Microquasar jets interacting with their environments P. Bordas,1 J. M. Paredes1 and V. Bosch-Ramon2 1 2 Departament d’Astronomia i Meteorologia, Universitat de Barcelona, Martı́ i Franquès 1, 08028, Barcelona, Spain pbordas@am.ub.es; jmparedes@ub.edu Max Planck Institut für Kernphysik, Saupfercheckweg 1, Heidelberg 69117, Germany vbosch@mpi-hd.mpg.de Summary. Microquasars (MQ) are X-ray binary systems showing relativistic jets. We present a model to estimate the properties of these jets when interacting with the surrounding interstellar medium (ISM). Given the analogies between MQ jets and those present in active galactic nuclei (AGN), we suggest that the large-scale emitting structures observed in the latter could be present in the surroundings of MQs as well. We provide some estimates for the radiative outcomes of the studied regions, showing that cocoon and bow shock regions may be detectable by the present observational facilities. 1 Model Outline Our model is based on twin jets emerging from the central source in two opposite directions. The supersonic jets end in strong shock fronts at the location where they impact on the ambient gas. The matter carried by the jets inflate the cocoon that is overpressured with respect to the environment. The cocoon therefore expands sidewards and a bow shock is driven into the surrounding ISM. By inflating the cocoon the jets create their own high-pressure but low-density environment, protecting them from disruption due to turbulent gas entrainment. This ensures that the jets do not widen much on their way through the lobes, and thus the momentum and energy transported by the jets are delivered through the jet shocks without significant losses to continue pumping energy in the cocoon and ISM shocked structures. See Fig. 1 for an illustrative picture of our scenario. We use a model that adopts the same key ideas as those applied to the study of AGN/environemnt interaction. We follow the pioneer works on this field ([1], [2]) that initially stated the main concepts concerning the mechanisms for the formation of luminous radio-lobe sources. We adapt to MQ, in a similar way as [3], [4] and [5] for extragalactic sources, the self-similar treatment developed to explain observed 2 P. Bordas, J. M. Paredes and V. Bosch-Ramon extended radio structures in radio galaxies and radio-loud quasars. We have roughly estimated the particle acceleration efficiency in the considered regions applying a first-type Fermi type shock acceleration model.We aim at giving some predictions concerning the non thermal and thermal radiative outcome of the outflow/medium interaction. This will allow to constrain later on the physics of these phenomena in MQs via comparison with observational data, to be presented in a future work. Fig. 1. Zones treated in our model: 1 unshocked ISM; 2 shocked ISM; 3 shocked jet material; 4 unshocked jet material. The strong shocks separating zones 1 and 2 (the bow shock) and 3 and 4 (reverse shock) are able to accelerate non-thermal particles and increase the temperature, leading to synchrotron and Bremsstrahlung processes. 1.1 Self-similar treatment The model assumes an averaged energy rate Q0 outflowing in the jet. The mass density distribution of the external ambient gas is modeled by a power law, ρ = ρ0 (r/r0 )−α where r is the distance from the compact object and r0 is a scale length. In the cases where MQs are situated in the ISM of the Galactic plane, the ambient gas has roughly a constant density ρ0 and α = 0. The cocoon and the bow shock evolution is self-similar once the jet extends beyond a characteristic length scale given by the basic parameters that govern the whole structure formation, L0 = (ρ20 Q0 /Ṁ03 )−1/4 . Here, Ṁ0 = Q0 /(Γj − 1)c2 is the mass transport rate of the jet, that travels with a Lorentz factor Γj . Taking reasonable values for the parameters involved (see Table 1) we find L0 ∼ 105 cm, obviously smaller than the jet length even in its forming point. As pointed out by Falle (1991) [3], once the jet is larger than L0 , MQ Jets Interactions 3 Table 1. Parameter values used throughout the model. parameter Symbol Value Injection point z0 50Rg Jet’s Lorentz factor Γj 1.02 Jet kinetic luminosity Q0 1036 erg/s Fraction of non thermal particles χ 1%, 5% injected e± spectral index P 2.0 Magnetic field at z0 B0 105 Compression ratio r ∼4 Self-similar ratio R ∼2 ISM particle density nISM 100 cm−3 dimensional arguments demand that the axial coordinate describing the jet position and the advance velocity follow respectively the relationships Ljet = c1 (Q0 /ρ0 )1/5 t3/5 and L̇jet = 3Ljet /5t, where t is the age of the jet and c1 ∼ 2 is a dimensionless constant that depends on the thermodynamical properties of the jet material and on the assumed source self-similar ratio R. 1.2 Particle acceleration The high pressure jump at the forward and reverse shock fronts makes of these regions a suitable place for the first-order Fermi process to operate. In the context of this particle acceleration model, the rate of energy gain by particles of charge e in a region where a magnetic field Bjet is present can be written ec2 B as (dE/dt)accel = 1.5 · 104 η jet where we have taken a diffusion coefficient D both for up and downstream zones given by some factor η times the Bohm diffusion coefficient, D = η 31 rgyro c with rgyro the particle gyroradius. The differential form of the resulting particle energy spectrum can be expressed r+2 as (see [6] for a detailed calculation) N (E) ∝ E −P where P ≈ r−1 depends on the ratio of the densities at both sides of the shock front r. The maximum energy that a particle can reach will be limited by the more important energy loss mechanism actually present in the region. In our case, the relevant losses are the escape losses of particles and those from synchrotron and relativistic Bremsstrahlung processes. Under the conditions assumed in the jet reverse shock (the hot spot) and the ISM forward shock (the bow shock), we estimate the maximum particle energy in 10 TeV and 0.1 TeV, respectively. This shows us that, with equipartition magnetic fields, synchrotron emission will yield luminosities up to ∼ 8 · 1034 erg/s and ∼ 3 · 1034 erg/s, and Bremsstrahlung up to ∼ 5 · 1032 erg/s and ∼ 1026 erg/s, for the cocoon and the shock ISM regions, respectively. Moreover, the specific luminosity will peak at νmax ∼ 1018 Hz in the cocoon and at νmax ∼ 1014 Hz in the shocked ISM gas. 4 P. Bordas, J. M. Paredes and V. Bosch-Ramon 2 Model results and conclusions Regarding the shocked ISM region we have estimated the relativistic Bremstrahlung and synchrotron efficiencies since some fraction of the shocked particles can be accelerated to non-thermal energies at the shock front. We have taken an equipartition magnetic field present throughout the region. To estimate the thermal Bremsstrahlung efficiency, a shocked gas temperature of ∼ 3 · 109 K in the cocoon and ∼ 1.2 · 104 K in the bow shock region have been derived from the thermodynamical properties of the shocked material produced either in the reverse shock/hot spot or in the forward shock/bow shock region. In comparing both thermal and non-thermal contributions, we have to chose a phenomenological value for the thermal-non-thermal energy conversion. Looking at the efficiencies of the radiative processes takin place in the studied zones, we can see that relativistic Bremsstrahlung may be efficient for reasonable non-thermal to thermal energy ratios (∼ 0.05) only in the bow shock region. Otherwise, the synchrotron process may produce significant amounts of radiation in both the cocoon and the bow shock, although the overall production would be probably dominated by the former. Concerning the thermal Bremsstrahlung radiative outcome, we see that the dominant component will be the bow shock one. We conclude that the cocoon and the bowshock regions could be efficient emitters of thermal and non thermal radiation that may be detected at radio frequencies and, less likely, at X-rays. We note that for the case of a high mass system with a very bright companion, even at the distant regions we are concerned here from the MQ the inverse Compton process could be significant and should be considered ([7]). Moreover, accelerated protons could also produce significant gamma-ray emission via proton proton interactions with the interstellar medium, generating as well lower energy radiation via the secondaries produced in the same proton proton collisions ([8]) References 1. 2. 3. 4. 5. 6. Scheuer P. A. G.; MNRAS 61 166, 513 (1974) Blandford R. D., Rees M. J.; MNRAS 61 169, 395 (1974) Falle S. A. E. G.; MNRAS 61 250, 581 (1991) Kaiser C. 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