PHOTOIONIZATION AND MAGNETIZED WINDS: HII REGIONS AND PLANETARY NEBULAE FRANCO AND GUILLERMO GARC JOSE A-SEGURA Instituto de Astronom a-UNAM, Mexico 1. Introduction Photoionized nebulae are generated by hot stars located at the two ends of the stellar mass spectra (and near the extremes of their evolutionary tracks): H ii regions are excited by recently formed massive stars, and Planetary Nebulae (PNe) are generated by low mass stars evolving toward the white-dwarf phase (see Osterbrock 1989). They display a variety of fascinating shapes, with irregular forms delineated by dusty laments and bright rims, and with a complex network of velocity elds, ionization fronts, shock waves, and instabilities. At large scales, integrated over time and space, these objects can have a strong impact in the evolution of gaseous galaxies. For instance, massive stars inject large amounts of radiative energy which photoionizes and disrupts the parental clouds, setting the eciency of star formation at galactic scales (e.g. Cox 1983; Franco et al. 1994; Shore & Ferrini 1994; Diaz-Miller et al. 1998). In contrast, evolved low mass stars do not have such a disrupting eect but they provide a generous gas mass return rate. Thus, PNe ejecta can maintain the gaseous component at the late stages of galaxy evolution, and are responsible for the enrichment of several heavy elements. H ii regions form a class of relatively well studied objects but there are no clear denitions of the dierent types. They are sometimes classied as ultracompact, compact, and extended HII regions (e.g. Habing & Israel 1979). Ultracompact H ii regions (UCHIIs) have small sizes, of about 0:1 pc, and are located in the inner, high-pressure, parts of the parental molecular cloud (e.g. Kurtz et al. 1994; Xie et al. 1996). Compact H ii regions (HIIs) have larger sizes, 0:1 0 0:3 pc, and are carving their way out of the parental clouds. Extended H ii regions, on the other hand, have sizes of up to several parsecs and they represent the mature state of these objects. 86 FRANCO AND GUILLERMO GARC JOSE A-SEGURA Thus, one can sketch a simple evolutionary link with the size growing in time and, after Stromgren (1939) and Kahn (1954) set the physical basis to their modeling, the details of the expansion has been studied with a variety of dierent analytical and numerical tools, and under dierent cloud conditions, over the last four decades (see Yorke 1986; Franco et al. 1989,1990; Garcia-Segura & Franco 1996). In the case of PNe, there are a variety of dierent morphological classes. They have been cataloged as bipolar, elliptical, point-symmetric, irregular, spherical, and quadrupolar (see Manchado et al. 1996). They are formed by the mass ejected at the nal stages of low-mass star evolution, and the shapes are created by at least two interacting winds. Dust shells around AGB stars, the progenitors of PNe, do not show signs of asphericity and, during the transition from the AGB to the post-AGB phase, one or more physical processes responsible for the shape of these objects must be initiated. The origin of aspherical nebulae remains as one of the fundamental problems of PNe formation and evolution, and stellar rotation and magnetized winds can produce the observed morphologies. 2. H ii Regions Star clusters are formed inside molecular cloud complexes, which are composed of a collection of high-density condensations interconnected by a more diuse intercloud medium. The internal density distributions in clouds are proportional to r0w , with an average value of w 2 (e.g. Arquilla & Goldsmith 1985; Gregorio Hetem et al. 1988), and there are also disk-like fragments (e.g. Torrelles et al. 1983; McCaughrean & O'Dell 1996). The high-density condensations, or cloud cores, have peak densities of about 107 cm03 and peak temperatures above 102 K (e.g. Bergin et al. 1996; Hofner et al. 1996). These observed values already indicate that the gas thermal pressures are large inside the cloud cores. In addition, the existence of large non-thermal \turbulent" velocities, of several km s01 , and strong magnetic elds, ranging from tens of G to tens of mG (see Myers & Goodman 1988 and references therein), imply that the total pressures are obviously higher and the cores of massive molecular clouds are highly pressurized regions. The resulting maximum core pressures (generated by their own self-gravity) could reach values in excess of 5 2 1006 dyn cm02 (see Garcia-Segura & Franco 1996). Thus, H ii region expansion in high-density cores will be aected by their large total pressures. Numerical and analytical models of H ii region evolution under these conditions (i.e., n(r) / r0w and disk-like density distributions, and large total pressures) provide many details of the ows (Franco et al. 1989, hereafter FTB89; Franco et al. 1990, hereafter FTB90; Garca-Segura & Franco 1996, hereafter GF). PHOTOIONIZATION AND MAGNETIZED WINDS 87 For constant stellar UV uxes and uniform ambient densities, the expansion of H ii regions has well dened evolutionary phases (see Spitzer 1978 and Osterbrock 1989). During the formation phase, the radiation eld creates an ionization front that, in a recombination time, reaches the initial 2 3 Stromgren radius (Stromgren 1939) RS = 3 F? =4 n20 B 1=3 , where n0 is the ambient density, F? is the total number of ionizing UV photons per unit time, B = 2:6 2 10013 cm3 s01 is the hydrogen recombination coecient to all levels above the ground level. For a dusty cloud, the initial radius is smaller and is given by RS;dust ' RS e0 =3 (FTB90), where is the optical depth due to dust absorption. This simple formula agrees with the results of radiative transfer calculations, and indicates that the initial Stromgren radius is probably smaller than is usually considered (Daz-Miller et al. 1998; hereafter DFS). In addition, the radiation pressure on dust grains is transferred to the ionized gas and, at late times, a central hole can be created in dusty H ii regions (Mathews 1967). After the formation time, due to the pressure dierence with the surrounding medium, the recently formed H ii regions expand and drive a strong shock wave ahead of the ionization front. The expansion continues until the photoionized gas reaches pressure equilibrium with the ambient interstellar medium (GF). If the ionization front encounters a strong negative density gradient and overruns it, then the expansion will enter into its \champagne" phase (Tenorio-Tagle 1982; FTB90). 2.1 High Ambient Pressures and the UCH ii Class The photoionized region reaches its equilibrium temperature, Ti 104 , K in a relatively short time-scale, and expands (in a nearly isothermal fashion) into the neutral medium whose pressure is P0 . Assuming that the ion density ni is equal to the electron density ne (i.e., for a pure hydrogen nebula), the thermal pressure of the ionized region is Pi = 2ni kTi , where k is Boltzmann's constant. The advance of the ionization front is controlled by recombinations in the photoionized gas and, for a region of radius RHII , the 03=2 . The corresponding average ion density is < ni >= [3 F? =(4 B )]1=2 RHII 0 1 03=2 . For a constant density internal pressure is Pi = 3 k2 Ti2 F? = B 1=2 RHII medium and Pi P0 , the HII radius grows as RHII / t4=7 , and the internal pressure decreases as Pi / t06=7 . The expansion continues until Pi ! P0 , and the internal pressure tends to a constant value. These limits show that, for a constant density medium, evolves as a function of the pressure dierence from 4/7 to zero. When pressure equilibrium is reached, the ion 01 cm03 , density is simply given by ni;eq = (P0 =2kTi ) ' 3:6 2 104 P7 THII ;4 where P7 = P0 =1007 dyn cm02 , and THII;4 = Ti =104 K. The stagnation radius of the H ii region, then, corresponds to a Stromgren radius at this 1=3 2=3 02=3 pc , where F = equilibrium density RS;eq 2:9 2 1002 F48 THII 48 ;4 P7 88 FRANCO AND GUILLERMO GARC JOSE A-SEGURA 0.06 0.04 R(pc) Shock Sonic Point 0.02 Ionization Front 0 0 Figure 1. UCH with P7 = 1. ii 1 2 4 t (10 yr) 3 4 5 region evolution, for a star with F48 = 1, in a high-pressure medium F? =1048 s01 . The interstellar pressure at the solar circle is about PISM 10012 dyn 0 cm 2 , and the equilibrium values for single massive stars (with F48 1) are ni;eq 0:4 cm03 and RS;eq 30 pc (the corresponding sizes for \naked" OB associations can reach a few times 102 pc). The time scales at which these equilibrium values are reached, however, are very long, teq > 107 yr, and most massive stars move out of the main sequence earlier. For high-pressure cores with P7 1 and rc 0:1 pc (see GF; Xie et al. 1996), the resulting UCH ii could be stable and long lived. The equilibrium stage is reached in time scales of the order of teq 104 yr, and the corresponding values are very similar to the observationally derived sizes and electron densities in ultracompact H ii regions, UCH ii (see Kurtz et al. 1994). 2.2 Density Gradients If the star is located near the core boundary, or moves towards the edge, the ionization and shock fronts can move out of the core and the gas accelerates out of the high-density core. The relative position of the exciting star, then, denes whether the UCH ii reaches pressure equilibrium or not. For static or slowly moving stars, which are born near the center of the core, the ultracompact stage can be long lasting. Otherwise, when the stars are born at a distance smaller than RS;eq from the boundary, the ionized ow is accelerated outwards and the UCH ii stage is a transient one (a possible example of this type of transient UCH ii region is G29.96, which is probably younger than 105 yr and has a champagne ow: see Lumsden & Hoare 1996 and Watson & Hanson 1997). The evolution in decreasing density stratications displays a rich variety of hydrodynamical phenomena with internal shocks, receding ionization fronts, rapid evaporation of cloud cores, and the creation of new clumps in the expanding shocked shell (FTB89; FTB90; Rodriguez-Gaspar et al. 1995; 89 PHOTOIONIZATION AND MAGNETIZED WINDS GF; Franco et al. 1998). For spherical clouds with density distributions consisting of a central core (with radius rc and constant density n0 ) and an envelope with a power-law density stratication, nH2 (r) = n0 (r=rc )0w , the H ii region growth is approximated by (FTB90) R(t) ' Rw " 7 0 2w 12 1+ 4 9 0 4w 1=2 ci t Rw #4=(702w) : (1) The expansion phase has a critical exponent, wcrit = 3=2, which is independent of the initial conditions and is not aected by dust absorption. For w < 3=2, the interface between the ionization front and the leading shock accumulates neutral gas. For w = wcrit , the ionization front and the shock front move together without a neutral interface. For w > 3=2, the ionization front overtakes the shock front and proceeds to ionize the whole cloud. Once the whole ionized cloud is set into motion, the expanded core feels the strongest outwards acceleration, and there is a wave driven by the fast growing core. Thus, fast ows can be generated in steep density gradients. For instance, ow velocities between 20 and 30 km s01 are generated in w 2 distributions, and the speeds can increase to more than 100 km s01 for w > 3. This implies that UCH ii can be formed in high-pressure cores with Rs < rc , but a rapid evaporation of the core occurs when Rs > rc (Rodriguez-Gaspar et al. 1995). For a gaseous disk, with a density distribution along the z -axis equal to n(z ) = n0 G(z=H ) [where n0 is the density at midplane, H is the 2 2 scale height, and G(z=H ) is the disk stratication; say, e0z=H , e0z =H , or sech2 (z=H )], the density fall-o is steeper than r03=2 . Thus, ionization front can become unbounded (during the expansion, however, the ionization front can recede; see FTB89). The initial shape of the ionized region is dened by photoionization equilibrium, but initial size of the H ii region as a function of the azimuthal angle . 2.3 Fragmentation of the Shocked Shell The shock generated by the expanding H ii region collects and accelerates the ambient gas and, after radiative losses become important, a cold and dense shell forms. The ionization front is located at the inner boundary of the shell, and their evolution is subject to instabilities. In particular, the ionization front exacerbates the growth of the thin shell instability and the models performed by GF, which assume ionization equilibrium to dene the location of the ionization front, show that these instabilities generate a rapid fragmentation of the shell. The shapes of the resulting fragments are similar to those observed in cometary globules and elephant trunks, and the ow instabilities appear under a wide variety of conditions. Figure 2 shows the instability for an H ii region evolving in a disk-like cloud. The model 90 FRANCO AND GUILLERMO GARC JOSE A-SEGURA -22.0 -21.5 -21.0 -20.5 -20.0 log density (g/cm3) -19.5 2.0 Z (pc) 1.5 a d b e c f 1.0 0.5 2.0 Z (pc) 1.5 1.0 0.5 2.0 Z (pc) 1.5 1.0 0.5 0.0 0.5 1.0 R (pc) 1.5 2.0 0.5 1.0 R (pc) 1.5 2.0 Expanding H ii region evolving in a disk-like molecular cloud. Panels a-c; stable shell of an adiabatic shock. Panels d-f; shell fragmentation in a radiative shock. Figure 2. illustrates the continuous formation of clumps by the shocked shell. The presence of a strong stellar wind also generates clumpy structures and the composite structures formed around massive stars with strong winds and expanding H ii regions display a complex behavior (see Franco et al. 1998). The wind-driven shell forms large density clumps and the UV photon eld creates long photoionized ngers in the directions that are free of clumps. Also, the radiation eld with energies just below the Lyman limit creates a photodissociated region (PDR) between the H ii region and the rest of the molecular cloud (e.g. Bertoldi & Draine 1996). This shell of HI gas, with its photodissociating front, adds new complications to the dynamical evolution (Roger & Dewdney 1992; DFS). In addition, hot stars produce large composite H ii regions with PDRs, but intermediate mass stars produce only PDRs (DFS found that the the minimum stellar temperature required to create a sizable PDR is about 1:3 2 104 K). 3. Planetary Nebulae: Toroidal Fields and Collimation It is commonly accepted that the formation of PNe involves the action of at least two interacting stellar winds (Kwok, Purton & Fitzgerald 1978; Balick PHOTOIONIZATION AND MAGNETIZED WINDS 91 1987; Kwok 1994; Aller 1993). It has been shown by Langer (1997,1998) and Garca-Segura et al. (1998) that luminous blue variables (LBVs) and asymptotic giant branch (AGBs) stars can reach critical rotation. GarcaSegura et al. (1998) have shown that the result is a slow, massive, equatorially conned outow. The striking similarity of the shapes of some PNe and LBV nebulae (i.e., compare the \Hourglass Nebula", MyCn18, with the \Homunculus Nebula" surrounding Carinae) indicates that the same physical processes may be responsible for their morphologies. If this is the case, the main cause of bipolarity could be due to stellar rotation. Asymmetries of the precursor AGB wind are not the only factor responsible for the shaping of PNe. Using the thin shell approximation, Begelman & Li (1992) obtained self-similar solutions of aspherical nebulae produced by a fast rotating neutron star with a magnetized fast wind. Their procedure did not include wind asymmetries, and the aspherical shapes were due solely to the tension of the toroidal magnetic eld. This was later applied by Chevalier & Luo (1994) to the case of PNe winds and found similar steady-state aspherical results. More recently, with the aid of 2-dimensional MHD simulations in cylindrical coordinates, Roz_ yczka & Franco (1996) found that the timedependent evolution has a very complex behavior and jet-like features and collimated outows can be created (see Figure 3). The 3-D computations performed by Garca-Segura (1997) corroborate 2-D results, with the main dierence that the collimated gas can be probably subject to kink instabilities. Thus, the formation of jets and ansae are conrmed in 3-D, axis-free, calculations. Now Garca-Segura et al. (1998) is performing 2-D, spherical calculations, including the eects rotation and magnetic elds that seem to be responsible for the wide variety of observed nebular morphologies. The magnetic eld in an outowing wind from a rotating star has a toroidal component that decreases with distance as r01 . The precise form of the oequator distribution of this toroidal component is unimportant, provided that the eld is suciently strong to cause a deformation in the shocked wind region (Roz_ yczka & Franco 1996). The radial eld component decreases as r02 , and can be neglected, so the used eld conguration obeys r 1 B = 0. The main eects of the magnetic eld is the elongation of the nebula in the polar direction, and the creation of jets. The generation of a jetlike outow has been described by Roz_ yczka & Franco (1996). First, the outer part of the magnetized shocked wind region becomes magnetically rather than thermally dominated (the magnetic energy density gets larger than the thermal energy density). Second, the tension of the toroidal eld slows down the expansion in the directions perpendicular to the symmetry axis, while the expansion in the direction parallel to the axis proceeds unimpeded. Third, a ow from the equatorial parts of the shocked wind 92 FRANCO AND GUILLERMO GARC JOSE A-SEGURA Interacting winds: magnetic fast wind interacting with a slow AGB wind. Both winds are spherically symmetric and the fast post-AGB wind has a toroidal magnetic eld. Figure 3. region toward the symmetry axis is initiated, leading to the formation of stagnation regions at the axis and to the formation of jets. The gas arriving at the polar regions of the nebula forms relatively dense blobs which can be identied with the ansae observed in PNe (such as the ones in NGC 7009; see Lopez et al. 1993). Perhaps the most important issue that has to be stressed here, is that magnetic collimation becomes very ecient (even for a spherically symmetric outow) after the ow has been processed by a shock. Also, the collimation is operative up to very large distances, even when the resulting jets develop kink instabilities. Note that external anisotropic density distributions are not required but, if they occur, they can produce even more elongated structures. When stellar rotation is included in the AGB wind, a high-density region with a compressed B -eld is generated near the equatorial plane (see Ignace, Cassinelli & Bjorkman 1998). In this case, all the eects described above occur faster and have a stronger impact in the evolution of the resulting nebula: the magnetic eect is enhanced, and a higher degree of collimation is achieved. Thus, a combination of rotation and a magnetic eld can naturally account for some of the most interesting features in PNe. This however does not preclude that other eects (such as external density anisotropies) can take place at the same time, resulting in even richer morphological structures. PHOTOIONIZATION AND MAGNETIZED WINDS 4. 93 Summary Molecular clouds are composed of a collection high-density clumps, with densities reaching 107 cm03 . These dense clumps, or cloud cores, are supported by non-thermal motions and seem to be the actual sites of star formation. The initial shape and early evolution of the H ii regions, then, are controled by the core density distributions. Depending on these distributions, and the corresponding stellar UV eld, the photoionized regions can either reach pressure equilibrium inside the high-pressure cores (with sizes and densities similar to those observed in UCH ii regions), or create blister-type H ii regions with champagne ows. Disk-like cores can generate photoionized regions with a bipolar shape, and the ows are accelerated along the steeper density gradients. In all cases, the density inhomogeneities engulfed within the ionization fronts are smoothed out in short timescales, but new clumps are continuously created by the fragmentation of the dense shells generated by the shock fronts. Instabilities in the ionization/shock front drive the fragmentation of the shell, and the resulting nger-like structures can explain the existence of elephant trunks and cometary-like globules in most H ii regions. Finally, when one includes the external dissociation front, a double shock structure with a complex behavior is formed. The dissociation front destroys additional molecular gas and, eectively, diminishes the productivity of star formation. In the case of PNe, the ambient density structure is strongly modied by winds from the progenitor star. Stellar wind asymmetries and magnetic elds from rotating stars, along with the ionizing ux from the star, can create the wide range of observed PNe morphologies and magnetically collimated outows (jets). This magnetic collimation is also operative in young stellar objects and can be responsible for the generation of protostellar jets. Perhaps the most important issue here is that magnetic collimation, and jet formation, becomes very ecient after the ow has been passed through a shock. All these features warrant further research, and future studies should shed more light on magnetic collimation in shocked regions. We are grateful to our good friends Rossy Diaz-Miller, Tim Freyer, Beto Lopez, Norbert Langer, Mordecai-Mark Mac Low, Michal Rozyczka, and Steve Shore who have collaborated with us in dierent aspects of the work reported here. We also thank Frank Bertoldi for suggestions on PDRs. This work was partially supported by DGAPA-UNAM, CONACyT grants 400354-5-4843E and 400354-5-0639PE, and by a R&D CRAY Research grant. Part of the computations were performed at the Supercomputer Center of UNAM. 94 FRANCO AND GUILLERMO GARC JOSE A-SEGURA References Aller, L. H. 1993, in Planetary Nebulae, ed. R. Weinberger & A. Acker (Dordrecht: Kluwer), 1 Arquilla, R. & Goldsmith, P. 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