early times most of the energy emitted by the cooling gas is absorbed in the cool shell close to the contact discontinuity. At first only the most energetic emission passes through, while lower energies are completely absorbed. As the emitting region expands, the optical depth in the cool shell drops. The absorption decreases, first at high energies, later at lower energies. As time passes, more of the low-energy emission emerges, so that even though the total emission decreases, the emerging emission from the reverse shock increases. Circumstellar Interaction 117 Fig. 4. The upper line shows the energy emitted by the whole cooling region, while the lower line is the emerging luminosity after absorption. In this case all the emission below 1 kEv is absorbed. 7 Discussion A model has been developed for the emission from the reverse shock created by the interaction between supernova ejecta and the dense circumstellar gas. By combining multi-level calculations of the most abundant ions with a hydrodynamic model our model gives a better description of the interaction than earlier models. When applied to observations our model can be used to trace the density structure and composition of the ejecta, and can thus give valuable information on the progenitor star and the explosion physics. References 1. 2. 3. 4. T. C. R. R. K. Nymark et al: in prep (2004) Fransson, P. Lundqvist, R. Chevalier: Ap.J. 461, 993 (1996) Chevalier, C. Fransson: Ap.J. 420, 268 (1994) Mewe, J.R. Lemen, G.H.J. van den Oord: A & AS 65, 511 (1986) Part IV Supernovae: GRB Connections Search for Correlations BATSE Gamma-Ray Bursts and Supernovae J. Polcar1 , M. Topinka2, G. Pizzichini3 , V. Hudcová4 , E. Palazzi5 , R. Hudec6 , and N. Masetti7 1 2 3 4 5 6 7 Astronomical Institute Ondřejov, Czech republic polcar@physics.muni.cz Astronomical Institute Ondřejov, Czech republic toast@lascaux.asu.cas.cz TESRE Bologna, Italy pizzichini@bo.iasf.cnr.it Astronomical Institute Ondřejov, Czech republic vhudcova@sunkl.asu.cas.cz TESRE Bologna, Italy palazzi@tesre.bo.cnr.it Atronomical Institute Ondřejov, Czech republic rhudec@asu.cas.cz TESRE Bologna, Italy masetti@tesre.bo.cnr.it 1 Introduction Gamma-ray bursts (GRBs) since the time of their discovery 30 years ago [1] has been remaining a great puzzle of todays high energy astrophysics. Since a successful BeppoSAX [2] mission we know that gamma emission is followed by an afterglow ranging from X-ray to radio wavelengths. The origin and thus the source is hidden because of the optically thick environment in leading fireball model of GRB [3] and could not be observed directly. Tremendous and rapid energy release is suspected to be a manifestation of a gravitational energy release and forming of a black hole either in a case of a death of a collapsing massive star in supernova-like explosion or in coalescing of two neutron stars. There are several pieces of observational evidence supporting the theory that gamma-ray bursts are somehow connected to supernovae (SNe). Fe K line in GRB afterglow spectra and derived high local density of environment place GRBs to originate in star-forming regions. In some cases (e.g. GRB980326 or GRB970228) an optical afterglow reveals a possible underlying supernova lightcurve. (e.g. GRB030329) [5]. Last but not least we have two examples of an excellent space and time correlation between GRB and SN, namely GRB980425 with SN1998bw [4] and GRB030329 with SN 2003dh, which reinforce the GRB and SN link. Several more or less successful attempts has been made in a search for the correlation between GRBs and SNe and reversely between SNe and GRBs (e.g. [6, 7]). Excluded two clear examples mentioned above there is no other close space and time correlation proved during the era of precise GRB detectors We decided to make a more complete analysis in this field, to revise the previous attempts, we try a bit different approach based on looking at both 122 J. Polcar, et al. statistics of space and time correlation and on physical properties of possibly correlated events and state a clearer conclusion of our result. 2 Search for Spatial and Temporal Correlation 2.1 Data In general at the beginning we have two sets of events we want to study and trying to find a correlation. We corrected and unified used catalogues and made a database of objects including their physical properties. We used a current BATSE catalogue (current to April 2003) for GRBs detected by CGRO BATSE during the BATSE era 1991-2000 which is maintained with a public access. A large uncertainty is in error boxes in the mean of BATSE circular error box convention and its median value is 3.11 deg. An accuracy in time is set to a day of discovery. We got 2040 GRBs in the catalogue. As a source of SNe we used combined data from Asiago Padova [9], Harvard [10] and SAI [11] catalogues of SNe. A positional error of a supernova is negligible with respect to the size of a typical GRB error box and is assumed to be zero. We used 1845 SNe in the catalogue (occured in the BATSE era). 2.2 Matching alias Pair Creation We developed a fast matching engine for matching database data from selected two catalogues BATSE GRBs and SNe. Almost all of the code programmed is written in Perl under Linux OS. The most crucial question in every matching process is not only what to match but how to match. In other words what is a criteria that two objects (in our case GRB and SN) make a pair. We looked for a space and temporal coincidences. We stated that GRB and SN are spatially matched if a position of a SN falls into a GRB error box. In time domain is the situation more complicated. There are two reasons for that: 1) It is not theoretically clear what is the time delay between eventual gamma-ray emission of a SN (which could be observed as a GRB) and its optical emission. An idea is to determine the time of gamma-emission which we call the time of explosion of SN from the time of maximum and the type of a SN in the following recipe. Accurate time delay is a extremely complex function of the mass of progenitor, initial energy, rotation status of the progenitor, its chemical composition, circumstellar environment and, of course, it is crucially based on an explosion engine and explosion mechanism used in the model and to define it properly is beyond todays limit of SN knowledge. We simplified our problem and divided SNe into two groups: a) Type Ia SNe assumed to be an explosion of a white dwarf due to accretion flow process in a binary system. Search for Correlations BATSE Gamma-Ray Bursts and Supernovae 123 b) Core collapse SNe which covers the rest of SN types. We tried to guess approximately the appropriate time delay between the time of maximum and the time of explosion according to [8] and our own studies of well observed known typical examples of SN. The time delay and a width of a time interval which corresponds to the level of uncertainty we used in our analysis is 17 ±14 days for core collapsed SNe and 20 ± 7 days for type Ia SNe. Note that the mass of a white dwarf undergoes well-defined Chandrasekhar limit as well as the physics of white dwarves is better understood so the time delay is more accurate then in the core collapse branch where much more free parameters play the role. Note that taxonomy of SNe is usually based mainly on observational features. Still there is large divergency between each SN of the same type, worse the classification features can even change in time as the SN evolves. 2) Note that only a fraction of cataloged SNe provide an information about the date of maximum only the time of discovery is quoted and not all SNe have a type defined or they have it defined with doubts. We decided to approach this in a spirit of statistics and we forced the time delay between the time of maximum and the time of discovery to be median (−4 days) of all known time delays. In the case we don’t know the type of SN we used weighted average of all types and time delays. More uncertainty we have larger time interval window we make. 2.3 Results As a result of our matching procedure we got 19 spatial and temporal coincidences making possibly connected GRB/SN pairs (if not said otherwise we will omit the word possibly). A plot of all spatially and temporally correlated pairs also with GRB error boxes are shown in Fig. 1. Note that we a priori don’t know how many of these coincidences are made due to any real correlation and how many is there just by chance. Let us suppose that a fraction f of SNe is linked to GRBs. We tried to determine the significant level of our result. We have two possibilities to test our results for statistical confidence, a computer simulation such a rotation of a catalogue or Monte-Carlo simulation and an analytical statistical solving. If both distributions were homogeneously distributed over entire sky estimating of random coincidences would be calculated easily. Unfortunately this is not the case. Because this is a preliminary version and we have only limited space the details will be presented later. 3 Search for Physical Properties Correlations 3.1 Introduction As resulted above the number of all events and the number of pairs is still too small to find any significant conclusion. We suggest another method to check 124 J. Polcar, et al. Fig. 1. Final Match - SN/GRB pairs the possible correlation. We suppose not only that a fraction of GRBs and SNe is correlated but also that this fraction is intrinsically physically different. Thus we can look for pairs and check if they differ from the rest of the sample. We analyzed both GRBs and SNe. None of GRBs detected by BATSE has a redshift measured. In the analysis below we assume that if there is a redshift of a SN known in a pair it is also a redshift of a corresponding GRB. If the pair is really correlated we get a right value if not we get a random value which doesn’t show any deviation from the rest of the sample in the average. 3.2 Results From the variety of graphs obtained we pinpoint only interesting and suspicious ones. These are absolute magnitude of SN vs isotropic energy equivalent of GRB which shows a surprising correlation affected not only by strong dependency on redshift, duration of GRB vs hard to soft ratio of GRB which shows excess in longer and softer GRBs. See Fig. 2 and Fig. 3. 3.3 Caveats There is several crucial caveats in our analysis which put huge uncertainty and lower down the confidence level of our result. Surprisingly the more fatal problems are at the side of SNe. a) Error boxes of GRBs are (were in 1991-2000) incredibly large in the sense of precise astronomical measurement in optical bands. b) On the other hand BATSE catalogue is an excellent source of calibrated and reduced data belonging to one detector with no need to recalculate the data. Search for Correlations BATSE Gamma-Ray Bursts and Supernovae 125 Fig. 2. Abs. magnitude of SNe vs isotropic energy equiv. of GRBs Fig. 3. Hard to soft ratio of GRBs vs duration (T90) of GRBs c) There is a limiting flux in CGRO BATSE detector and what is worse a telescope to telescope, survey to survey and day to day changing magnitude limit in observing SNe. Some faint events could remain undetected. d) Neither GRBs nor SNe were not detected by all-sky and 24 hours monitors. The sky covering at one time is only 30in SN sky coverage is much worse, the selection effect is very high and probability function of observing a particular location at the sky is impossible to reconstruct. Due to this (and partially due to c) ) there is still a non-negligible chance that we haven’t seen GRB (which lasts generally for few seconds only) of a particular SN and via versa. This is the main problem of our search and of determining the validity of our results. e) There is an uncertainty in guessing the time of maximum of SN if there is one or two observation only. f) There is an uncertainty in guessing the time delay between gamma and optical SN emission. 126 J. Polcar, et al. g) There are several pieces of evidence that majority of GRB explosions is beamed into a narrow cone (Frail).Thus a total number of GRBs and possible related SNe is much larger than observed number of these events and because the size of the beaming angle is a function of emission frequency there could be a SN connected to invisible GRB if we assume larger opening angle for longer frequencies. h) In general there is a large number of quite well-localized GRBs which were investigated very carefully for an occurrence of possible optical afterglow but with no success even if the observational conditions were good and the observations followed in few minutes. These are called “dark bursts” and they should be counted statistically. The fractional number of these is speculative. 3.4 Conclusions Even although there is infinity list of caveats it there is a chance to get meaningful result from such analysis. At this moment we are not able to conclude if there is any positive or negative or no correlation between GRBs and SNe. We plan to rebuild the database and check the results with more robust methods we have already developed such a catalogue rotation, Monte-Carlo simulation and we are also about to provide a more complete analytical statistical theoretical background. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Klebesadel, R.W., Strong, I.B., and Oslon, R.A. 1973, ApJ 182, L85 http://bepposax.gsfc.nasa.gov/bepposax/ Piran, T. 1998, astro-ph/9810256 Galama, T. J., 1998, Nature 395, 670 Stanek, K. Z. 2003, ApJL, 591, 17 Hudec R., Hudcova, V., and Hroch, F, 1999, A&AS 138, 45-476 Wang, L., Wheeler,J.G., 1998, ApJ 504, L87 Petschek, A.G. Supernovae, Springer Verlag New York 1996 http://merlino.pd.astro.it/~ supern/snean.txt http://cfa-www.harvard.edu/iau/lists/Supernovae.html http://www.sai.msu.su/sn/ Part V Supernovae: Progenitors/Remnants Complex Molecules in NGC 2359. The Gas Chemistry of a Core-Collapse Supernova Progenitor J. R. Rizzo1 and J. Martı́n-Pintado2 1 2 Departamento de Fı́sica, Universidad Europea de Madrid, Urb. El Bosque, E-28670 Villaviciosa de Odon, Spain, jricardo.rizzo@fis.cie.uem.es Depto. de Astrofı́sica Molecular e Infrarroja, Instituto de Estructura de la Materia (CSIC), Serrano 121, E-28006 Madrid, Spain, martin@damir.iem.csic.es Summary. We describe here the results of millimeter line observations of several complex molecular lines (CS, SiO, HCO+ , HCN, CN and H13 CO+ ) toward the WolfRayet nebula NGC2359. The observations were carried out along a strip radially to the nebula, in order to draw abundance and excitation conditions as a function of the star distance. This is the first chemical study of this kind of objects, which draws the physical and chemical state previous to a core-collapse SN explosion. Moderate densities (up to 104 cm−3 ) and high kinetic temperatures (up to 80 K) are inferred from our analysis. Many features of the SN and of the evolution of its remnant should be strongly affected by the physical and chemical state of the Wolf-Rayet stars and their environs. 1 Background The Wolf-Rayet (W-R) stars are known as the last evolution phase of massive stars (> 25 M ), before supernova. This relatively short-lived phase (∼ 105 yr; [1]) is characterized by a rather strong UV radiation and a fast, copious stellar wind (v∞ > 2000 km s−1 ; Ṁ ≈ 3 105 M , yr−1 ). Then, it is expected that the circumstellar medium (CSM) should be hardly devastated by the W-R stage, and also by the previous evolution stages (LBV, RSG, Of). The study of the W-R environs is worth doing because: (1) It would constitute a clue observational evidence about the evolved massive stars. The history of a massive star evolution is written in its surroundings; (2) It talks us about the physical and chemical conditions of the CSM when SN occurs. The SNR evolution depends not only on the stellar input, but also on the medium where it expands. Nowadays, we know more than two hundreds of W-R stars in the Galaxy [2]. Of those, just a few cases have associated molecular gas in its CSM [3, 4, 5]. 130 J. R. Rizzo and J. Martı́n-Pintado Even more, in all these cases the total amount of molecular mass is relatively low, up to H2 column density of 1021 cm−2 . NGC 2359, the W-R nebula surrounding HD 56925 (WR7 in the catalogue of van der Hucht [2]), is the target best studied in its molecular counterpart. CO was firstly detected by Schneps et al. [6], and extensively mapped by Rizzo et al. [5] and Cappa et al. [7]. Very recently, a higher resolution and sensitivity work [8] has revealed the existence of three stratified kinematical components, associated to previous evolution episodes, probably during the LBV phase of HD 56925. The molecular hydrogen has been extensively mapped by StLouis et al. [3]. They have found intense emission toward the southeast of the nebula, but they could not establish the dominant mechanism of excitation. An important contribution in this sense was provided by Rizzo et al. [9], who detected ammonia (NH3 ) for the first time in this kind of sources. The NH3 molecule was detected in the external part of the molecular cloud, towards a maximum of CO column density. Since the NH3 is a fragile molecule, easily dissociated, the authors proposed the release of NH3 from grain mantles as the formation mechanism of NH3 [10]. As a next step in the knowledge of this source, we have carried out the first search for complex molecules in NGC 2359, by observing several rotational transitions at 1.3, 2 and 3 mm. We report here the preliminary results of these observations, and discuss about the column densities, abundances and dominant chemistry in the southeastern part of NGC 2359. 2 Observations The observations were performed using the IRAM 30-m radio telescope at Pico Veleta (Spain), during august 2002. Each position was observed in positionswitching mode. The multi frequency capability of the telescope, both at 1.3 + 3 mm and 1.3 + 2 + 3 mm, allowed us to simultaneously observe different transitions of the same molecule. We used filter banks of 256 × 100 kHz width, 1024 × 1MHz width, and an autocorrelator of variable spectral resolution as backends. The velocity resolutions obtained varied from 0.1 to 0.5 km s−1 . The observed transitions, frequencies and telescope parameters (HPBW and beam efficiency) are sketched in Table 1. The positions observed were located along the same strip observed in the CO isotopes [8]. The strip crosses the surrounding molecular cloud more or less radially to HD 56925, as indicated in Fig. 1. 3 Results The Fig. 1 shows the CO 2–1 emission [8] in two velocity intervals: the false color plot shows the integrated emission between 52 and 55 km s−1 , while the contours trace the integrated emission between 48 and 51 km s−1 . The squares Complex molecules in NGC 2359 131 Table 1. Telescope parameters Molecule C18 O CS CS CS CN CN HCN HCN SiO HCO+ H13 CO+ Transition Frequency HPBW Beff GHz 1–0 2–1 3–2 5–4 1–0 2–1 1–0 2–1 2–1 1–0 1–0 109.78216 97.98968 146.96905 244.93561 113.49098 226.87476 88.63185 177.23871 86.84699 89.18852 86.75429 22 25 17 10 22 11 28 14 28 28 28 0.75 0.76 0.69 0.49 0.74 0.53 0.77 0.63 0.78 0.77 0.78 Fig. 1. Location of the positions observed, superimposed to the CO 2–1 emission in the southeast of NGC 2359 indicated as A-E point to the observed positions. These five points have been chosen in order to draw possible chemical changes in a radial direction to the W-R star, or in a direction perpendicular to the interface between the ionized and the molecular gas. Some relevant spectra are shown in Fig. 2. The selected spectra are from the points B, C and D and have been chosen in order to show some relevant aspects of the survey. Despite the intensity variations, we note a change of 2–4 km s−1 from position B to D, as well as an increase in the linewidths. Relative intensities are also variable from one position to another. 132 J. R. Rizzo and J. Martı́n-Pintado Fig. 2. A sample of the spectra observed in NGC 2359 The column density estimates, by assuming optically thin emission, are sketched in Table 2. The kinetic temperatures assumed was 30 K for position A to D, and 80 K for position E. These assumptions are based on the analysis of Rizzo et al. [8] about kinematics, density and kinetic temperature. Table 2. Molecular species detected in NGC 2359 Pos. N(CO) N(13 CO) N(CS) N(HCO+) N(CN) N(HCN) A B C D E 6.8(15) 2.7(16) 2.7(16) 2.1(16) 3.4(15) 9.8(14) 3.2(15) 1.8(15) 1.3(15) 1.4(14) 1.4(12) 8.0(12) 7.4(12) 1.2(13) 1.5(12) 9.6(11) 2.6(12) 1.1(12) 1.7(12) 4.8(11) < 5.4(12) 4.6(12) 4.4(12) 7.7(12) < 2.6(12) 1.5(11) 7.2(11) 3.6(11) 5.9(11) 2.3(11) Number in parenthesis refer to power of 10 (in cm−2 ) 4 Discussion Although these results should be regarded as preliminary, we can arrive to several interesting ideas about the chemistry and excitation conditions in the molecular gas associated to NGC 2359. First of all, the mere detection of some of these molecules confirm the existence of regions of high density (at least 104 cm−3 ) in the environs of evolved massive stars. This result is on the line Complex molecules in NGC 2359 133 of cases of SN interacting with the CSM in external galaxies (see the review of Fransson in these Proceedings), although in our own Galaxy the presence of dense circumstellar gas seems unusual. A high relative abundance of CN with respect to HCN (above 10) is computed in all positions. This fact, together with the nondetection of SiO, may indicate that the photodissociation of some fragile molecules is important [12, 11], especially toward the interface with the optical nebula. 5 Conclusions and Future Work The few cases where W-R nebulae are bound by molecular material are special sites where we can learn about the impact of W-R and predecessors onto its surroundings. Further investigations (mainly in 1mm lines) might disclose new features about the interplay of evolved massive stars and its surrounding CSM. This kind of observational studies should be extended to other objects, such as LBV nebulae, dusty W-R stars and young SNR’s. In several external galaxies, the light curves of SN are explained by the presence of very dense (106 cm−3 ) circumstellar gas around the progenitor massive star. In contrast, our Galaxy does not seem to show such amount of gas, nor such high densities. This is a remaining open question worth to be analyzed in the near future. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. N. Langer, W.-R. Hamann, M. Lennon et al: A&A 290, 819 (1994) K. van der Hucht: New Astronomy Reviews 45, 135 (2001) N. St.Louis, R. Doyon, F. Chagnon, D. Nadeau: AJ 115, 2475 (1998) A. P. Marston, J. Welzmiller, M. A. Bransford, M. A. Black, P. Bergman: ApJ 518, 769 (1999) J. R. Rizzo, J. Martin-Pintado, J. G. Mangum: A&A 366, 146 (2001) M. H. Schneps, A. D. Haschick, E. L. Wright, A. H. Barrett: ApJ 243, 184 (1981) C. E. Cappa, M. Rubio, W. M. Goss: AJ 121, 2664 (1999) J. R. Rizzo, J. Martin-Pintado, J.-F. Desmurs: A&A 411 465 (2003) J. R. Rizzo, J. Martin-Pintado, C. Henkel: ApJ 553, L181 (2001) D. R. Flower, G. Pineau des Forets: MNRAS 268, 724 (1994) W. T. Reach, J. Rho: ApJ 511, 836 (1999) R. Bachiller, M. Perez Gutierrez, M. S.N. Kumar, M. Tafalla: A&A 372, 899 (2001) Second Epoch Global VLBI Observations of Compact Radio Sources in the M82 Starburst Galaxy J. D. Riley1 , A. Pedlar1 , T. W. B. Muxlow1 , A. R. McDonald1 , R. J. Beswick1 , and K. A. Wills2 1 2 Jodrell Bank Observatory, University of Manchester, Macclesfield, Cheshire. SK11 9DL. UK jriley@jb.man.ac.uk Department of Physics and Astronomy, University of Sheffield, Sheffield. S3 7RH. UK Summary. We have presented the results of a second epoch of global Very Long Baseline Interferometry observations, taken on 23 February 2001 at a wavelength of 18 cm, of the central kiloparsec of the nearby starburst galaxy Messier 82. These observations were aimed at studying the structural and flux evolution of some of the compact radio sources in the central region that have been identified as supernova remnants. The objects 41.95+575 and 43.31+592 have been studied, expansion velocities of 2500 ± 1200 km s−1 and 7350 ± 2100 km s−1 respectively have been derived. Flux densities of 31.1±0.3 mJy and 17.4±0.3 mJy have been measured for the two objects. These results are consistent with measurements and predictions from previous epochs. 1 Introduction The nearby (3.2 Mpc distant) starburst galaxy Messier 82 (M82) has a high inferred star formation rate of 1.7 to 2.2 M yr−1 for stars with masses greater than 5 M ([6])which leads to an expected supernova rate of 0.05 to 0.1 yr−1 . As a result M82 is an ideal laboratory for the study of radio supernovae in a starburst environment and such studies can yield important information on the properties of the interstellar medium (ISM). The central region of M82 hosts in excess of 60 compact radio sources, most of which have now been identified as shown in [3] and the references therein. Of these sources 16 have been identified as Hii regions with at least 30 of the others identified as supernova remnants (SNR). Several studies have been conducted of these compact sources. [3] used the Multi Element Radio Linked Interferometer Network (MERLIN) to study the spectral indices of the sources to aid in identification. Others have concentrated on the SNR studying them at various angular scales such as [4] using MERLIN and two using Very Long Baseline Interfer- 136 J. D. Riley et al. ometry (VLBI) techniques: [5] using the European VLBI Network (EVN) and [2] along with [7] and this paper using a global VLBI network. These studies have primarily been focused at measuring the expansion velocities and deceleration parameters of the SNR and thereby testing the models put forward in [1]. 2 Observations and Data Analysis The observations were made on 23 February 2001 using a 19 station global VLBI network at a wavelength of 18 cm. The network consisted of eleven antennas of the Very Long Baseline Array (VLBA) in the USA, 6 antennas from the EVN, the NASA Deep Space Network (DSN) antenna at Robledo, Spain and a single Very Large Array (VLA) dish. This network was virtually identical to the 20 station network used by [2] on 28 November 1998, with only the NASA DSN antenna at Goldstone, USA missing compared to the first epoch. The data were taken in spectral line mode using 128 channels each of bandwidth 0.125 MHz, yielding a total bandwidth of 16 MHz. Observations were made of several sources, the target source being the central kiloparsec of M82, with J0958+65 being observed throughout the run as a phase calibration source. The sources 3C84 and J0927+39 were used for fringe fitting and bandpass calibration, with 3C84 alone being used for flux scale calibration. The data were acquired and correlated using the Mark IV/VLBA system and the data reduction and image analysis were conducted using the Astronomical Image Processing System (aips) which is provided and maintained by the National Radio Astronomy Observatory (NRAO) in the USA. 3 Compact Source: 41.95+575 The source 41.95+575 (Fig. 1) is the most compact of the sources in M82 and does not exhibit a shell structure, but appears to be more bipolar in nature. Difficulties were encountered when trying to measure the expansion of this object. The angular expansion velocity is quite low and leads to an expected expansion of about 1 mas in the time between the two epochs. The other problem is that changes in the small scale structure make finding common reference points between epochs to measure the expansion difficult. The most reliable method of making expansion measurements in this source was found to be moment fitting. This was conducted using the aips task momft. Using this method on data from both epochs we arrive at sizes and other parameters for the source mentioned in Table 1. From these results we calculate a total angular expansion of 0.77 ±0.37 mas yr−1 along the major axis. The expansion along the major axis has been measured in the past [2, 8] and more recently in [4]. The results presented here are both consistent with Global VLBI Observations of Compact Radio Sources in M82 200 400 600 800 1000 b) 200 40 40 30 30 20 20 10 10 MilliARC SEC MilliARC SEC a) 0 600 800 0 -10 -10 -20 -20 -30 -30 -40 400 137 -40 30 20 10 0 -10 MilliARC SEC -20 -30 30 20 10 0 -10 MilliARC SEC -20 -30 Fig. 1. Maps of 41.95+575 from both epochs of the global VLBI observations convolved with a 3.5 mas circular beam. a) Epoch 28 November 1998 map with contours at (1, 2, 4, 8) × 173.6 µJy beam−1 . b) Epoch 23 February 2001 map with contours at (1, 2, 4, 8) × 114.4 µJy beam−1 . those from [4, 8]. Using the standard distance to M82 of 3.2 Mpc it is possible to calculate that the linear expansion speed from the center, along the major axis, perpendicular to the line-of-sight is 2500 ±1200 km s−1 . It is necessary to note that as this source appears to be bipolar in nature the expansion along the major axis may be greater than the value quoted here due to orientation effects. Table 1. The sizes of the source 41.95+575 calculated using moment fitting for both of the recent global VLBI epochs. Epoch 28 Nov 1998 23 Feb 2001 Major Axis Error Position Angle (mas) (mas) (degrees) 21.4 23.1 ±0.8 ±1.4 54.63 58.82 In the 2.2 years between the observations the flux density of 41.95+575 has decreased from 43.8±2.3 mJy to 31.1±0.3 mJy. This in line with expectations that the source continues to decrease at a rate of 8.5 % per year. 4 Compact Source: 43.31+592 The compact source 43.31+592 (Fig. 2) is a typical shell-type SNR. The expansion measurements of this source posed problems due to evolution of the small-scale structure which did not allow accurate Gaussian fitting to the four knots of emission identified in [2]. Instead, the center of the source in the maps 138 J. D. Riley et al. 150 200 250 300 b) 40 40 30 30 20 20 10 10 MilliARC SEC MilliARC SEC a) 100 0 100 120 140 160 180 0 -10 -10 -20 -20 -30 -30 -40 80 -40 40 30 20 10 0 -10 MilliARC SEC -20 -30 -40 40 30 20 10 0 -10 MilliARC SEC -20 -30 -40 Fig. 2. Maps of 43.31+592 from both epochs of the global VLBI observations convolved with a 4 mas circular beam. a) Epoch 28 November 1998 map with contours at (1, 1.5, 2, 2.53) × 100 µJy beam−1 . b) Epoch 23 February 2001 map with contours at (1, 1.5, 2, 2.53) × 66 µJy beam−1 . was found for each epoch and the flux in 2 mas-thick annuli was integrated around each annulus using the aips task iring. A plot of the integrated flux in each annulus against the distance from the center was made (see Fig. 3). The position of the peaks for each epoch were then used to calculate the expansion speed of the SNR. The 1998 data exhibit increasing errors towards the outer edge of the SNR due to confusion between diffuse emission and the background noise. The peak for the 1998 epoch appears at a radius of 19 mas and in the 2001 epoch the peak appears at 21.5 mas. As a result the angular expansion speed is 1.13 ± 0.32 mas yr−1 which corresponds to a linear expansion speed of 7350±2100 km s−1 . These preliminary results are consistent with the results in both [2, 4, 5]. The flux density of the source has changed from 19.5 ±0.1 mJy during the 1998 epoch to 17.4 ±0.3 mJy during the 2001 epoch. 5 Conclusion Two of the compact radio sources in M82 that have been identified as SNR have been studied at two epochs with global VLBI techniques. The source 41.95+575 is expanding at a speed of 2500±1200 km s−1 , which is consistent with previous measurements. The flux continues to decline at a rate of 8.5 percent per year and during the latest epoch stood at 31.1±0.3 mJy. 43.31+592 is expanding at a speed of 7350 ± 2100 km s−1 , which continues to support the proposal [2] that the SNR is in or close to free expansion. This result is in conflict with models proposed in [1]. The ultimate goal of better constraining the expansion velocities and measuring the deceleration parameters for these SNR can only be achieved by further observations at this resolution. In order to allow for enough expansion Global VLBI Observations of Compact Radio Sources in M82 139 Fig. 3. Results of integrating around annuli from the center of the SNR 43.31+592. The results for 2001 epoch shown by filled circles and for 1998 epoch by unfilled circles to occur to allow detection it has been suggested that this will be done every 4 to 5 years. References 1. R. A. Chevalier, C. Fransson: Ap.J. 558, L27 (2001) 2. A. R. McDonald, T. W. B. Muxlow, A. Pedlar, M. A. Garrett, K. A. Wills, S. T. Garrington P. J. Diamond, P. N. Wilkinson: MNRAS 322, 100 (2001) 3. A. R. McDonald, T. W. B. Muxlow, K. A. Wills, A. Pedlar, R. J. Beswick: MNRAS 334, 912 (2002) 4. T. W. B. Muxlow et al.: These Proceedings 5. A. Pedlar, T. W. B. Muxlow, M. A. Garrett, P. J. Diamond, K. A. Wills, P. N. Wilkinson, W. Alef: MNRAS 307, 761 (1999) 6. A. Pedlar: In IAU Symposium 205: Galaxies and their Constituents at the Highest Angular Resolutions, 366 (2001) 7. A. Pedlar and T. W. B. Muxlow and J. D. Riley: These Proceedings 8. W. M. Trotman: MSc Thesis, University of Manchester (1996) Secular Decrease and Random Variations of Cassiopeia A at 151.5 and 927 MHz E. N. Vinyajkin, V. A. Razin Radiophysical Research Institute (NIRFI), 25 B. Pecherskaya st., Nizhny Novgorod, 603950, Russia evin@nirfi.sci-nnov.ru razin@nirfi.sci-nnov.ru Summary. Long-term measurements of the radio flux density of Cassiopeia A relative to Cygnus A have been carried out at 927 and 151.5 MHz. It was found the following mean secular decrease rates of the radio emission of Cassiopeia A: (0.72 ± 0.03)% year−1 at 927 MHz (for the period 1977-2002) and (0.88 ± 0.09)% year−1 at 151.5 MHz (for the period 1980-2002). These values of the secular decrease rate obtained over the period of the last 25 years are substantially less than those of Baars et al. (1977). This indicates to the slowing down of Cassiopeia A radio emission secular decrease. In addition to this large scale time variation of Cassiopeia A flux density the measurements have also shown a small scale (a few years) time variations over the smooth secular decrease. 1 Introduction The secular decrease rate d = S −1 dS/dt of the radio emission of young supernova remnant Cassiopeia A was determined in many early investigations using relatively few measurements (sometimes only 2-3 measurements) of its flux density S at different epochs. However, if we want to measure not only some mean d over a long time interval but also to reveal some possible time variations of S, we have to make more measurements. In addition, measurements at a given frequency ν should be carried out using the same or rather similar radio telescopes and identical measurement procedures. This report presents the results of long-term (1977-2002) measurements of the flux density of Cassiopeia A relative to that of Cygnus A at 927 and 151.5 MHz. 2 Measurements of the Cassiopeia A radio flux density relative to Cygnus A at 927 MHz In the very beginning of August 2002 we carried out the measurements of the Cassiopeia A radio flux density relative to Cygnus A at the Radio Astronom- 142 E. N. Vinyajkin, V. A. Razin ical Observatory “Staraya Pustyn ” (geographical latitude 55◦ 39 , longitude 2h 54.5m) using 10-m radio telescope at 927 MHz. These measurements are an extension of the long-term ones initiated in 1977 [1-3]. Using one and the same radio telescope makes it possible to obtain a uniform observational material. The measurement method consisted as before of successive registration of Cassiopeia A and Cygnus A radio emission relative to definite reference areas. One record of Cygnus A had the following sequence of antenna pointings lasted totally 6 minutes: reference area - source - reference area (“off” - “on” “off”). The sequence of the same duration for Cassiopeia A was the following: first reference area - source - second reference area (“off1” - “on” - “off2”). The reference areas for Cassiopeia A have the following coordinates: right ascension αoff1 = αCasA −0h 40m , αoff2 = αCasA +0h 40m , declination δoff1; 2 = δCasA , that one for Cygnus A has, respectively: αoff = 20h 12m, δoff = 45◦ 05 (coordinates for epoch 1950.0). The radio emission of sources was registered at such time intervals when the elevation difference of Cassiopeia A and Cygnus A by its absolute value did not exceed 7◦ at an average elevation of both the sources 72◦ . These conditions define the time and duration (about 2 hours) of one session of measurements. As a result of two sessions we obtained the following ratio of Cassiopeia A and Cygnus A flux densities at 927 MHz: (SCasA /SCygA )927 MHz = 1.096 ± 0.011 for the epoch 2002.58. Fig. 1. Flux density of the Cassiopeia A radio emission relative to that of Cygnus A at 927 MHz versus time. Figure 1 shows all values of (SCasA /SCygA )927 MHz for all years of measurements using RT-10 at 927 MHz obtained from measured values by multiplying by 0.89 to take into account the difference of brightness temperatures in the direction of Cygnus A and its reference area. Secular Decrease of Cassiopeia A at 151.5 and 927 MHz 143 3 Interferometric measurements of the Cassiopeia A radio flux density relative to Cygnus A at 151.5 MHz In August - September 2002 we carried out the measurements of Cassiopeia A radio flux density relative to Cygnus A at the Radio Astronomical Observatory “Staraya Pustyn ” using the interferometer consisting of two 14-m radio telescopes at 151.5 MHz. One session of measurements consisted of a one hour record of Cygnus A fringes near the upper culmination, then that of Cassiopeia A near also the upper culmination and calibrations by the noise generator. For this interferometer with a base of 31λ both sources are practically point ones. By each measurement session we defined the amplitude ratio of fringes of Cassiopeia A and Cygnus A equal to the ratio of their flux densities. There were five measurement sessions. As a result we got: (SCasA /SCygA )151.5 MHz = 0.91 ± 0.01 for the epoch 2002.67. Figure 2 shows the values of (SCasA /SCygA )151.5 MHz for all years of measurements using the interferometer RT-14+RT-14(2) at “Staraya Pustyn ” at 151.5 MHz. 4 Analysis of the results of long-term measurements of Cassiopeia A flux densities at 927 MHz Figure 1 shows the measurement results of the Cassiopeia A radio flux density relative to Cygnus A at 927 MHz (SCasA /SCygA )927 MHz ≡ r927(t) made during 25 years (1977-2002) using one and the same 10-m radio telescope at the NIRFI Radio Astronomical Observatory “Staraya Pustyn ”. The straight line of Fig. 1 r927(t) = m927 (t − t927 ) + c927, where t927 = 1990.2 is the mean epoch of measurements at 927 MHz, m927 = dr927(t)/dt = −(8.467 ± 0.390) · 10−3 year−1 , c927 = r927(t927 ) = 1.172 ± 0.003, shows a weighted least-squares fit. The average value of the secular decrease rate of the Cassiopeia A radio emission over the time interval 1977-2002 is equal to d927 MHz (1977−2002) = 100 · m927 /c927 = −(0.72 ± 0.03)% year−1 . (1) 5 Analysis of the results of long-term measurements of Cassiopeia A flux densities at 151.5 MHz Figure 2 shows the measurement results of the Cassiopeia A radio flux density relative to Cygnus A at 151.5 MHz (SCasA /SCygA )151.5 MHz ≡ r151.5(t). The straight line of Fig. 2 144 E. N. Vinyajkin, V. A. Razin r151.5(t) = m151.5 (t − t151.5) + c151.5, where t151.5 = 1991.8 is the mean epoch of measurements at 151.5 MHz, m151.5 = dr151.5(t)/dt = −(8.779 ± 0.851) · 10−3 year−1 , c151.5 = r151.5(t151.5 ) = 0.996 ± 0.008, shows a weighted least-squares fit. The average value of the secular decrease rate of the Cassiopeia A radio emission over the time interval 1980-2002 is equal to d151.5 MHz(1980−2002) = 100 · m151.5 /c151.5 = −(0.88 ± 0.09)% year−1 . (2) Fig. 2. Flux density of the Cassiopeia A radio emission relative to that of Cygnus A at 151.5 MHz according to the measurements at “Staraya Pustyn ” versus time. Fig. 3. Flux density of the Cassiopeia A radio emission relative to that of Cygnus A at 151.5 MHz according to the measurements at “Staraya Pustyn ” and the data of [4-6] versus time. The measurement results of (SCasA /SCygA ) of other authors at 151 and 152 MHz are available in the literature for the interval 1966-1993 [4-6]. Fig. 3 shows the results of all known measurements at ≈ 151.5 MHz (17 epochs altogether) including “Staraya Pustyn ” data together with a straight line of a weighted least-squares fit. The average value of the secular decrease rate of the Cassiopeia A radio emission over the time interval 1966-2002 is equal to d151.5 MHz (1966−2002) = −(0.81 ± 0.04)% year−1 , (3) that coincides within the limits of errors with the value (2) obtained at the observatory “Staraya Pustyn ” over the interval 1980-2002. 6 Discussion We can see from Fig. 1 that the decline of Cassiopeia A flux density with time is not uniform. For example, in the beginning of the 1980’s, the decrease Secular Decrease of Cassiopeia A at 151.5 and 927 MHz 145 was more rapid than at the end of this decade. In addition, in 1979-1980 Cassiopeia A flux density even increased. It is interesting to compare the obtained values of the secular decrease rate of Cassiopeia A radio emission at 151.5 MHz (2) and 927 MHz (1) with the values of d followed from the empirical formula given in [7] dν (% year−1 ) = −(0.97 ± 0.04) + (0.30 ± 0.04)log10 (ν/1000 MHz). (4) Fig. 4. Comparison of the values of the Cassiopeia A secular decrease rate according to formula (4) from [7] (solid curve gives the values of d without account of errors, the dash ones do that with the account of errors) and the values (1) and (2) at 927 and 151.5 MHz, respectively. Figure 4 shows d(ν) according to formula (4) (with an account of the errors the values of d according to formula (4) from [7] lie between dash lines in Fig. 4) and the values of d (1) and (2) according to our measurements. As seen from Fig. 4 the values of d obtained mainly by the measurements in the last quarter of the 20-th century are substantially less by the absolute value than the values of d obtained by the measurements in the third quarter of the 20-th century. This testifies to the slowing down with time the decrease of Cassiopeia A radio emission (see also [8]). At the same time the values of the secular decrease rate at 151.5 MHz (2) and 927 MHz (1) do not contradict to the conclusion on the secular flattening of the Cassiopeia A radio spectrum made in [7, 9, 10]. 7 Conclusion As a result of long-term (1977-2002) measurements of the radio flux density of Cassiopeia A relative to Cygnus A at 927 and 151.5 MHz using a single radio telescope (radio interferometer) at a given frequency, we have found the following mean secular decrease rates of the radio flux of Cassiopeia A: d927 MHz (1977−2002) = −(0.72 ± 0.03)% year−1 , d151.5 MHz (1980−2002) = −(0.88 ± 0.09)% year−1 . 146 E. N. Vinyajkin, V. A. Razin Our values of d obtained by the measurements during the last 25 years are substantially less by the absolute value than the values d(151.5 MHz) = −(1.22 ± 0.05)% year−1 and d(927 MHz) = −(0.98 ± 0.04)% year−1 which follow from the formula (4) [7]. This indicates to the slowdown of Cassiopeia A radio emission secular decrease. In addition to this large scale time variation of Cassiopeia A flux density the observations have also shown a small scale (a few years) time variations over the smooth secular decrease. Acknowledgement. This work has been supported by the International Science and Technology Center under the ISTC project No. 729. References Vinyajkin E. N., Razin V. A.: Australian Journal of Physics 32, 93 (1979) Vinyajkin E. N.: Astronomical and Astrophysical Transactions 11, 325 (1996) Vinyajkin E. N.: Astrophys. and Space Sci. 252, 249 (1997) Parker E. A.: Mon. Not. R. Astr. Soc. 138, 407 (1968) Read P. L.: Mon. Not. R. Astr. Soc. 178, 259 (1977) Agafonov M. I.: Astron. Astrophys. 306, 578 (1996) Baars J. W. M., Genzel R., Pauliny-Toth I. I. K., Witzel A.: Astron. Astrophys. 61, 99 (1977) 8. Reichart D. E., Stephens A. W.: Astrophys. J. 537, 904 (2000) 9. Dent W. A., Aller H. D., Olsen E. T.: Astrophys. J. 188, L11 (1974) 10. Vinyajkin E. N., Razin V. A., Khrulev V. V.: Soviet Astronomy Letters 6, 324 (1980) 1. 2. 3. 4. 5. 6. 7. Self-Consistent Model of Ions and Electrons Acceleration at Shock Wave Front in Supernova Remnant G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko RFNC-VNIIEF, 607190, Sarov, Nizhni Novgorod region Summary. The present work cites the approach (based on [5, 7]), which allows a self-consistent computing of spectral and temporal/spatial characteristics of the accelerating ions and electrons, as well as the motion of the plasma that accelerates the particles at different stages of SN shell expansion. It is also describes the numerical method, which was developed specifically for resolving of the respective equations system. The examples of the method use are given. 1 Introduction Presently, Fermi mechanism of charge particles (ions and electrons) acceleration at the shock wave front, which is formed in the area of Supernova (SN) blast during its shell expansion, is considered to be one of possible effects leading to cosmic rays formation [1]. The same mechanism [2, 3] is considered to be responsible for filling of the SN area with relativistic electrons. In the work [4] it is given an overview of qualitative approaches to the ions acceleration problem that are based on the aforementioned mechanism. In the later work [5] it is described an example of the respective quantitative model development and use: obtaining and numerical solution of the equations, which describe the shock wave motion caused by SN shell expansion, the ions acceleration at the shock wave front, as well as accounts for the influence of the accelerated ions on the shock wave motion and structure. In order to address the electrons acceleration problem, rougher approaches are used (e.g. see [6, 7]), where the shock wave dynamics and the effect of its modification by accelerating ions either are not considered [6], or described in terms of a qualitative model [7]. 148 G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko 2 Physical Model The physical model, which is used for the plasma parameters description, is considered in more detail in the paper on the turbulent mixing development that is to be presented at this Conference [8]. The aforementioned model describes the SN shell expansion; its interaction with the stellar atmosphere and magnetic field; formation and motion of the shock waves in SN shell [9]; spectral radiation transport; and “gravitational” turbulent mixing of the plasma layers. The plasma motion is considered to be spherically symmetrical. In the present work, as well as in [5, 7], in order to describe the parameters of the “shell” and “atmosphere”, is used the approximation of “ideal” gas dynamics though with account for the influence of the cosmic rays on the plasma motion. So, let us write down that: ρ du = −∇ (P + Pc ) , dt (1) where Pc is the pressure of cosmic rays Pc = Pci + Pce. (2) . Each of the members in (2) (pressure of each cosmic ray component) is expressed through its ni,e (r, t, p) zeroth moment of the function with the help of the relation [5]. ∞ Pc,α (r, t) = 0 p2 dp nα (r, t, p) p2 1/2 2 p2 + (mα c) (3) In order to describe the ionic component of cosmic rays, we would use the spectral diffusion equation [4, 5] in a Lagrangian form: dϕi ∂Ji dΩ 1 ∂ϕi = − p + Qp,i Ω dt ∂m dt 3 ∂p (4) where ϕi = ni Ω, Ω = 1/ρ; Ji = ki (∂ni /∂r), ki = ki (p, r, t) is the diffusion coefficients, Qp,i (r, t) — ion source [4, 5]. Similar equation was used as the initial one for finding the electrons distribution function. The diffusion coefficient kp,e and the “source” Qp,e were preset in compliance with [7]. 3 Numerical Method Resolving of the aforementioned system of equations was fulfilled numerically using the method [10], which was developed previously for solution of radiation gas dynamics equations. Self-Consistent Model of Ions and Electrons Acceleration 149 This method is based on the ideology of “splitting” by physical processes. In order to resolve gas dynamics equations, it was used the implicit and conservative scheme with “artificial viscosity” (Richtmeier, Neiman). In order to resolve the radiation transport equations (considered in the spectral diffusion approximations), it was used the “running” method (“sweep”). To adapt the aforementioned method to the problem considered in the present paper, it was required to introduce additional members into the radiation transport equation namely two of the last members from the equation (4). Besides, when writing down the sources Qe and Qi , it was necessary to take into consideration “smear” of the shock wave front over the width of the computational grid cell h. In order to compute the distribution function of ions, for which the diffusion length ki /u h it was introduced into the source Qi co-multiplier q instead u1 Ωδ (r − Rf ) (see [5]), where qi (r, t) = max −Ω̇, 0 . (5) Such qi (r, t) allows calculating both ”direct” and “reverse” shockwave [9] including a natural transition to the case of a “weak” shock wave. As for the electrons, the situation is more complicated. As is known [7], the electrons are accelerated in the area of the shock wave front precursor and at the front itself. For those parameters of the problem, for which the front structure is modified to such extent that the gas dynamic discontinuity (i.e. the shock wave front) either is absent or becomes weak, it is possible to simply neglect the diffusion member in the equation for np,e . In those cases, when the discontinuity exists and contributes considerably into the electrons acceleration, the computation of the diffusion member in the equation for np,e using the replacement of the discontinuity with the front of a finite width might lead to the distortion of the electrons spectrum [4]. Considering the aforementioned along with the stability requirement to the monotonicity, the equation for np,e was resolved with account for the diffusion member, while using the “effective” diffusion coefficient: ke = ch . 3 (6) 4 Example of Calculation In order to illustrate the capabilities of the aforementioned method, let us consider the problem of the ions and electrons acceleration at the front of the shock wave, which is exited by a planar piston with a preset motion law in a uniform environment. Let us choose the environment parameters on analogy with [5], i.e. the magnetic field H1 = 10−5 oersted, the density ρ1 = 10−24 g/cm3 , the temperature T1 = 102 eV, the velocity u1 = 0. Supposedly, the ”piston” (i.e. SN shell) 150 G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko velocity is u2 = 108 cm/s. Besides, let us adopt the ions diffusion coefficient in the following form (in compliance with [5]): ki (p, ρ) = ρB c ρ0 , 3 ρ (7) where ρB is the larmor radius of an ion with the impulse p that was defined based on the unperturbed magnetic field H1 . In accordance with [7], the electrons diffusion coefficient ke is ∼ 1020 cm2 /s, which corresponds to the diffusion length ke /u2 ∼ = 1011 cm. Such scale is very small as compared with the characteristic size of the problem. Therefore, coming out of the above mentioned arguments described in i.2, it was understood that: hc ke = , (8) 3 where h is the characteristic size of the computational cell. Presumably, at the initial moment there were no accelerated particles in front of the piston in the medium, i.e.: ni (p, r, 0) = ne (p, r, 0) = 0. (9) The boundary conditions for gas dynamics were preset as follows: u (x, t)|x=u2 t = u2 ; u (x, t)|x=x2 = 0, (10) (11) where x2 is the “right” boundary of the computational area implying x2 u2 t. There were chosen the following boundary conditions for the diffusion equations: ni,e (p, t, x2) = 0; ∂ni,e (p, t, x2) = 0. ∂x x=u2 t (12) (13) We regarded medium as ideal gas with γ = 5/3. “Sources” in equations for ni,e were preset in mode analogous [5]: Qi,e (p, x, t) = η δ (p − pinj ) ρ qi 4πp2inj mi (14) where pinj is the momentum of the injected particles. Assuming pinj = 2 × 10−2 mi.e c, it was varied the dimensionless parameter η, which characterizes the injection tempo [5]. The computational results are shown below in figures. There were introduced the following scales: density — ρ1 , velocity — u2 , pressure — ρ1 u22 = p1 , Self-Consistent Model of Ions and Electrons Acceleration 151 time t1 = 1 year, distance — x1 = u2 t1 , momentum — πi,e = mi,e c, the dis3 tribution functions were considered as dimensionless over Ni,e = (πi,e ) /n1 , n1 = ρ1 /mp , mp — proton mass. Some results of the computation are presented below. Time dependence of total gas dynamic energy εg and energy of cosmic rays (CR) εCR are characterized with Table 1. As seen, the gas dynamic energy εg and normalized CR energy εCR / (ηεg ) are decreasing when injection coefficient η is increasing. Table 1. Time dependence of the energy components εg t η = 10−4 0.4×102 0.180×103 0.320×103 0.459×103 0 100 200 300 εCR η = 10−2 0.4×102 0.145×103 0.227×103 0.306×103 η = 10−4 0 0.85 0.261×101 0.461×101 η = 10−2 0 0.54×102 0.124×103 0.190×103 The profiles of CR density nCR before the piston for different values of η and t are shown in Fig. 1. As seen, this function weakly depends on η, x and t. There is CR pressure PCR for η = 10−4 and 10−2 in Fig. 2. Its profiles are similar to profiles of the CR density. The saturation of η — dependence begins to be noticeable when η = 10−2 . 1.40E-04 a n 1.20E-04 1.00E-04 8.00E-05 6.00E-05 4.00E-05 2.00E-05 0.00E+00 0. 100. 200. 300. 400. x 500. 1.00E-02 9.00E-03 8.00E-03 7.00E-03 n b 6.00E-03 5.00E-03 4.00E-03 3.00E-03 2.00E-03 1.00E-03 0.00E+00 x 0. 100. 200. 300. 400. 500. Fig. 1. The integral density of CR, ki = 10, solid lines — t = 100, dashed lines — t = 300: (a) — η = 10−4 ; (b) — η = 10−2 An effect of CR on the gas dynamics is illustrated in Fig. 3. Notice that total pressure P = Pg + PCR depends on x very slightly. Spectrums of the CR are shown in Figs. 4, 5. The function f(x0 , p, t) ≡ n(x0 , p, t)p4 is presented here for Lagrangian point x0 = 5. This function for 152 G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko 1.20E+00 3.50E-02 n n a 3.00E-02 b 1.00E+00 2.50E-02 8.00E-01 2.00E-02 6.00E-01 1.50E-02 4.00E-01 1.00E-02 2.00E-01 5.00E-03 x 0.00E+00 0. 100. 200. 300. 400. x 0.00E+00 0. 500. 100. 200. 300. 400. 500. Fig. 2. The pressure of CR, ki = 10, solid lines — t = 100, dashed lines — t = 300: (a) — η = 10−4 ; (b) — η = 10−2 9.00E-01 1.60E+00 n a 1.40E+00 n 8.00E-01 b 7.00E-01 1.20E+00 6.00E-01 1.00E+00 5.00E-01 8.00E-01 4.00E-01 6.00E-01 3.00E-01 4.00E-01 2.00E-01 2.00E-01 1.00E-01 x 0.00E+00 0. 100. 200. 300. 400. 500. 600. x 0.00E+00 0. 700. 100. 200. 300. 400. 500. 600. 700. Fig. 3. The gas dynamics pressure of CR, ki = 10, solid lines — t = 100, dashed lines — t = 300: (a) — η = 10−4 ; (b) — η = 10−2 0.00E+00 -1.00E+00 -2.00E+00 0.00E+00 0. 5. lg f 10. 15. 20. 25. -1.00E+00 -2.00E+00 -3.00E+00 -3.00E+00 -4.00E+00 -4.00E+00 -5.00E+00 -5.00E+00 -6.00E+00 -6.00E+00 -7.00E+00 -7.00E+00 -8.00E+00 -9.00E+00 0. 5. lg a 10. 15. 20. 25. b -8.00E+00 p -9.00E+00 p Fig. 4. The CR spectrum, ki = 10, solid lines — t = 100, dashed lines — t = 300: (a) — η = 10−4 ; (b) — η = 10−2 ions appears near constant, when t increase and η decrease. The spectrum of electrons decreases more noticeable when p increases. Additional data about effects of CR on shock structure (velocity profiles) are presented on Fig. 6. It’s seen that precursor appears in case η = 10−2 . Self-Consistent Model of Ions and Electrons Acceleration 0.00E+00 1.20E+00 0. -2.00E+00 153 5. 10. 15. 20. V 25. lg f 1.00E+00 -4.00E+00 8.00E-01 -6.00E+00 6.00E-01 -8.00E+00 4.00E-01 -1.00E+01 2.00E-01 -1.20E+01 -1.40E+01 p Fig. 5. The CR spectrum, ke = 0.1, solid lines — t = 100, dashed lines — t = 300 for η = 10−2 0.00E+00 400. x 410. 420. 430. 440. 450. Fig. 6. The gas velocity for ki = 10, t = 300, solid curve — η = 10−4 , dashed curve — η = 10−2 Conclusion The main result of the work consists on development method for through computation of CR acceleration. We plan use this approach for more realistic computation in future. Acknowledgement. This work was supported by ISTC (project #729). References Astrophysics of cosmic rays, ed. by V.L. Guinzburg (Nauka, Moscow, 1984) V.L. Ginzburg: Theoretical physics and astrophysics (Nauka, Moscow, 1975) I.S. Shklovski: Stars: their development life and death (Nauka, Moscow, 1984) E.G. Berezhko, G.F. Krymsky: Sov. Phys. Uspekhi 154 (1), 49 (1988) E.G. Berezhko, V.K. Elshin, L.T. Ksenofontov: ZhETF 109 (1), 3 (1996) L. Ball, J.G. Kirk: Astron. Astrophys. 303, 57 (1995) P. Duffy, L. Ball, J.G. Kirk: Ap. J. 447, 364 (1995) G.V. Dolgoleva, E.A. Novikova, V.P. Statzenko, V.A. Zhmailo: Proc.of the Conf. “Supernovae (10 years of SN 1993)” 9. R. Chevalier: Ann. Rev. Astron. Asrophys. 15, 175 (1977) 10. G.V. Dolgoleva: VANT (Problems of Atomic Science and Technology), Series “Methods and codes for numerical resolving of mathematical physics problems” 2 (13), 29 (1983) 1. 2. 3. 4. 5. 6. 7. 8. Development of Turbulent Mixing Semi-Empirical Model for Calculating MHD Parameters of Supernova Remnant G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko RFNC-VNIIEF, 607190, Sarov, Nizhni Novgorod region Introduction Presently, there are a lot of works dedicated to resolving radiation gas dynamic equations that describe Supernova (SN) shell expansion and interaction with the surrounding atmosphere. The effects defining such interaction are rather complicated and used to be considered within the framework of the simplest 1D spherical geometry [1, 2]. Such approximation is adequate only for considering stable laminar flows. However, SN shell deceleration leads to the development of Rayleigh-Tailor instabilities and further to turbulent mixing (TM) of the plasma layers. Typically, TM effect is simulated directly using 2D [3] or 3D [4] numerical methods. However, their accuracy and convergence require additional research. On the other hand, many problems on TM may be solved using different semi-empirical models, e.g. a “k − ε” model [5, 6] is used to calculate TM in laser fusion targets [7]. Our consideration of TM effects on MHD parameters of SN remnant is based upon such model. 1 Basic Equations The problem under consideration is characterized by the following two essential features (as compared to the problems on TM in hydrodynamics), namely: 1) plasma, where this mixing occurs, is collisionless; In the present work (coming out of [8], it is supposed that the “kinetic” instability is less significant for averaged plasma parameters than hydrodynamic instabilities; 2) plasma turbulence is accompanied by the development of magnetic field turbulent pulsations. 156 G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko The equations of magnetic radiation gas dynamics are taken for the basic ones [9, 10]. Using conventional [11] methods of statistical averaging of these equations and general expressions for the members, which contain momenta of the third and higher order, as well as several assumptions on the magnetic field and the related correlation functions, it is possible to obtain quite a general system of equations cited in [11]. The equations for averaged values are similar to standard 2T ideal MHD equations, but differ in some points. First. Because of TM additional members Qit and div J appear in the equation of ion energy, where Qit and div J where Qit = ρε; J - the ”turbulent” heat flow; ε is the rate of turbulent energy dissipation. In the electron energy equation we have to account for the ”joule” heating of electrons Qet = j 2 /σt , where σt is the turbulent conductivity. Second. The TM influences on averaged magnetic field as diffusion. To describe it we use equations (let toroidal component Hϕ = 0) Hϕ = rρg, where dg 1 (1) = div (ρDg ∇g) , dt ρ Dg is semi-empirical coefficient. Similar equations are used for magnetic potential in case of two-dimensional field. Third. The equations of state have the following form: pi,e = pi,e (Ei,e , cα , ρ), where pi,e means the preset functions, cα denotes the concentrations of different substances in the considered mixture. The diffusion equations are used to calculate cα . Dc is the coefficient of the turbulent diffusion - we assume below Dg = Dc . Fourth. The plasma motion excites the magnetic field pulsations. The equations for the mean-square characteristics of these pulsations might be obtained by way of combining the equations for the magnetic field perturbations, as well as density and velocity perturbations. A final form of such equations will depend upon a considered magnetic filed configuration. In case of a two-dimensional configuration, the magnetic filed should not violate the plasma motion symmetry. Therefore, with respect to ”equatorial” plane of the problem, it is possible to obtain the following: d πθθ 2λrθ ∂Hθ dπrr 2 =− 2 (2) ; = 0; πϕϕ ≡ (ρr) gϕϕ ; dt ρ2 ρ ∂r dt 2 dgϕϕ g ∂g ∂g k + (gσ − gϕϕ ) , (3) = 2Dc + dt ∂r r ∂r Dc where πrr = hr hr , πϕϕ = hϕ hϕ , πθθ = hθ hθ , σ ≡ ρ /ρ2 , hi is the component of the perturbed magnetic field, λrθ = hθ ur . The last function is defined with the help of equations that contain the correlation functions hθ ρ and ur ρ . Their quasi-steady-state approximation allows expressing of λrθ through the derivatives of ρ, H and V . So, to close the system (1)-(3) we used k − ε model in form [5, 6]. The equations for k and e are derived as a result of a certain generalization of the 2 Development of Turbulent Mixing Semi-Empirical Model 157 respective equations [6, 7] towards the problems with magnetic field [11]. Notably, accounting for magnetic filed pulsations requires a considerable widening and complication of the correlation functions equations. In the present work we will be limited with the problems, where it is possible to neglect the influence of the magnetic filed pulsations upon pulsations of the other gas dynamic values. So, as regards this particular approximation, the equations for k and preserve the form [6, 7], but presence of the magnetic field leads to appearing the Lorenz force in generation terms [5, 6]. 2 Computational Results Using the numerical method [7, 12], it was resolved the model problem of SN shell expansion and its interaction with the “atmosphere” and magnetic field. = 1.4M, full energy was E = 1051 erg. We assume the shell mass M At t0 = 1 year the main portion of the outburst star flies out freely (velocity profile is linear): the internal layer (He) has a constant density, while in the external layer (H) the density profile changes in a power-mode manner. The profiles of gas dynamic values at t t0 were obtained from the overview [13], whose data were used in [14]. Parameters of the “star wind” were chosen in accordance with [15]. MHD effects were calculated based on the standpoint that the magnetic field from the very beginning has only the “azimuthal” component, while the value g was taken as uniform. Besides, it was taken into account the field extrusion from the shell at t t0 . There were calculated the “ideal” gas equations of state for electrons and ions. Presumably, the ions and electrons temperature relaxation occurred due to the collisional mechanism [10]. As a result of the calculation, the data were obtained on spatial and tem ϕ = Hϕ /Hϕ(t0 ) (the poral characteristics of the gas dynamic values and H magnetic field component in the “equatorial” plane), as well as the meansquare pulsations of the velocity, density and magnetic field. They are shown in the Fig. 1(left), Fig. 2(left), and Fig. 3(right) at the time moments t = 10, 100 and 1000. The Fig. 1(right) represents He mass fraction at the time t = 1000. The TM effect is also obvious here. In the figures the following scales are used: the time t0 = 0.2 year, velocity V0 = 5 × 109 cm/s, density ρ0 = 10−24 g/cm3 . Expression for density pulsations follows from [16] in quasi-stationary approach with coefficients a = 0.6, κ = 0.45, b = 0.085, cD = 0.12: σ≡ 108b3 cD2 ρ 2 ≈ 2 ρ aκc2D kρ2 ∂ρ ∂r 2 , c = 1 + 1/κ + 1/3 − b . 3b 158 G.V. Dolgoleva, V.A. Zhmailo, E.A. Novikova, V.P. Statzenko 1 2 3 6 0.9 0.8 5 0.7 0.6 4 D lg U 0.5 3 0.4 0.3 2 0.2 1 0.1 0 0.5 1 lgr 1.5 0 2 92 94 96 98 100 102 r Fig. 1. (Left) Density profiles at t = 10 (1), 100 (2), 1000 (3); (Right) Profile of He mass fraction at the time t = 1000 0 0 -3 -0.5 -1 -4 -1.5 -5 -0.5 lg H -1 M -2 -6 -2.5 -1.5 lg H -7 -3 lg k M -3.5 0.4 -2 -8 0.6 0.8 1 1.2 1.4 lgr 1.6 1.8 2 -9 -2.5 -10 -3 -3.5 0.4 -11 -12 0.6 0.8 1 1.2 lgr1.4 1.6 1.8 0.5 2 1 lgr 1.5 2 Fig. 2. (Left) Profiles of magnetic field (Hϕ ), parameters of Fig. 1(left); (Right) Turbulent energy profile, parameters of Fig. 1(left) 0 0 -2 -2 lg V -4 -4 lg SMM -6 -6 -8 -8 -10 -12 -10 0.5 1 lgr 1.5 2 2.5 0.5 1 lgr 1.5 2 2.5 Fig. 3. (Left) Relative square of density pulsation, parameters of Fig. 1(left); (Right) Relative square of magnetic field pulsation, parameters of Fig. 1(left) Formula for the magnetic field pulsations follows from (2)—(3) in quasistationary approach: Development of Turbulent Mixing Semi-Empirical Model πϕϕ 2D2 = Hϕ2 k ∂g ∂r 159 2 + g ∂g + σ. r ∂r Conclusion It is formulated the system of equations describing MHD parameters of the flow, which appears as a result of SN shell expansion, with account for the “gravitational” turbulent mixing effects. These equations were numerically resolved, in order to obtain temporal and spatial characteristics of the main MHD functions and their mean-square fluctuations. A more detailed analysis of these results will be fulfilled later. The authors would like to acknowledge the contribution of G. Shargunova into the issuance of the present paper. Acknowledgement. This work was done under support of ISTC project #729. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. J. Raymond, D. Cox, B. Smith: Ap. J. 204, 290 (1976) W.J. Lyerly, S.P. Reynolds, K. Borkovsky et al: American ASM 188 (1996) Jun Byung-Il, M.L. Norman: Ap. J. 465, 800 (1996) D. Balsara, R. Benjamin, D. Cox: Ap. J. 536 (2), 800 (2001) V.A. Andronov, S.M. Bakhrah. E.E. Meshkov et al: DAN USSR 264 (1), 76 (1982) Yu.V. Yanilkin, V.V. Nikiforov, Yu.A. Bondarenko et al: 5rd International Workshop on the Physics of compressible turbulent mixing, Stony Brook, USA, 1995 V.A. Andronov, S.A. Belkov, A.V. Bessarab et al: ZhETF 3, 882 (1997) B.B. Kadomtzev: Collective phenomena in plasma (Nauka, Moskow, 1988) L.D. Landau, E.M. Lifshitz: Uniform media electrodynamics (Nauka, Moskow, 1962) Ya.B. Zeldovich, Yu.P. Reizer: Physics of shock waves and high temperature gas dynamic phenomena (Nauka, Moscow, 1967) E.V. Gubkov, V.A. Zhmailo, Yu.V. Yanilkin: Presentation for the VIII Seminar on Turbulent Mixing of Compressible Media, 8th IWCTM, Pasadena, USA, 2001 G.V. Dolgoleva: VANT (Problems of Atomic Sci. & Tech.), Ser. “Methods and Codes for Num. Resolving of Math. Phys. Problems” 2 (13), 29 (1983) V.S. Imshennik, D.K. Nadezhin: Sov. Phys. Uspekhi 156, 9 (1988) B.I. Jun, M. Norman: Ap. J. 465, 800 (1996) R. Chevalier: Ap. J. 259, 302 (1982). Statsenko V.P.: VANT (Problems of Atomic Sci. & Tech.), Ser. “Theoretical and Applied Physics” 3, 25 (1996). Magnetohydrodynamic Models for the Structure of Pulsar-Wind Nebulae Stephen P. Reynolds North Carolina State University,Raleigh, NC 27695, USA; steve reynolds@ncsu.edu Summary. The Crab Nebula is well-described at optical wavelengths and above by a steady-state magnetohydrodynamic model due to Kennel and Coroniti (1984). Can this class of model describe other pulsar-wind nebulae? I exhibit simple generalizations of KC models, for various values of σ, the ratio of magnetic to particle flux input at the wind shock. I calculate the evolution of the electron spectrum and synchrotron emissivity in the nebula assuming spherical symmetry, a steady state, and a purely toroidal magnetic field. Emission profiles depend on the initial magnetic field B0 , the electron spectral index s, and the angle of the toroidal axis with the line of sight, φ. I show integrated spectra and radial profiles for various cases, along with predicted variations of photon index Γ with radius in X-rays. Most models predict much smaller sizes in X-rays, and curves of Γ (r) which do not resemble observations. Further elaborations of the dynamics of PWNe seem necessary. 1 Introduction Pulsar-wind nebulae (PWNe) are bubbles of relativistic particles and magnetic field inflated by a pulsar, forming center-brightened radio and X-ray sources of synchrotron radiation [1, 2, 3, 4]. Most early work on PWNe assumed they were surrounded by shell supernova remnants (SNRs), seen or unseen, and interacted with the interior of those remnants. Before the passage of a reverse shock, the PWN would expand into unshocked ejecta in the SNR interior; afterwards, it would be compressed by the reverse-shock passage and expand much more slowly into the thermalized, shocked ejecta [2]. The most elaborate early model for the high-energy (optical and above) emission from PWNe was that of Kennel & Coroniti [3, 4] who solved the steady-state relativistic MHD equations in spherical symmetry with an azimuthal magnetic field to obtain velocity and density profiles of the outflowing relativistic material. They showed that a strong (high compression) MHD shock required a fluid dominated by particles, not magnetic field, as parameterized by σ ≡ (B/4π)/nγ 2 βmc2 , the ratio of magnetic (plus electric) energy flux to particle flux just upstream of the wind shock. Here n is the comoving 162 Stephen P. Reynolds density and γ the flow Lorentz factor. Applying the Rankine-Hugoniot jump conditions at the wind shock (radius rs ) showed that unless σ 1, the postshock fluid would remain at high speed, within a factor of 3 of the upstream (relativistic) speed – clearly inconsistent with the observed expansion of the Crab Nebula at v ∼ 2000 km s−1 . Behind the shock, pure flux-freezing meant that the toroidal magnetic field strength evolved as B ∝ ρr, with ρ the matter density. Kennel & Coroniti [4] were able then to follow the evolution of electron energies and predict both the integrated spectrum and the brightness profile of remnants. They specialized to the Crab Nebula and showed calculations primarily for that case. They were able to describe the optical through hard X-ray spectrum well, as well as the gross variation of nebular size with X-ray energy (“size” being typically the FWHM of emission measured with relatively crude imaging instruments). However, the high value of preshock Lorentz factor of the wind they found (γ ∼ 106 ) made it difficult to explain the radio emission which requires much lower energies, and more electrons, than would be produced by thermalizing this extremely relativistic wind. Since the advent of the newer generation of X-ray telescopes, beginning with ASCA and continuing with the Chandra X-ray Observatory and XMMNewton, we have seen an explosion in the number and variety of PWNe in X-rays, and have observed a much wider range of morphological type. It is of interest to ask if the class of steady-state MHD models proposed by KC can be generalized appropriately to describe other PWNe, and if not, to get an idea of what kind of extensions might be necessary. This is the project described in this paper. One major problem in modeling several larger, fainter PWNe such as 3C 58 [5] appears in comparing radio and X-ray images. In Kennel & Coroniti’s model for the Crab, synchrotron losses on outflowing particles cause the nebular size to decrease with frequency at optical and higher frequencies. In fact the Crab is considerably smaller at optical than radio frequencies, and continues to diminish in size roughly as R ∝ ν −0.15 up to 40 keV [6]. However, 3C 58 shows X-ray emission extending to near the edges of the radio emission, though it is faint there (Slane, private communication). These results call into question the MHD picture of transport of particle energy and magnetic flux throughout the volume of a PWN. It is straightforward to show from the MHD equations [3] that postshock flow solutions have accelerating and decelerating branches, with the latter beginning at v0 = c/3 and initially decelerating as r −2 (pure hydrodynamic, isobaric flow; magnetic energy is unimportant since σ must be small to fit the outer nebular boundary conditions). However, in this case B ∝ ρr ∝ 1/rv ∝ r, so the magnetic energy rises until it becomes dynamically important, slowing the deceleration and causing the velocity to approach a constant value, with B → 1/r. The full hydrodynamic solution can be well approximated by a simple analytic form: defining u ≡ v/v0 , u(r) = 1 (1 − u∞ ) + u∞ , r2 (1) Magnetohydrodynamic Models for the Structure of Pulsar-Wind Nebulae 163 where the asymptotic velocity is v∞ /c = σ/(1 + σ) (Fig. 1). Fig. 1. Solid lines: σ = 0.001. Dashed lines: σ = 0.0032. Dotted lines: σ = 0.01. Dot-dashed lines: σ = 0.032. 2 Particle evolution and luminosity calculation Electron energies E evolve due both to radiative and adiabatic losses: Ė = (dE/dV )(dV /dt) − aB 2 E 2 , where for synchrotron losses a = 1.57 × 10−3 cgs. This equation can be integrated to give [4, 7] E(t) = E0 α1/3 E0 α1/3 2 = 2 1/3 aB0 r0 −8/3 −10/3 1 + aE0 B α dt 1 + E0 u dz z v0 (2) where α ≡ ρ/ρ0 , z ≡ r/r0 , and u ≡ v/v0 . The quantity Ef ≡ (aB02 r0 /v0 )−1 is a “fiducial energy”, that an initially infinitely energetic electron would have after radiating in a field B0 for a time r0 /v0 (basically a parameterization of B0 ). From this result, the evolution of an arbitrary distribution can be calculated: 2 4/3 ρ dE0 dV0 dE0 E0 . = N (E0 (E)) α = N (E0 (E)) N (E) = N (E0 ) dE dV dE E2 ρ0 (3) Given the approximate dynamics above, the electron distribution and synchrotron emissivity can be calculated numerically at each radius. If magnetic field lines are circles in an equatorial plane, an elementary rotation can give brightness profiles as a function of aspect angle φ between the polar axis and the line of sight. The synchrotron emissivity was integrated numerically to generate the brightness profiles shown above, for an injected flat power-law N (E) = KE −s with s < 2 as deduced from observed PWN radio spectra. The flat spectra cause a “bump” to appear just below the high-energy cutoff that appears as a result of radiative losses. 164 Stephen P. Reynolds Fig. 2. Flat-spectrum, high-σ case: s = 1.0, σ = 0.01, Ef = 910 erg, and Emin = 10−5 erg. From left to right, lines show the spectrum and emissivity at five radii (outside in): r/r0 = 10, 8, 6, 4, 2. Fig. 3. Same parameters as above. Note curvature of the integrated spectrum due to the energy-loss “bump”. The solid line on the right is the 1–10 keV photon index; the profiles are for aspect angle φ = 0◦ (B in the plane of the sky). Fig. 4. Steeper-spectrum, low-σ case: s = 1.5, σ = 0.001, Ef = 9.1 × 105 erg, and aspect angle φ = 90◦ . Magnetohydrodynamic Models for the Structure of Pulsar-Wind Nebulae 165 3 Conclusions Steady-state MHD models of pulsar-wind nebulae can be well approximated by a simple velocity law, which then dictates the evolution of the injected electron distribution and the integrated spectrum and profile of emission, depending on σ. Spectral properties also depend on B and spectral index s. Varying the aspect angle changes the flux normalization but has no effect on the integrated spectrum and little on the profile shape at photon energies for which losses are important. For very flat injected spectra (s ∼ 1), the effects of the energy-loss “bump” are significant, causing concave-up curvature over a broad frequency range. The models are in significant conflict with the observed radial dependence of photon index Γ in X-rays (e.g., G21.5-0.9 [8]), which appears roughly linear with r. All models drop in size by at least a factor 2 between radio and X-rays, but some observed PWNe do not show this. Unless magnetic-field strengths are unrealistically low, most X-ray profiles have HWHM radii only 3–6 times the injection radius – also perhaps at odds with observations. We conclude that there are significant discrepancies between the predictions of the simple MHD models and X-ray observations of PWNe. Nonsteady or nonspherical flows, and/or electron transport by diffusion as well as convection (e.g., [9]), may be necessary to explain the observations. References 1. 2. 3. 4. 5. 6. 7. 8. 9. K.W. Weiler, N. Panagia: Astron. Astrophys. 90, 269 (1980) S.P. Reynolds, R.A. Chevalier: Astrophys.J. 278, 630 (1984; RC84) C.F. Kennel, F.V. Coroniti: Astrophys.J. 283, 694, (1984) C.F. Kennel, F.V. Coroniti: Astrophys.J. 283, 710 (1984) K. Torii, P.O. Slane, K. Kinugasa et al: Pub. Astron. Soc. Japan 52, 875 (2000) W. Ku, H.L. Kestenbaum, R. Novick et al: Astrophys.J. 204, L77 (1976) S.P. Reynolds: Astrophys.J. 493, 375 (1998) P.O. Slane, Y. Chen, N.S. Schulz et al: Astrophys.J. 533, L29 (2000) S.P. Reynolds, F.C. Jones: Proc. 22nd ICRC (Dublin), 2, 400 (1991) Part VI Cosmology Critique of Tracking Quintessence Sidney Bludman Deutsches Elektronen-Synchrotron DESY,Hamburg University of Pennsylvania, Philadelphia; bludman@mail.desy.de Summary. Recent observations show that quintessence, if it exists, must now be ”crawling”, even if it once was tracking. This means that any quintessence field stopped tracking relatively early, that the quintessence potential now has appreciable curvature, so that the equation of state wQ(z) is reducing fast for accessible red-shifts. The observational bound on wQ rejects constant wQ and inverse-power potentials, but allows the SUGRA potential for a range of initial curvature values. 1 The Dark Energy Density is now Exactly or Nearly Static 1.1 Kinematics of the expanding and accelerating Universe Supernovae Ia, weak gravitational lensing, the growth of large scale structure, and angular diameter measurements all directly explore the space-time geometry by measuring the luminosity distance dL(z) = (1 + z)η or the angulardiameter distance dA (z) = η/(1 + z), from which the comoving distance η≡c z dz /H(z ) = c 0 t dt /a(t ) (1) 0 to individual distant supernovae, chosen to be standard candles, or to distant galaxies is inferred. (The conformal coordinate distance to the horizon, η, describes the proper time evolution of the scale factor a.) Assuming a homogeneous and isotropic (Robertson-Walker) flat universe, the Friedmann expansion rate is κ 2 ρ = 3H 2 , where H ≡ ȧ/a. (2) Quantum field theory requires that G be inherently positive, so that we write κ 2 = 8πG ≡ 1/MP , where MP = 2.44e18 GeV is the reduced Planck mass. While quantum theory requires that the total energy density 170 Sidney Bludman ρ in Friedmann’s equation (2) be positive, the derived quantity, the pressure P = −d(ρc2 a3 )/da3 , may be positive or negative. In terms of geometrical quantities, κ 2 P/c2 = −(2Ḣ + 3H 2 ), (3) κ 2 (ρ + P/c2 ) = −2Ḣ = −dH 2 /dN = −(κ 2 /3)(dρ/dN ), (4) the enthalpy is and the over-all barotropic index is 2 γ ≡ −d ln ρ/3dN = (ρ + P/c2 )/ρ = − (d ln H/dN ). 3 (5) Here the logarithm of the cosmological scale factor N ≡ ln a = − ln(1 + z), so that dN = Hdt. This equation of state and its quintessence component do not depend on the Hubble radius H −1 , but on its derivative i.e. not on the comoving distance η, but on dη/dz, d2 η/dz 2 . In cosmologies satisfying the Weak Energy Condition ρ + P/c2 > −1, γ > 0, so that the expansion slows down monotonically. We will not consider alternate gravity theories, such as extra dimensions, in which the Friedmann equation (2) is modified. In cosmology, the scalar curvature R ≡ 6[ä/a + (ȧ/a)2 ] = 6(Ḣ + 2H 2 ) = 6H 2 (aä/ȧ2 + 2) (6) is inherently positive, while the acceleration, äa/ȧ2 = −a · d(H −1 /a)/dt = 1 − 3γ/2, (7) must range from 1 down to −2, for γ ranging from 0 down to 2. At present, P/ρ = wQ ΩQ < −1/3, the expansion of the universe is accelerated. Gravity is attractive when d(1/aH)/dt > 1, repulsive when d(1/aH)/dt < 1. We now know that, until about red-shift z ≈ 0.7, attractive gravity dominated the cosmological fluid. Later, once the expansion rate in equation (5) outpaced the growth of the Hubble radius H −1 , anti-gravity dominated. Because the barotropic index (5) and its quintessence component (13) depend on the first and second derivatives of the comoving distance η, the quintessence evolution wQ (z) depends on first and second derivatives of the observed luminosity distances [1]. In practice, quintessence is appreciable only for small red-shift. This means that, before wQ (z) can be determined, the inherently noisy luminosity distance dL (z) data must be parameterized. For this, and other reasons, along with a large number of high red-shift supernovae, precise knowledge of other cosmological parameters will be needed [4, 3, 2], and can still determine only one or two parameters characterizing the potential, such as wQ0 , (dwQ /dz)0 . Nevertheless, this direct observation of acceleration in the present universe already supports the possibility of an inflationary early universe, which is otherwise not directly observable. Critique of Tracking Quintessence 171 While programs to measure luminosity and angular diameter distances are underway, we already know that we live at a time when w¯Q < −0.78 (95% CL), h ≡ H0 /100 = 0.72±0.05, (8) that the radiation/matter equality took place at red-shift zeq = 3454+385 −392 [7, 12, 8, 9, 5, 10, 6, 11], dark energy began dominating over matter 6.3 Gyr ago, and the cosmological expansion has been accelerating since red-shift zc ≈ 0.7 [13, 6]. The background density, ΩQ0 = 0.71±0.07, ρB = (11.67a + 0.003378)/a4 meV 4 , (9) is now ρB0 = 11.67 meV 4 and was ρBi = 0.003378 GeV 4 at fiducial red-shift z = 1012 . The supernova observations fit an average wQ (z), w¯Q(N ) = N wQ (N ) dN /N. 0 Because the supernova observations average over a small range in z, in which the quintessence field and wQ (z) change relatively little, the fitted w¯Q < −0.78 bound is also an approximate bound on wQ0 . Where necessary, we will fix h2 = 1/2, so that the present critical density and smooth energy density are ρcr0 = 40.5 meV 4 , ρQ0 = 28.8 meV 4 . We will show that these observational constraints (8) already allow only crawling quintessence (Section III) or potentials that are now fast-rolling(Section IV). We go beyond the many earlier treatments of the tracking condition [14, 19, 17, 18, 20, 15, 16] and of inverse power potentials [21, 22], by calculating the post-tracker behavior in the present quintessence-dominated era, to consider the range of initial conditions that would lead to tracking, and to treat the numerical problems encountered in cosmological dynamics, particularly in the freezing and tracking epochs. But first we will review (Section II) the attractor condition, in order to show how the basin of attraction shrinks for potentials satisfying the observational constraints (8). 1.2 Quintessence dynamics The universe is flat, presently dominated by smooth energy, and recently accelerated, since red-shift z 0.5 [13]. Canonical quintessence models the smooth energy dynamically by a spatially homogeneous light classical scalar field, with canonical kinetic energy K = φ̇2 /2, minimal gravitational coupling, zero true cosmological constant, rolling down its self-potential V (φ). With this canonical form, the scalar field equation of motion φ̈ + 3H φ̇ + dV /dφ = 0, has the first integral (10) 172 Sidney Bludman V (N ) = ρQ − dρQ /6dN = ρQ (1 − wQ )/2, (11) where the energy density and pressure are P/c2 = φ̇2 /2 − V (φ), ρQ = φ̇2 /2 + V (φ), (12) and the quintessence barotropic index γQ (N ) ≡ −d ln ρQ /3dN = ((ρ + P/c2 )/ρ)Q ≡ 1 + wQ (13) lies between 0 and 2. A cosmological ”constant” Λ(N ) that satisfies the Weak Energy Condition and decays with time is equivalent to a classical homogeneous scalar field, with kinetic energy K = −dΛ(N )/6dN and potential energy V (N ) = Λ(N ) + dΛ(N )/6dN . Because the scalar field does not cluster on supercluster scales, its Compton wavelength is 300 M pc, so that its mass mQ = d2 V /dφ2 1.5E − 36 meV must be very small. While a scale-dependent cosmological ”constant” would be no more than a kinematic generalization of classical General Relativity, dynamical quintessence also allows spatial inhomogeneities and quantum effects. From the energy integral (12), φ̇2 = 2(ρQ − V ), (κdφ/dN )2 = 6x2 , where 2 x ≡ φ̇2 /ρ = 3γQ ΩQ is the quintessence kinetic energy fraction of the total energy density. The ratio of kinetic/potential energy K/V = (1+wQ )/(1−wQ has the rate of change ∆(N ) − 1 ≡ d ln((1 + wQ)/(1 − wQ ))/6dN . For the roll, we obtain λ ≡ −d ln V /κdφ = 3γQ /ΩQ · ∆, (14) and κdφ/dN = 3γQ ΩQ , 2 dwQ/dN = 3(1 − wQ )(∆ − 1). (15) The total barotropic index is γ = γB ΩB + γQ ΩQ = 1 + wB ΩB + wQ ΩQ , (16) where the dimensionless ratios, ΩQ , ΩB ≡ ρB /(ρ+ρQ ), are the energy density fractions in quintessence and in background, and γQ , γB ≡ −d ln ρB /3dN are their corresponding barotropic indices. Equations (14, 15) are a two-element non-autonomous system for the dependent variables φ, wQ . Integrating equation (14), we obtain an implicit relation N κφ(N ) = 6(ρQ − V )/(ρB + ρQ ) dN, (17) −∞ between φ and V (φ), so that, if the equation of state wQ (N ) can be observed, the potential can be reconstructed. Besides λ, the potential depends on the curvature η ≡ κ 2 d2 V /dφ2 . When the curvature is small, φ̈ is negligible in the equation of motion (10). When the potential is flat ( ≡ λ2 /2 1), the kinetic energy φ̇2 /2 is negligible in the quintessence energy (12). During ordinary inflation, both these conditions Critique of Tracking Quintessence 173 hold (slow roll approximation): the expansion is dominated by the cosmological drag and the field is nearly frozen, (γQ = φ˙2 /ρQ 1, wQ ≈ −1). In quintessence, on the other hand, the acceleration began only recently, so that the roll and curvature may still be appreciable. The slow roll approximation is generally invalid for quintessence, so that the dynamical equations need to be integrated numerically. Because cosmology intrinsically involves very different time scales and phase transitions, the scalar field dynamical equations are inherently stiff. We ultimately handled the kination/freezing and freezing/tracking transitions by an implicit Adams backward differentiation method (Maple lsode(backfull)), with a limited step-size and a very large number of digits. Unless its potential has a false minimum (phase transition), the quintessence field rolls monotonically towards a minimum at φ = ∞ or at some finite φmin : either way, the potentials we consider are always convex (β > 0). We define Γ ≡ V d2 V /dφ2/(dV /dφ)2 ≡ η/2 and Γ − 1 = d(1/λ)/κdφ ≡ 1/β(φ). The first, third and fourth rows in Table 1 list three potentials with constant inverse curvature 1/β = d2 ln V /κ 2dφ2 /λ2 : the cosmological constant, inverse power, and exponential, for β = 0, const ≡ α, ∞ respectively. On √ the second row, where α̃ ≡ γQ /α, the constant wQ model interpolates between the inverse power potential, when α̃κφ 1, and the exponential when α̃κφ 1. The bottom row in Table 1 is the more realistic SUGRA potential, in which β(φ) varies for φ MP . In place of the phase variables φ, wQ ≡ (P/ρ)Q , we may use x(N )2 ≡ 2 φ̇ /2ρ = (κdφ/dN )2/6, y(N )2 ≡ VQ /ρ, for which the equations of motion are [19, 17, 18, 20] dx/dN = −3x + λ 3/2y2 + 3xγ/2 (18) dy/dN = −λ 3/2xy + 3yγ/2 (19) √ 2 √ dλ/dN = − 6λ x/β or d(1/λ)/dN = 6x/β. (20) The overall equation of state of our two-component mixture of background and quintessence, γ = γQ ΩQ + γB ΩB = 2x2 + γB (1 − x2 − y2 ), is a timedependent function of the scalar field φ(N ). Thus, x2 + y2 = ΩQ , 2x2 = ΩQ γQ , x2 /y2 = K/V = (1 + wQ )/(1 − wQ ), d ln(x /y )/dN = 6(∆ − 1). 2 2 (21) (22) (23) (24) The three-element system (20-22)) is autonomous, except for the slow change in γB (N ) from 4/3 to 1, while gradually going from the radiation-dominated to the matter-dominated universe, around red-shift zeq = 3454 . The magnitude of V must be chosen so that the value V0 = ρcr0 y02 = ρcr0 (1 − wQ (0))/2, is reached at present. For example, tracking solutions to 174 Sidney Bludman 1/(4+α) inverse power potentials, require mass scale M = (V0 φα , listed in the 0) penultimate column of Table 2. For α < 0.2, this mass scale is close to observed neutrino masses and to the present radiation temperature, possibly suggesting some role for the neutrino mass mechanism or for the matter/radiation transition, in bringing about quintessence dominance. For larger α values, this mass scale can be considerably larger, suggesting the larger scales we know in particle physics. 1.3 Equation of state and sound speed While the evolution of a homogeneous scalar field depends only on its equation of state wQ = P/ρQ c2 , the evolution of its fluctuations depends also on the effective sound speed c2s = (dP/dφ̇)/(dρQ /dφ̇). With the linear form for the kinetic energy K = φ̇2 /2 that canonical quintessence assumes, c2s = c2 and dwQ/dz > 0. Non-linear forms for the kinetic energy, like k-essence [23], would allow violations of the Weak Energy Condition and give different sound speed and structure evolution . k-essence has the theoretically attractive feature that evolution towards the de Sitter solution wQ = −1 comes naturally out of the radiation-dominated era and predicts dwQ /dz < 0 [24]. Nevertheless, despite this difference in sign of dwQ/dz, k-essence is hardly distinguishable from quintessence, unless c2s ≈ 0 since the surface of last scattering [25]. We will consider only canonical quintessence evolution with the Friedmann expansion rate (2). 2 Attractor Conditions on Quintessence Potentials The quintessence potential enters the equations of motion only through its logarithmic slope or roll λ ≡ −d ln V /κdφ. The existence of a stable attractor also depends, however, on the potential curvature β(φ). Both the slope and the curvature, λ, β are listed in Table I, for five different potentials. In this section, we discuss the instantaneous attractor solution that the equations of motion generally possess, when λ is nearly stationary in equation (?), either because the roll is very slow, λ 1, or very fast, λ 1/β [20]. The first attractor possibility will be realized in the distant future, when quintessence dominates (ΩQ → 1). If the equation of state softens (γQ → 0 wQ → −1), the cosmology will become asymptotically de Sitter. Otherwise, we have the constant wQ model on the second line of Table 1. The second attractor possibility generally existed in the backgrounddominated past, ΩQ << 1, when the Tracking Condition [19, 20, 15, 22, 16] β(φ) ≈ const obtained. Defining λtr ≡ 3γQtr /ΩQ , the tracking condition is λ ≈ λtr or ∆ ≡ λ/λtr = γQ /γQtr ≈ 1. (25) Critique of Tracking Quintessence 175 1 0.8 0.6 y 0.4 0.2 0 0.1 0.2 0.3 0.4 0.5 x Fig. 1. Phaseportraits of attractors for three different quintessence potential forms, moving from red-shift z = 1012 arriving at ΩQ0 = 0.71 now, to become asymptotically de Sitter in the distant future. Each potential has been parameterized to make the roll fast (α = 6) on the right, relatively slow (α = 1) on the left. In the background-dominated era, all attractors are linear (track). As quintessence begins dominating, both (dashed) constant wQ attractors remain linear and remain Friedmann; both (solid) inverse power attractors, starting late, curve slowly towards de Sitter; both (dotted) SUGRA attractors, starting early, curve rapidly towards de Sitter. The shaded trapezoidal region on the upper left is the presently allowed part of phase space. Table 1. Potentials described by roll λ = −d ln V/κ dφ and curvature η = d2 V/V d(κ φ)2 . V (φ) exp −λκφ 1 sinhα (α̃κφ) −α φ const φ−α · exp 1 (κφ)2 2 η(φ) = λ2 Γ λ(φ) λ = const > 3γB (αα̃) coth(α̃κφ) α/κφ 0 α/κφ − κφ λ2 = const > 3γB (αα̃)2 [(1 + α) coth2 (α̃κφ) − 1] α(α+1) (κφ)2 0 (κφ)4 ] [α(α + 1) − α(κφ)2 + (κφ)2 1 β(φ) 0 1 α cosh2 (α̃κφ) Γ −1 = 1/α ∞ (α+(κφ)2 ) (α−(κφ)2 )2 NAME exponential −2 const wQ = (2+α) inverse power cosmological const SUGRA Here the equation of state along the attractor [20], is approximately constant at γB β/(β + 2) as long as the roll is fast. The constant wQ potential is a minimal attractor, for which γQtr remains constant, even after the roll becomes slow. The √ tracking condition (?) requires either fast roll (λ 1) or large curvature ( 6x β). When the curvature is small (β 1), tracking will be poor and stop early, while λ ∼ β is already slow-rolling. Except for the constant wQ model, tracking precedes abruptly out of a protracted frozen state wQ ≈ −1 in the background-dominated era [15]. This necessary freezing comes directly about from undershoot initial conditions ΩQi < ΩQtr . (Indeed, if the initial density ρQi is small enough , the field crawls to its present value ρQ0 , without ever tracking.) But starting from overshoot initial conditions 1 ΩQi > ΩQtr , freezing starts later, only after a kination era, during which (κdφ/dN )2 ≈ 6ΩQ allows φ(N ) to grow rapidly with ΩQ . 176 Sidney Bludman To explain the present smooth energy, tracking must have begun before now and for a broad range of initial conditions, the tracking basin of attraction. This range of initial conditions is bounded: too much overshoot would make the phase trajectories freeze and track only in the future; too much undershoot would make the quintessence energy density start to freeze and crawl early. If the potential is now slow-rolling (λ0 < 1), the attractor can only have been reached early or from a narrow tracking basin of attraction. Indeed, in the static limit (cosmological constant), the present smooth energy arises out of the unique initial condition ρQi = ρQ0 . Figure 1 shows the complete attractor trajectories where x2tr (λ) = ΩQ γQtr /2, 2 (λ) = ΩQ (1 − γQtr /2), ytr ΩQ (λ) = 3γQtr /λ2 < 1, (26) (27) (28) while tracking and while quintessence-dominated, for three potentials (constant wQ (dashed), inverse power (solid), SUGRA (dotted)), all chosen to reach ΩQ0 = 0.71 at the present time. For each potential, the attractor trajectories appear on the left for slow-rolling parameter α = 1, on the right for fast-rolling parameter, α = 6. While tracking in the radiation-dominated era, the softer equations of state γQ = 4/9, wQ = −5/9 have constant potential/kinetic energy ratio 3.5; the stiffer equations of state have γQ = 1, wQ = 0 have constant potential/kinetic energy ratio 1. We stress how the three potential forms evolve differently in the quintessence-dominated era: the constant wQ potential orbits keep their tracker values, the SUGRA potential orbits curve strongly towards the y-axis (cosmological constant, wQ = −1). The presently observed trapezoidal region in phase space marginally allows the α = 1 inverse power potential, but comfortably allows the SUGRA potential for a range in parameter α. The quintessence barotropic index is constant and the field scales in any kination phase (γQ = 2), during freezing (γQ = 0), and tracking, the slope during tracking (γQ = γB β/(β + 2)). During (y/x)tr = (1 − wQ )/(1 + wQ ) gradually increases from 1/2 + 3/β in the radiation-dominated era to 1 + 4/β in the matter-dominated era. Later, as quintessence dominates, this slope steepens significantly. 3 Acceptable Inverse Power Potentials Require Fine-Tuned Initial Conditions 3.1 Tracking solutions scale in the background dominated era For the simple inverse power law potentials V (φ) = M 4+α /φα , (29) Critique of Tracking Quintessence 177 the curvature β = α = constant, so that the equation of motion (?) has solutions that scale exactly in both the radiation- and the matter-dominated eras. As quintessence becomes appreciable, these inverse power trajectories curve towards the x = 0 (asymptotic de Sitter) axis. These inverse power potentials arise naturally in supersymmetric condensate models for QCD or instanton SUSY-breaking [26, 27, 28], but require appreciable quantum corrections when φ MP . The tracker is a fixed attractor for an exponential, but a slow-moving (instantaneous) attractor for α > 1 inverse power potentials. The second column in Table 2 gives the range in tracker values wQtr , from γB α/(α + 2) − 1 = (α−6)/3(α+2), during the radiation-dominated era, to −2/(α+2), during the matter-dominated era. The third column gives the initial ΩQ at z = 1012 , for an attractor solution to evolve to the present ΩQ0 = 0.71. The next five columns, between the two vertical double bars, summarize the post-tracker, present values for inverse power potentials. The observational constraint (?) requires α ≤ 1. Table 2. Tracker and present (ΩQ0 = 0.71) attractor solutions for inverse power potentials. α wQtr log ΩQtri 6 0..-0.25 -10.9 1 -0.555..-0.667 -29.3 0.5 -0.733..-0.80 -35.2 0.1 -0.937..-0.952 -41.9 0 -1 -44.1 M 5.3 PeV 2.3 keV 4.8 eV 12.1 meV 2.5 meV wQ0 -0.41 -0.76 -0.86 -0.97 -1 x20 .210 .083 .049 .011 0 y02 .499 .626 .661 .698 .71 η0 λ0 κφ0 log ΩQi range 2.69 1.519(fast) 3.949 -42..-0.5 1.65 0.908 1.101 -41..-1.5 1.42 0.689 0.73 -42.1..-9.1 1.36 0.351(slow ) 0.285 -42.2..-35.5 0 0 (static) -44.1 The penultimate column tabulates the scalar mass scales needed, in order to reach ΩQ0 = 0.71. For small α, the mass scale needed is small, of the order of the present radiation temperature, and φ0 < MP , so that quantum corrections are still small. For large α, quintessence would have dominated early enough to interfere with structure formation in the matter-dominated era and quantum corrections would now need to be applied [13]. 3.2 Poor Trackers Have Small Basins of Attraction In this sub-section, we extend the original arguments [15] against tracking for α < 5 inverse power potentials, because any tracking quintessence approximates an inverse power potential in its early stages, and because the numerical methods are interesting. For an inverse power potential, λ ∼ V 1/α ∼ (yH)2/α , the third equation (22) integrates to λ = λ0 (yH/y0 H0 )2/α in terms of present values of y, H, λ. Integrating equations (20, 21) then shows (Figure 2), for each of α = 6, 1, the range of trajectories, that will flow onto the present shaded values ΩQ0 = 0.71, wQ ≤ −0.78. All trajectories, sooner or later, reach their attractors, but track only if this happens before quintessence dominance. The last column of Table 2 lists 178 –12 Sidney Bludman –10 –8 –6 –4 –12 –2 –10 –8 –6 –4 –2 0 0 α=6 –12 –10 –8 –6 α=1 –10 –4 log a=-log (1+z) α=0.5 –10 –20 –20 –30 –30 –40 –40 –2 –12 0 –10 –10 –8 –6 –4 log a=-log (1+z) α=0.5 –2 0 –10 –20 –20 –30 –30 –40 –40 Fig. 2. Evolution of quintessence energy density, log ρQ (GeV 4 ) on vertical axes, for four inverse power potentials α = 6, 1, 0.5, 0.1, from red-shift z = 1012 , to the present value ρQ0 = 0.71ρcr0 . In all figures, the central, trajectory is the attractor, starting with tracker slope d ln ρQ/dN = −6γB /(2 + α). The lower curve is the maximal undershoot trajectory, which freezes immediately and then crawls slowly to join the attractor now. The upper curve is the maximal overshoot trajectory, which kinates with slope -6, before freezing late and now reaching the attractor. Poor trackers must freeze early, out of a narrow range in log ρQi. the range of initial ΩQi values at z = 1012 , from which phase trajectories would have frozen and tracked by now. Starting from more undershoot, down to log ΩQi = −42.1, the phase trajectories would stay nearly frozen, crawling to the present value log ΩQ0 = −0.15. The solid curves in Figures 2 show, on the left and right respectively, the limiting trajectories for inverse power α = 6, 1 potentials that start from red-shift z = 1012 and flow onto the attractor by the present. Fast rolling alpha = 6 trajectories, out of a broad basin of attraction, would track by now to wQ0 = −0.41, which is excluded observationally. As α decreases, wQ0 decreases, but the basin of attraction shrinks. For α < 1, the presentlytracking range in initial values of ln ΩQi is already more than fifteen orders of magnitude narrower than the initial range of the good trackers originally proposed [15] for α = 6. For a cosmological constant (α = 0), the present value is realized only if it is initially fixed at its present value ρQ = 28.8 meV 4 . Critique of Tracking Quintessence 179 For inverse power potentials, the observations that wQ is already close to the cosmological constant value −1, would thus require α < 1, so that the energy was always potential dominated (x << y). These relatively slow-roll trajectories never track, but ”crawl” [29] towards their present values, only because they were initially tuned close to these values. We must consider potentials with post-tracker large curvature (small β(N )). 4 Conclusions 4.1 Acceptable potentials must show large curvature now The observations will allow phase trajectories that are presently insensitive to initial conditions, only if the curvature, 1/β(φ), increases rapidly near the present epoch κφ ∼ 1. Table 3. Quintessence potentials which track early, but crawl now. Potential V (φ) Theoretical Origin References M 4 [cos(φ/f) + 1] String, M-theory pseudo Nambu-Goldstone light axion [38, 14, 34, 37] M 4+α φ−α · exp 1 (κφ)β /2 SUGRA, minimum at (κφ)β = 2α/β [26, 27, 28] 2 4 [A + (κφ − κφ )α ] exp(−λκφ) MP Exponential modified by prefactor, m to give local minimum; M-theory [39, 40] For example, the SUGRA models on the last line of Table 1 have minima √ at κφ = α. Far below this minimum, they behave and track like inverse power potentials, but near the minimum, the curvature increases rapidly. This makes the SUGRA phase trajectories, shown by dotted curves in Figure 1 for α = 6, 1, scale in the background-dominated era, but then curve down to lower wQ0 values, in marginal agreement with observations, for a large range in α values. This important post-tracking behavior is illustrated by the popular potentials listed in Table 3. (A longer list of potentials is given in references [32, 31, 33, 30].) These potentials require fine-tuning of their parameters, but may yet be distinguished from true cosmological constants by combined supernova and CBR observations in the next decades [4, 30]. Thus, canonical quintessence requires fine-tuning of initial conditions and/or the functional form of the quintessence potential. 4.2 Outlook We have considered neither models with a true cosmological constant [41], quantum corrections to classical quintessence, k-essence [25, 23], nor large extra dimension or brane cosmology models [36, 35], for which the Friedmann equation is modified at very early times. Within canonical quintessence, two conclusions emerge concerning the attractor solutions to the equations of motion: 180 Sidney Bludman For an early attractor to produce a smooth energy, that is now insensitive to initial conditions, canonical quintessence requires a potential curvature β(φ) that is now changing rapidly, for a wQ (z) that is now fast-changing. Otherwise, dynamical vacuum energy appears hardly distinguishable, theoretically and phenomenologically, from the small cosmological constant it was designed to explain or from a time-dependent cosmological constant. In the second place, the future de Sitter attractor is inevitable, unless wQ holds constant or our decelerating universe reheats and reverts to acceleration. While, in the very early hot universe, ordinary inflation did once end and revert to acceleration, in our late, cool universe, this seems unlikely to happen again. Unless the smooth energy disappears in the future, the de Sitter horizon will have two consequences: (1) For reasons canonical quintessence cannot explain, we now live in a transient, special time, after matter-domination and large scale structure formation. (Because k-essence uses the radiation/matter transition to explain this special time, k-essence enjoys a conceptual advantage over quintessence.) (2) The future event horizon makes some future events causally disconnected, so that galaxies outside the Local Supercluster [42] and indeed asymptotic particles and an S-matrix will ultimately become unobservable [45, 44, 43]. Thus cosmological observations already stress the special time when we live and may ultimately require modifying basic quantum mechanical concepts Acknowledgement. We are indebted to Martin Block for help with the numerical solution of cosmology’s stiff equations. References 1. I. Moar, R. Brustein, J. McMahon and P. J. Steinhardt, Phys. Rev. D65 2002, 12303. 2. T. Nakamura and T. Chiba, Mon. Not. R. Astron. Soc. 306 (1999), 696. 3. D. Huterer and M. S. Turner, Phys. Rev. D60 (1999), 081301; Phys. Rev. D64(2001). 4. J. A. Frieman, D. Huterer, E. V. Linder and M. S. Turner, arXiv:astroph/0208100 (2002). Supernova Acceleration Probe http://snap.lbl.gov . 5. D. N. Spergel et al, submitted to Astro. Ph. (2003). 6. J. L. 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Robert2 and V.Vitale3, for the MAGIC collaboration 1 2 3 Institut de Fı́sica d’Altes Energies (IFAE), Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain domingo@ifae.es, cortina@ifae.es, Grup de Fı́sica de les Radiacions, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain arnau.robert@uab.es Max Planck Institut für Physik, Föhringer Ring 6, 80805 München, Germany vitale@mppmu.mpg.de Summary. SuperNova Remnants (SNR) are generally believed to be the source of the galactic Cosmic Rays (CR). Although there is now strong evidence of electron acceleration at SNRs, which mainly comes from X-ray and a few TeV observations, there is yet no confirmation that nucleus acceleration is also at work. This observational quest has remained one of the most important problems of high energy astrophysics during the last 50 years, but it is likely to be solved in the few next, when telescopes like MAGIC start observing. The MAGIC Telescope is designed to cover the 30 GeV - 3 TeV (∼ 1025 - 1027 Hz) energy range with high sensitivity. With the detection and spectral characterization of SNR in a wide range of evolution stages and physical parameters at GeV/TeV energies we expect to confirm or rule out the current models of hadron acceleration. 1 SNR and the CR problem SNR were proposed as the source of the galactic CR already 50 years ago [1], based on a rough energetics argument. SN typically generate 1051 erg of kinetic energy. A SN production rate of 0.02 yr−1 is enough to explain the observed CR energy density (∼ 0.3 eV/cm3 ) if we assume that CR stay in our galaxy in the order of 107 yr. The current models consider CR first order Fermi acceleration [2, 3] in the shocks that are generated when the remnant shell expands into the interstellar medium, during the Sedov phase. CR are deflected by the random galactic magnetic field, so they do not point back to their source. However they can produce VHE γ-rays (electrons through synchrotron, bremsstrahlung or inverse Compton (IC) and ions through the decay of neutral pions produced in ions-nucleus collisions) close to the source which are not deflected. The identification of the parent particle of the VHE γ radiation needs a multiwavelength approach, using the radio 186 Domingo, Cortina, Robert and Vitale for MAGIC collaboration and the non-thermal X-ray spectra to discriminate between the electron- and hadronic-initiated components. The radio and X-ray spectra of a number of SNR are in good agreement with electron synchrotron emission. Moreover, three SNR have been detected at TeV γ-ray energies: • Cas A: HEGRA has detected TeV γ-rays [4] both consistent with electron IC or π 0 decay from hadronic interactions. • SN1006: CANGAROO has detected TeV γ-rays [5] that strongly indicate electron IC scattering off the microwave background. However, HEGRA CT1 data do not prefer the leptonic model [6]. • RXJ1713: CANGAROO has recently reported a TeV γ-ray detection [7], whose origin is still controversial [8, 9]. In conclusion, the case is good for electron CR acceleration, but there is yet no observational confirmation that hadronic acceleration also takes place. 2 VHE detection technique Very high energy (>109 eV) γ-rays are detected using the so-called imaging atmospheric Cherenkov technique. At these high energies the γ-rays interact in our atmosphere and develop electromagnetic air showers. The highly relativistic charged particles in the shower emit Cherenkov light flashes as they travel through the atmosphere. At ground level, Cherenkov photons are collected by the telescope reflector and focused into a camera of photomultipliers. A width A length disp Image plane asymmetry B α distance θ B Shower axis Shower axis Light pool on ground Light pool on ground impact parameter Fig. 1. Cherenkov light produced in the development of a γ-ray air shower and shower image at the camera telescope characterized with Hillas parameters The images of the Cherenkov flashes registered at the camera can be parameterized with an ellipse, which is characterized by a set of parameters (Hillas Observing SNR in VHE γ-rays with the MAGIC Telescope 187 parameters, see figure 1). These parameters are used to discriminate γ-rayinduced showers from the much more abundant CR-induced showers. The number of photons inside the image provides a rough estimate of the energy of the primary γ-ray. The major axis of the ellipse points to the source. 3 Extended source analysis methods MAGIC uses several alternative methods to extract the position of the γ-ray source: • SHOWER AXIS INTERSECTION METHOD [10]: Source location should be near the intersection of the axis of two different showers. For every pair of images a candidate source position is calculated and finally a skymap is obtained. • FALSE SOURCE METHOD [11]: The sky is divided into a grid. The standard point-source analysis is applied for each point of the grid. A skymap is performed with the excess events that have survived to the selection cuts for each testing point. • DISP METHOD [12]: The distance between the image centroid and the source position, along the image major axis, (disp parameter) can be extracted from a combination of several Hillas parameters using MonteCarlo simulations. A skymap is constructed with the points that each disp parameter fixes. 4 The MAGIC Telescope MAGIC [13] is a second generation Cherenkov telescope at the IAC site in the Canary island La Palma. MAGIC decreases the energy threshold for γ detection to around 30 GeV. This is one order of magnitude lower than the current Cherenkov telescopes (see figure 2). Its good angular resolution around 0.1◦, and an energy resolution around 30% at 30 GeV (substantially better than previous satellite-based detectors like COS-B and EGRET) will allow to perform a more accurate analysis of the SNR γ-ray signals and be able to distinguish between current theoretical models. 5 First SNR candidates MAGIC will be more sensitive than current Cherenkov telescopes in the energy range of 0.1 to 1 TeV (particularly at high zenith angles). We expect to detect SNR that are at the limit of detection of current telescopes (see table 1). 188 Domingo, Cortina, Robert and Vitale for MAGIC collaboration EGRE T (1 m onth) AGILE (1 month) GLAS T (1 m onth) VERITAS ~HESS ~CANGAROO III CEL EST MA E Wh ipp GI MA C GI VE C( RIT le lar ge AG HE RO GR AS Ze MIL nit hA AC ng TS yst em VE R les ITAS ( larg ) e Z.A .) (Sensitivities for 50 hours observation time) Fig. 2. Sensitivity of the MAGIC Telescope compared with other HE and VHE gamma Observatories Table 1. Integral flux of four VHE already detected SNR, F(E>E0 ), over the detection energy threshold E0 , and estimated observation time, T5σ , needed for MAGIC to have a 5σ significance detection SNR name F(E>E0 ) (phcm−2 s−1 ) Cas A RXJ1713 SN1006 Tycho 5.8×10−13 (> 1 TeV) 5.3×10−12 (> 1.8 TeV) 1.7×10−11 (> 300 GeV) (5.8×10−13 ) (> 1 TeV) T5σ (h) ∼ ∼ ∼ ∼ 30 15 10 40 MAGIC’s improved angular resolution and sensitivity at the unexplored energies of few tens of GeV open the opportunity of identifying sources of the 3rd EGRET catalogue with SNR. Extrapolation of EGRET measurements has allowed to estimate observation times for 5σ detection (see table 2 and also reference [14]). An alternative to focus on individual objects is to perform a survey of an extended region of the galactic plane, where a large enough population of SNR is expected (like the HEGRA galactic plane survey [15]). The observed average VHE γ-ray flux can be compared to the prediction of general models for SNR VHE emission [16]. Observing SNR in VHE γ-rays with the MAGIC Telescope 189 Table 2. Integral flux over the MAGIC energy threshold Eth and estimated observation time to have a 5σ significance detection, for positional coincident associations of unidentified EGRET sources with SNR that are good candidates for MAGIC 3EG J name SNR name F(E>Eth ) T5σ (phcm−2 s−1 ) (h) 0617+2238 IC443 8.12×10−10 1.05 0634+0521 Monoceros 2.90×10−10 4.55 1746-2851 Gal.Center 3.21×10−9 0.09∗ 1800-2338 W28 1.47×10−10 1.88∗ 1856+0114 W44 1.27×10−9 0.22∗ 2020+4017 γ-Cygni 1.26×10−9 0.39 6 Conclusions The MAGIC telescope is a new Cherenkov telescope with an energy threshold for γ-ray detection around 30 GeV. Its expected flux sensitivity, angular and spectral resolution at the unknown energy region between 30 and 300 GeV will probably allow to detect and characterize a large number of SNR, with the final aim of proving or rejecting the idea that shell-type SNR are the source of the CR. References I.S. Shklovskii: Dokl. Akad. Nauk. SSSR 91, 45-478 (1953) A. R. Bell: MNRAS 182, 147 (1978) A. R. Bell: MNRAS 182, 443 (1978) F.A. Aharonian et al: A&A 370, 112 (2001) T. Tanimori et al: ApJ 497, L25 (1998) HEGRA Collaboration, 28th ICRC proceedings, astro-ph/0307334 (2003) T. Muraishi et al: A&A 354, L57 (2000) R. Enomoto et al: Nature 416, 823 (2002) O. Reimer et al: A&A 390, L43 (2002) C.W. Akerlof et al: ApJ 377, L97 (1991) V.P. Fomin et al: Astropart. Phy. 2, 137 (1994) R.W. Lessard et al: submitted to Elsevier (2000), astro-ph/0005468 J.A. Barrio et al: The MAGIC Telescope Design report, Preprint MPI Institute Report MPI-PhE-98-5 (1998) 14. D. F. Torres et al.: Physics Reports 382, 303 (2003) 15. F.A. Aharonian et al: A&A 395, 803 (2002) 16. L.O’C. Drury, F.A. Aharonian, H.J. Voelk: A&A 287, 959 (1994) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Lobster Eye: Innovative X-Ray Telescopes for Deep Sky Monitoring René Hudec1 , Adolf Inneman2 , Ladislav Pı́na3 , and Libor Švéda4 1 2 3 4 Astronomical Institute of the Academy of Sciences of the Czech Republic, CZ-251 65 Ondrejov, Czech Republic rhudec@asu.cas.cz Center for Advanced X- ray Technologies, Reflex sro, Prague, Czech Republic inneman@reflex-co.cz Czech Technical University, Faculty of Nuclear Science, Prague, Czech Republic ladislav.pina@reflex-co.cz Department of Astronomy, Astronomical Institute of the Charles University, Prague, Czech Republic woody@sirrah.troja.mff.cuni.cz Summary. We refer on novel X-ray telescopes with high sensitivity as well as large field of view. The results are very promising, allowing the proposals for space projects with very wide-field Lobster-eye X-ray optics to be considered. The novel telescopes will monitor the sky with unprecedented sensitivity and angular resolution of order of 1 arcmin. 1 Introduction Wide field X-ray telescopes with imaging optics are expected to represent an important tool in future space astronomy projects, especially those for deep monitoring and surveys in X-rays over a wide energy range. The LobsterEye wide field X-ray optics has been suggested in 1970s by Schmidt ( [1], orthogonal stacks of reflectors) and by Angel ( [2], array of square cells) but has not been constructed until recently. Up to 180 deg FOV may be achieved. This novel X-ray optics offers an excellent opportunity to achieve very wide fields of view (FOV, 1 000 square degrees and more) while the widely used classical Wolter grazing incidence mirrors are limited to roughly 1 deg FOV. 2 Lobster X-ray Telescopes The Lobster Eye Wide Field X-ray telescopes in Schmidt arrangements are based on perpendicular arrays of double-sided X-ray reflecting flats. In the first prototypes developed and tested, double-sided reflecting flats produced by epoxy sandwich technology as well as gold coated glass foils have been used [3]. 192 Hudec, Inneman, Pı́na & Švéda Fig. 1. The schema of Lobster Eye telescopes, ray-tracing and optical focal image. Recently, micro Schmidt lobster eye arrays with foils thickness as low as 30 microns have been developed and tested in order to confirm the capability of these systems to achieve fine angular resolutions of order of a few arcmin. The thin foils are separated by 70 microns gaps in these prototypes. On the other hand, large lobster eye systems with Schmidt geometry have been designed and constructed, achieving dimensions up to 300 × 300 × 600 mm. Their optical tests have confirmed the expected performance according to calculations (computer ray-tracing). The X-ray tests of the large LE modules are planned in collaboration with the Max Planck Institute of Extraterrestrial Physik in Garching, Germany at their X-ray test facility Panter in Neuried later this year. The calculations and the measurement results indicate that Lobster Eye Telescopes 193 the lobster eye telescope based on multiarray of modules with thin and closely spaced glass foils (analogous to those already assembled and tested) can meet the requirements e.g. of the ESA ISS Lobster mission (including the angular resolution and with better transmission) and can hence represent an alternative to the recently suggested MCP technique [4, 5]. Fig. 2. The large LE telescope prototype (300 x 300 mm plates) and the optical focal image. For the Angel geometry, numerous square cells of very small size (about 1 × 1 mm or less at lengths of order of tens of mm, i.e. with the size/length ratio of 30 and more) are to be produced. This demand can be also solved 194 Hudec, Inneman, Pı́na & Švéda by modified innovative replication technology. First test modules with LE Angel cells have been successfully produced. First linear test module has 47 cells 2.5 × 2.5 mm, 120 mm long (i.e. size/length ratio of almost 50), surface microroughness 0.8 nm, f = 1300 mm. Second test module is represented by a L-shaped array of 2 × 18 = 36 cells of analogous dimension. The surface microroughness of the replicated reflecting surfaces is better than 1 nm. An innovative technique for production of 120 × 120 mm sized modules with large number of 3 × 3 mm cells, 120 mm long, is under development. The large modules of Kirkpatrick-Baez X-ray optics based on multiple and large flats in K-B geometry have been also suggested for future space missions. The K-B modules are based on orthogonal stacks of thin reflectors, each reflector represents a parabola in one dimension. Hence the production technology may be analogous to those developed for Lobster Eye Schmidt lenses. The modular concepts of Schmidt LE modules, of the large segmented Wolter telescopes (such as XEUS), and of large segmented K-B telescopes are similar: all are based on either plane parallel or curved flats and foils. This means that the development of high quality X-ray reflecting foils and flats with high mechanical stiffness and low volume density is extremely important for most of the future X-ray astronomy large aperture projects. The segmented K-B telescopes have the advantage of being highly modular on several levels. All segments are rectangular boxes with the same outer dimensions. The Schmidt LE X-ray lenses prototypes developed and tested so far are summarized in Table 1. We have started the study and the design of a first space borne test experiment to be flown onboard the small Czech scientific satellite in the collaboration with the Institute of Atmospheric Physics of the Academy of Sciences of the Czech Republic in Prague. This satellite should use a modified Russian Nadezhda type spacecraft bus. The onboard LE X-ray telescope should use an array of 10 × 10 mini Schmidt modules with a Xray pixel detector in the focal plane. The FOV covered will be 50◦ × 50◦ and the angular resolution better than 3 arcmin. Table 1. LE Schmidt modules developed so far. Here plates have dimensions of d × l × t and are arranged with spacing a. The modules have focal length f and field of view FOV. Module size thickness distance length eff. angle foc. length resolution FOV energy d[mm] t[mm] a[mm] l[mm] a/l f[mm] r[arcmin] [◦ ] [keV] macro 300 0.75 10.80 300 0.036 6000 7 16 3 middle 80 0.3 2 80 0.025 400 20 12 2 mini 1 24 0.1 0.3 30 0.01 900 2 5 5 mini 2 24 0.1 0.3 30 0.01 250 6 5 5 micro 3 0.03 0.07 14 0.005 80 4 3 10 Lobster Eye Telescopes 195 Conclusions The use of very wide field X-ray imaging system could be without doubts very valuable for many areas of X-ray and gamma-ray astrophysics. Results of analyses and simulations of lobster-eye X-ray telescopes have indicated that they will be able to monitor the X-ray sky at an unprecedented level of sensitivity, an order of magnitude better than any previous X-ray all-sky monitor. Limits as faint as 10−12 erg cm−2 s−1 for daily scanning observation as well as the angular resolution < 4 arcmin in soft X-ray range are expected to be achieved allowing monitoring of all classes of X-ray sources, not only X-ray binaries, but also fainter classes such as AGNs, coronal sources, cataclysmic variables, as well as fast X-ray transients including gamma-ray bursts and the nearby type II supernovae. More details on the advantages of LE X-ray telescopes in scientific analyses of SNe are given in [5]. The various prototypes of both Schmidt as well as Angel arrangements have been produced and tested successfully, demonstrating the possibility to construct these lenses by innovative but feasible technologies. Both very small Schmidt lenses (3 × 3 mm) as well as large lenses (300 × 300 mm) have been developed, constructed, and tested. This makes the proposals for space projects with very wide field lobster eye optics possible. Acknowledgement. We acknowledge the support provided by the Grant Agency of the Czech Republic, grant 102/99/1546, and by the Ministry of Industry and Trade of the Czech Republic, Center of Advanced X-ray Technologies, FB-C3/29/00 and FD-K3/052. The analyses of scientific aspects are linked to the grant A3003206 of the Grant Agency of the Academy of Sciences of the Czech Republic. References 1. Schmidt W. H. K., 1975, Nucl. Instr. and Methods 127, 285. 2. Angel J. R. P., 1979, Astroph. J. 364, 233. 3. Inneman A. et al.: Progress in lobster eye X-ray optics development, 2000, Proc. SPIE, vol. 4138, p. 94–104 4. Fraser, G. W. et al.: LOBSTER-ISS: an imaging x- ray all- sky monitor for the International Space Station, Proc. SPIE, 2002, Vol. 4497, p. 115–126 5. Sveda L. et al.: SNe and Lobster Eye X–Ray Telescopes, 2003, this volume. SNe and Lobster Eye X-ray Telescopes Libor Švéda1 , René Hudec2 , Adolf Inneman3 , Ladislav Pı́na4 , and Stefan Immler5 1 2 3 4 5 Astronomical Institute of the Charles University, Prague, Czech Republic woody@sirrah.troja.mff.cuni.cz Astronomical Institute of the Academy of Sciences of the Czech Republic, CZ-251 65 Ondrejov, Czech Republic rhudec@asu.cas.cz Center for Advanced X-ray Technologies, Reflex sro, Prague, Czech Republic inneman@reflex-co.cz Czech Technical University, Faculty of Nuclear Science, Prague, Czech Republic ladislav.pina@reflex-co.cz Department of Astronomy & Astrophysics, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802 immler@astro.psu.edu Summary. To date, several thousand supernovae (SNe) have been discovered in the optical, whereas only 19 were detected6 in the X-ray band (0.1 − 100 keV) [6, 7]. The SNe listed in Tab. 1 were detected exclusively by imaging instruments such as ROSAT, XMM-Newton or Chandra [6]. Current All-Sky Monitors (ASMs) do not have sufficient sensitivity to detect the X-ray fluxes given in the table. Missions in progress with a sufficient sensitivity have a small FOV and observations are triggered only in the case of a detection in the optical band. 1 Supernovae and X-rays Based on the presence or absence of hydrogen lines in their spectra, SNe are classified as Type II and I, respectively. To date no type Ia SN has been detected in X-rays. These SNe are believed to be nuclear detonations of carbon+oxygen (C+O) white dwarfs when they exceed the Chandrasekhar limit through accretion. Due to recurrent pulsations of the progenitor, fast shells (several hundreds km/s) are ejected from the progenitor. During periods of quiescence, no stellar wind is blown into the CSM due to the low mass of the progenitor. This leads to the formation of a complicated, yet low density CSM structure with interacting shells of different expansion speeds. The relatively slow expanding ejecta (< 5000 km/s) cannot hence form a shock region that could give rise to the thermal X-ray emission. No X-ray emission from the 6 as of May 2003 198 Švéda, Hudec, Inneman, Pı́na & Immler shock region has been recorded from a Type Ia SN to date, and is neither expected at a detectable flux level. The remaining types Ib, Ic, IIP, IIL, IIb, and IIn are believed to be the result of the massive star evolution. The division between these types is not always very clear, one SN can be classified as one type at first, although the spectrum or the light curve can evolve and fits to another type description later. 2 The X-ray Luminosities of SNe The X-ray luminosities of all detected SNe are in the range of 1037 −1041 erg/s. The X-ray emission is largely the result of the interaction of the ejecta with the CSM, which is present as a result of the SN progenitor stellar wind. Progenitors of Type II SNe following the core collapse of massive stars have high mass-loss rates [Ṁ∼(10−4 − 10−6 ) M /yr] and low wind velocities of typically vw ∼10 km/s. Type Ib/c SNe, likely to originate from more compact stars, have lower mass-loss rates [Ṁ∼(10−5 −10−7 ) M yr−1 ] and significantly higher wind velocities of vw ≤1000 km/s. Table 1. X-ray SNe detected in soft X-rays [7, 6] Name SN SN SN SN SN SN SN SN SN SN SN SN SN SN SN SN SN SN SN 1978K 1979C 1980K 1986J 1987A 1988Z 1993J 1994I 1994W 1995N 1998bw 1998S 1999em 1999gi 2001ig 2002ap 2002hh 2002hi 2003bg Type d [Mpc] II 4.5 IIL 17.1 IIL 5.1 IIn 9.6 IIP 0.05 IIn 89 IIb 3.6 Ic 7.7 IIP 25 IIn 24 Ic 38 IIn 17 IIP 7.8 IIP 8.7 II 11 Ic 10 II 5.1 II ··· Ic/pec 19.1 t − t∗0 [day] 4500 5900 35 3300 2370 6 79 1180 440 0.4 64 4 29 4 25 ··· 9.2 fX 10−14 erg cm−2 s−1 204 3.9 1.5 119 0.9 130 2.3 11 40 23-40 27 1.0 0.1 0.7 0.2 16.1 200 40 LX 38 10 ergs−1 48 14 0.5 140 110 20 1.6 85 175 40-70 92 0.7 0.1 1.2 0.2 5 5 5 SNe & LE Telescopes 199 3 X-ray Thermal Flash Another possibility for X-ray emission from SNe, albeit not yet detected, is a thermal flash occurring during the SN explosion itself and lasting for approx. 1000 s. The flash occurs as the blast wave, expanding outwards from the core collapse, hits the photosphere (i.e., the outer gaseous envelope). The shock wave is predicted to heat this gas to high temperatures (105 − 106 K), so the gas begins to emit strongly in the soft X-ray region [3]. The peak luminosity (bolometric) can reach ∼1045 erg/s. This luminosity resembles the X-ray luminosity, because the emission is dominated by X-rays or hard UV during this phase. Such a flash can be detected up to z ∼ 0.2 (supposing Lx = 1044 erg/s, 2 fx = 10−12 erg/s/cm , open universe with Ω0 = 0.35 and second order approximation) in case of no absorption. One can estimate the decrease of luminosities caused by the intergalactic absorption up to several tens of percent at z ∼ 3. The absorption in the material around the SN itself or in the material in our Galaxy will play a major role. If the total column density n ∼ 1021 cm−2 (Milky Way and host galaxy together) together with photoelectric cross-section [1] σ ∼ 3×10−22 cm2 for soft X-rays is taken into account, we get a limiting z ∼ 0.05. This is equivalent to d ∼ 200 Mpc. Fig. 1. The SNe redshift distribution [2]; the shaded area is related to the SNe discovered in the years 1993-1998. The redshift distribution of detected SNe up to z = 1 [2] is plotted in Fig. 1. Two distributions are plotted. One shows the distribution of all detected SNe whereas the shaded area is related to the SNe discovered in five year period (1993-1998). The number of detections for z < 0.05 in these five years is ∼ 270. We take this number as the lower limit for SNe explosion rate at lower z (observable by LE) region. 200 Švéda, Hudec, Inneman, Pı́na & Immler 4 The SNe detection rate in X-rays The number of X-ray SNe as a result of CSM interaction is unclear. If we take the data from Tab. 1 into account, we see that the luminosities of already detected SNe in X-rays are quite low and are detectable only by longer integration time observations. We should note that many of the SNe in the Tab. 1 were detected a long time after the explosion. The SNe detected several days after the outburst and having extremely low X-ray flux were detected mostly with XMM-Newton or Chandra satellites. Together with the low X-ray flux and the low sky coverage of detectors capable to detect such a flux the data from the Tab. 1 should be considered as incomplete and informative. 5 SNe and the Lobster Eye X-Ray Telescopes In contrast, the thermal flash lasting only ∼ 1000 s would be much easier to be observed with innovative sensitive wide-field X-ray telescopes. These Lobster Eye X-ray telescopes exhibit very large fields of view with fine sensitivities and still reasonable angular resolution. The first laboratory samples of these telescopes have been successfully designed, developed, manufactured and tested (Hudec et al., this volume). The recent extended calculations and simulations indicate that these telescopes can cover field of view of order of 1 000 square degrees or more and achieve angular resolution of few arcminutes, gain of 1000 or more, and sensitivities up to 10−12 erg s−1 cm−2 in scanning mode. Together with the optical SNe detection rate and estimates of the Lobster Eye FOV we estimate the total number of the SNe thermal flashes observed by the LE experiment to ∼10 per year. The Lobster Eye X-ray telescope hence seems to be an ideal instrument for SNe observations and is especially unique to observe the SN thermal flash. 6 The Lobster Eye Ray Tracing We have developed a ray tracing code for testing and designing LE systems. Some optical measurements have already been performed, together with ray tracing models, to verify our results and to find out the effect of the imperfect LE fabrication and/or various foil distortions. We have proposed several prototypes for the LE optics. Our starting point was the desired angular resolution (∼4 arcmin) and focal length f = 375 mm and we combined it with existing technology used to create recent prototypes. The chosen parameters are consistent with the proposed ESA Lobster ISS mission[4]. These prototypes were designed to get an optimal gain in several energy bands. SNe & LE Telescopes 201 We have obtained an angular resolution of ∼ 3.5 arcmin and a gain of > 1000 for gold-coated plates with a dimension of 78.0 mm × 11.5 mm × 100 µm and 300 µm spacing between the plates and soft (below 2.5 keV) X-ray photons. 7 Model vs. Experiment To verify the results of our ray tracing simulations we compared the model with the X-ray experiment of test non-astronomical point-to-point focusing LE system. This kind of optics was fabricated in the REFLEX company [5]. Active dimensions of the plates are 1.7 cm × 3 cm × 100 µm (width × depth × thickness). Front area is ∼ 1.7 × 2.0 cm. Spacing between plates is ∼ 300 µm. The optics was located in the middle between the source and the detector (distance 1.2 m). Fig. 2. The experiment (left) and the model (right) of the point-to-point focusing system. The distance between the source and the detector was 1.2 m. We used 8 keV photons. The image has the width of 24.6 mm. The model is artificially over exposed to fit the experimental data and to make directly illuminated areas visible. The measurements were performed using 8 keV photons and a 512 × 512 pixel CCD camera. The pixel size of the used camera was 24 × 24 µm. One of the measured images (the smaller part) is plotted in the leftmost part of Fig. 2. As can be seen in Fig. 2, the size of the focal spot is very similar in the model and in the experiment. Also the gain fits very well (measured gain ∼ 570, modeled gain ∼ 584). 202 Švéda, Hudec, Inneman, Pı́na & Immler Conclusions Only a few supernovae were observed in X-rays so far and the observation was made a long time after the explosion mostly. The LE telescope performance analysis indicates that it would be a unique instrument for the soft X-ray SNe observations and for detecting the prompt X-ray SNe emission (thermal flash). Our estimates show that the lower limit for the LE SNe thermal flash year detection rate would be ∼ 10 up to z ∼ 0.1 − 0.2 (the estimate should be considered as a very conservative). Acknowledgement. We acknowledge the support provided by the Grant Agency of the Czech Republic, grant 102/99/1546, and by the Ministry of Industry and Trade of the Czech Republic, Center of Advanced X-ray Technologies, FB-C3/29/00 and FD-K3/052. References 1. http://ads.harvard.edu/cgi-bin/bbrowse?book=hsaa&page=199 2. Barbon, R. et al.: The Asiago SN Catalogue — 10 years, 1999, A&AS, vol. 139, p. 531–536 3. Ensman, L., Burrows, A.: Shock breakout in SN 1987A, ApJ, 1992, vol. 393, p. 742–755 4. Fraser, G. W. et al.: LOBSTER-ISS: an imaging x-ray all-sky monitor for the International Space Station, Proc. SPIE, 2002, Vol. 4497, p. 115–126 5. Inneman A. et al.: Progress in lobster eye X-ray optics development, 2000, Proc. SPIE, vol. 4138, p. 94–104 6. Immler, S.: http://www.astro.psu.edu/~ immler/supernovae list.html 7. Immler, S., Lewin, W. H. G.: X-ray SNe, astro-ph/0202231 v2 27 Mar 2002 BART Status Martin Jelı́nek1 , Petr Kubánek1 , Martin Nekola1 , and René Hudec1 Astronomical Institute of Academy of Sciences of the Czech Republic, Ondřejov http://www.asu.cas.cz/ Summary. The Burst Alert Robotic Telescope is a small aperture robotic telescope. The recent configuration consists of a Meade 25 cm tube and two small wide field cameras (for R and I Johnson’s filters). The primary scientific goal of this telescope is to provide immediate optical observations of high energy events such as GRBs provided by satellites. In the meantime, the long-term monitoring of selected sources is performed. Most of this time is dedicated to active galaxies and cataclysmic variables which are being also observed with INTEGRAL. 1 Introduction After movement failure, disabling the robotic telescope for three months, the BART robotic telescope is again in operation. It has got a new WF camera and, additionally, there is another camera being tested. Fig. 1. One of the BART’s WF cameras. 204 Jelı́nek et al. 2 Hardware BART itself is built on top of the Meade LX200 mount, which is available on the market. Optical system consist of the Meade 25cm tube itself equipped with the SBIG ST9E camera and with appended Wide Field cameras, which are Meopta 64mm, 1:1.7 lens with an SBIG ST8 cameras. System is further equipped with several custom-made improvements including lens anti dew heating, electronic focuser and others. The system did observe during routine observation four gamma-ray bursts, in delays ranging from 90 seconds after receiving position to several hours. (Longer delay has nothing to do with the software, it’s caused by other factors — daytime, weather etc.) The optical counterpart was not found, the delay after trigger was too long and the transient (even if it was found) was too faint to be found on our frames. Further improvements of the telescope and expected short-delay GRB alerts may bring more success to this project. 3 Software The telescope has recently received a new version of operating software. This new, modular solution is designed to be both fast and simple to use. It supersedes the original (rather testing) Python based operating software, allowing faster response to the GRB alerts and better observation planning. It’s written in pure C and runs on Linux. System is built so it’s able to react to the GRB alert in a few seconds, the last and only real-time alert of this telescope was the GRB020317, with the delay 90 seconds, but from this delay, 70 seconds were caused by waiting for the camera to finish the previous exposure. It is now proved on several testing alerts, that BART is able to start taking images of the GRB region right after finishing the mount slew, in about 20 seconds. Fig. 2. BART WF non-detection of GRB030124. 10x 120s exposure stacked. [1, 2, 3] BART Status 205 Fig. 3. The HETE error box of GRB020305; background is part of BART WF.[4, 5, 6] 4 GRB observations The robotic telescope reacted to five GRB alerts during the first half of the year 2002. Table 1 summarizes the basic information. Delay is the time between the trigger and the first exposure. The only realtime response to a GRB alert was to trigger 020317, achieving the response time of 90 seconds, others were delayed due to daytime and/or waiting for the clear sky. 4.1 GRB 020305 This long burst was detected by HETE. The GCN notice was issued 10.5 hours after the trigger, only few minutes before the BART started observation. The delay therefore is not real-time, but with only 30 minutes was the fastest reply mentioned in GCN notices. On the wide field images from BART there were no new objects found up to magnitude 14, the narrow field images covered only 40% of the HETE error box with limiting mag 17. [5]. The Optical Table 1. GRBs followed by BART GRB delay WF limit NFlimit grb020124 grb020305 grb020317 grb020331 11.5h 10.45h 57.8m 5.54h >14 (15) >14.3 (16) >13 (14.5) >13 17(18.5) 16 206 Jelı́nek et al. Afterglow was later found by Price [6]. No object can be reliably confirmed up to noise level of the wide field image. The narrow field image did not cover this position. 4.2 GRB 020317 This gamma ray burst is up to now the only burst which might be observed with BART in real-time. The burst was somewhat peculiar, approx. 2 seconds long, with peculiar spectra. [7] The GRB was reported in 34 seconds, the position came in 56.3 minutes. BART’s reaction took 90 seconds, so the first images were obtained in 57.8 minutes after trigger. Further image analysis is planned, preliminary analysis went to eliminating of an OT candidate found on the first 10 stacked images and reported in GCN12781. Acknowledgement. We acknowledge the support provided by the Grant Agency of the Academy of Sciences of the Czech Republic (grant 3003206), and by the ESA PRODEX (Contract 14527/00/NL). References 1. Ricker G., et al.: GRB 020124 (=H1896): Localization of a Long GRB by HETE, GRB observation report number 1220 2. Price P., et al.: GRB 020124: Optical afterglow, GRB observation report number 1221 3. Jelinek M., et al.: GRB 020124: Optical observations, GRB observation report number 1236 4. Ricker G., et al.: GRB 020305 (=H1939): Localization of a GRB by HETE, GRB observation report number 1262 5. Jelinek M., et al.: GRB 020305: Optical observations, GRB observation report number 1264 6. Price P., et al.: GRB 020305: Candidate optical afterglow, GRB observation report number 1266 7. Ricker G., et al.: GRB 020317 (=H1959): Localization by HETE of a low fluence GRB, GRB observation report number 1280 8. Ricker G., et al.: GRB 020331 (=H1963): The Easter Burst Detected by HETE, GRB observation report number 1315 1 Internet presentation may be found on http://lascaux.asu.cas.cz/

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