Annu. Rev. Astron. Astrophys. 1992. 30: 705-742
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Mutual tidal capture of two disk galaxies during a close, planar passage was illustrated by Holmberg (1941), using an optical analog computer to perform N-body integrations. However, these calculations were part of an investigation into the origins of galaxy clustering, and Holmberg elsewhere - perhaps reluctantly - rejected the idea that repeated tidal encounters would cause galaxies to merge. Thus Zwicky (1959) seems to have been the first to propose that very close encounters might lead to ``considerable disruption of both systems [or] total mutual capture''. This possibility was also mentioned by Alladin (1965) in his analytic study of fast - in other words, hyperbolic - encounters of spherical galaxies. But an appreciation of the terrible strength of inelastic effects in slower encounters remained largely lacking, although TT estimated that the relative orbit of NGC 4038 / 9 had decayed from e = 0.8 to e = 0.5 as a result of the most recent passage, and that even more severe orbital decays seemed necessary to account for the the half-dozen objects which they described as each resembling ``a single luminous ball, from which protrude several tentacles or filaments''.

Evidence for violent tidal friction was thereafter sought in self-consistent simulations. At the same time, evidence began to collect that disk galaxies might be surrounded by massive dark halos (Ostriker & Peebles 1973); it was noted that such halos would increase the merger cross-sections of visible galaxies (e.g. Toomre 1977). The simplest N-body simulations modeled the encounter of a pair of spherical galaxies. As White (1978) pointed out, these experiments are perhaps best viewed as reproducing the dynamics of dark halos.

Spherical Systems

N-body models illuminated the mechanisms responsible for rapid orbital decay. In head-on collisions, decay results from the gravitational compression arising when the two galaxies nearly coincide; this compression causes a slightly greater axial force to be felt between them as they try to separate than they experienced at corresponding distances during their approach (Toomre 1974; van Albada & van Gorkom 1977; White 1978; Miller & Smith 1980). By stirring up the material in each galaxy at the expense of their orbital energy, this mechanism brings about the rapid merger of even the most centrally concentrated systems in only a few passages. In off-axis collisions, the collective response is dominated by those particles which orbit within their respective galaxies in the same direction as the two galaxies pass each other (White 1978, 1979; Roos & Norman 1979; Villumsen 1982, 1983). Such particles are again promoted onto less-bound orbits, receiving both binding energy and angular momentum from the relative motion of the two galaxies, and producing broad tail-like structures. Orbital decay is more rapid if the victim galaxies rotate internally in the same direction as their passage, since more of their constituents then match the angular speed of the perturber (White 1979).

All in all, it seems unlikely that any bound pair of galaxies can forever escape merging. In some cases the decay time-scale may be quite long, and it can become difficult to delineate the conditions leading to an eventual merger (e.g. Navarro 1989). However, White (1978) found that parabolic encounters between identical spherical galaxies with half-mass radii greater than their pericentric separation generally lead to rapid capture and merger on the subsequent orbital passage.

Fluctuating gravitational fields during the merging process tend to transfer binding energy between different components of the system, but such fluctuations damp down before a complete redistribution takes place. This incomplete violent relaxation only partly erases the original ordering of material in binding energy; the centers and outskirts of merger remnants remain dominated by particles from the respective centers and outskirts of the victim galaxies. Thus radial population gradients present in the progenitors may well survive the merging process (White 1980; Quinn et al. 1990).

After a merger, the remnant relaxes progressively outward on a time-scale comparable to the local crossing time. Outside the relaxed region at any typical instant is material falling back onto the remnant for the first time on long-period, loosely-bound orbits. Still further out lie bound particles which have yet to attain apogalacticon, and at even greater radii are those which have become unbound during the merger. Multiple passages before merger generate more complicated structures since each passage launches a fresh outward surge of loosely-bound mass. The amount of material which escapes depends on the structure of the victim galaxies as well as the parameters of their encounter. In general the escaping stuff comes from the outskirts of the original galaxies; truncated victims such as King (1966) models generally lose only a few percent of their mass after merging in parabolic encounters.

The material which does not quite escape eventually phase-mixes to form an extended envelope around the body of the remnant. Simple arguments based on continuity of the energy distribution imply that this envelope will have an rho propto r-4 density profile (Jaffe 1987; White 1987; McGlynn 1990). Insofar as such a density profile provides a fair approximation, in projection, to the outer parts of a de Vaucouleurs law, the continuity of the distribution function may help explain why de Vaucouleurs profiles are frequently produced in mergers, as well as in other situations involving violent relaxation (e.g. van Albada 1982; McGlynn 1984).

To the extent that the small amount of mass lost can be neglected, the overall scale of a merger remnant may be estimated by a straightforward energy argument (Hausman & Ostriker 1978; White 1983b). The simplest version describes the merger, following a parabolic encounter, of two identical galaxies; in this case the total mass and binding energy of the remnant are just twice the mass and binding energy of a single victim. Then the gravitational radius (rg ident G M2 / |U|), mean velocity dispersion, and characteristic surface density of the remnant must be respectively double, equal, and half the corresponding values for the victims. Note, however, that these relations are only valid for the remnant as a whole; energy conservation alone does not predict the central properties of merger remnants, nor how different components become distributed in multi-component remnants.

The cores of merger remnants are constrained by Liouville's theorem, since a system with a de Vaucouleurs profile extending all the way to the center requires an infinite peak in its phase-space density (May & van Albada 1984). Thus if the victim galaxies have finite cores, the remnant they produce must also have a finite core. In practice, mergers of spherical isotropic galaxies seem to produce only a modest decrease in the maximum coarse-grained phase-space density (e.g. Melott 1982; Farouki, Shapiro, & Duncan 1983). Remnants generally have core radii comparable to those of the victim galaxies, but their central densities and velocity dispersions are often higher, contradicting the homology assumptions invoked in some early theoretical discussions.

Mergers of spherical galaxies produce remnants with fairly simple shapes and kinematics (White 1983b). Head-on encounters result in prolate remnants with anisotropic velocity dispersions, whereas if the encounter is not quite head-on, the result is a slowly-tumbling triaxial object. Encounters with a pericentric separation Rp gtapprox 0.5 Rh, where Rh is the victim half-mass radius, generally result in nearly-oblate remnants with figures supported largely by internal rotation. This last outcome might appear to dispute the notion that slowly-rotating elliptical galaxies are formed by mergers - since it may seem unlikely that progenitors falling from separations of ~ 1 Mpc would frequently pass within only ~ 1 or 2 kpc of each other on their first plunge. However, hierarchical clustering generally favors rather close encounters (Aarseth & Fall 1980). In addition, extended dark halos take up much of the orbital angular momentum, an effect left only implicit in the early single-component studies.

Disk / Halo Systems

Dark matter has been included in more recent models of merging disk systems to support approximately flat rotation curves, to help prevent violent bar instabilities, and to otherwise make the simulations more realistic. Mergers between equally-matched disk/halo galaxies were presented by Gerhard (1981), Farouki & Shapiro (1982), Negroponte & White (1983), Barnes (1988; 1992); in addition, Gerhard (1983a, b) and Barnes (1989) discussed models in which several disk/halo galaxies merge sequentially. Over the past decade, the particle number N has increased by two orders of magnitude, but perhaps the most significant difference between the latest models and their predecessors is the scale of the halos modeled. In the earlier calculations, halos of approximately the same mass and radial extent as the visible disks were employed, obviously insufficient to maintain flat rotation curves out to the radii seen in some galaxies. Halos used in some recent calculations have four or more times the mass and several times the radial extent of the luminous components.

The dynamics of encounters between such galaxies are largely governed by the interactions of their extended dark halos; consequently even passages in which the visible components completely miss each other at first can lead to rapid orbital decay. Roughly speaking, a pair of spherical, interpenetrating dark halos interact if they were single-component systems: the orbital angular momentum of the two halos is transferred to internal degrees of freedom, imparting spin and creating broad tidal tails. More tightly bound components, such as embedded disks and/or bulges, are not much braked by the tidal forces retarding the dark matter; instead, these components lose orbital angular momentum mostly by interacting with their own surrounding halos, once the latter have been decelerated (Barnes 1992). It is the interaction between such extended dark halos that brings two galaxies to a ``screeching halt'' and subsequent merger while the luminous tails extracted from their disks are still well-defined and visibly incriminating (Barnes 1988).

As in mergers of spherical systems, the incomplete violent relaxation of disk/halo models only blurs the original ordering in binding energy; the tightly-bound components which contained most of the luminosity in the original galaxies will be found near the center of the merger remnant. Luminous material dominates the central regions of merger remnants precisely because the dense luminous parts of the infalling galaxies remain largely undisturbed until they finally encounter each other and merge within a now-common envelope of halo material (Barnes 1988). This ends any worry that mergers between galaxies with larger dark halos might mix up the dark and luminous components, producing diffuse, extended remnants with extremely low surface brightnesses.

Thus even if the two galaxies originally encountered each other on a parabolic orbit, the luminous regions typically find each other only after their relative orbit has become more tightly-bound. As a result, the luminous stuff tends to have a substantially higher velocity dispersion in a disk/halo remnant than it did in the initial galaxies (Farouki & Shapiro 1982). In parabolic mergers of composite bulge/disk/halo systems, the velocity dispersions of those particles belonging to the bulges are ~ 40% higher in the final remnant than in the initial galaxies (Barnes 1988). It seems likely, as Farouki & Shapiro already noted, that this effect might well remove Ostriker's (1980) objection that disk-galaxy merger remnants should have markedly lower velocity dispersions than elliptical galaxies of the same total luminosity. What is more, actual observations indicate that merger remnants have velocity dispersions consistent with normal ellipticals of the same luminosity (Lake & Dressler 1986).

A more interesting challenge to the simple slogan that ``merging disk galaxies make ellipticals'' comes from the expected core radii - or equivalently from the peak coarse-grained phase-space densities - of merger remnants. Central disk phase-space densities are lower than the peak phase-space densities of many lower-luminosity ellipticals (e.g. Carlberg 1986; Vedel & Sommer-Larsen 1990). Moreover, the violence needed to convert a pair of dynamically cold disks to a hot, spheroidal remnant must swirl a good deal of vacuum together with the disk phase fluid, further lowering the coarse-grained phase-space density (e.g. Barnes 1992). Thus merging disk galaxies cannot form the cores of ellipticals unless they contain either substantial pre-existing bulges or else sufficient interstellar material to build such cores dissipatively (e.g. Kormendy 1989).

The shapes and kinematics of the remnants of disk/halo galaxy mergers are much more complex and diverse than those produced by mergers of spherical systems, but certain generalizations can still be made (White 1983b). Just as for spherical systems, mergers from high angular momentum orbits tend to produce oblate, rapidly-rotating remnants, while those resulting from head-on encounters are prolate. But this is more true for the halos of remnants than for their luminous contents; orbital decay tends to leave the latter with but a small part of the orbital angular momentum they possessed originally. In many of the numerical experiments, the final encounters of the most tightly-bound components are observed to be nearly head-on, producing remnants with nearly prolate centers supported largely by particles on box orbits (Barnes 1990).

Remnants with rapidly rotating luminous components can result from direct or nearly direct encounters which allow the spin and orbital angular momenta of the original disks to reinforce each other. Such remnants have nearly oblate figures and owe much of their flattening to rotational support (Negroponte & White 1983). The significant streaming motions in these remnants are due to the many particles in direct minor-axis tube orbits. Highly flattened remnants can also be produced by nearly retrograde encounters, but here the comparable numbers of particles on direct and retrograde minor-axis tube orbits give the resulting objects little, if any, net streaming motion (Barnes 1992).

Encounters between more inclined disks tend to produce rounder, more slowly-rotating remnants with more luminous material on major-axis tube orbits. In some cases the initial spins of the disks are ``remembered'' in the sense that circulation about the major axis in one direction is favored over circulation in the other direction (Barnes 1992); such differential population of the various orbit families can result in large misalignments between the spin and minor axes (Levison 1987). Recent studies of elliptical galaxies suggest that most have small kinematic misalignments, while a minority have spin vectors nearly parallel their major axes (Franx et al. 1991); if substantiated, this may still prove a serious obstacle to the production of ellipticals by mergers of inclined disk galaxies.

Finally, some experiments yield merger remnants with intrinsic axial twists or rapid figure rotation (Gerhard 1983a, b; Barnes 1992). The long-term stability of such configurations remains an open question; effects related to the diffusion of chaotic orbits, for example, may only show up on time-scales so long that they are completely obscured by the ``particle noise'' in the potentials of existing N-body models.

Gas Dynamics in Merging Disk Galaxies

If pressure forces are small, the gas in interacting galaxies follows the same trajectories as the stars, but shocks can transfer momentum between parcels of gas and thereby drive it off the stellar track. Long ago, Spitzer & Baade (1951) suggested that global shocks could sweep the gas from spiral galaxies during fast interpenetrating collisions, producing gas-poor disks resembling S0 galaxies, but this idea did not survive revised estimates of collision rates. Unless the encounter geometry is just right, the fraction of gas removed by direct impacts cannot be large. But tidal forces in slow passages can perturb the gas and stars alike over most of an entire disk, and if large-scale shocks develop in the gas, its flow may diverge markedly from that of the intermixed disk stars.

Self-consistent models of interacting gas-rich spirals (Negroponte & White 1983; Barnes & Hernquist 1991; Noguchi 1991) suggest that the most common result of such tidal perturbations is indeed not to eject the interstellar material but to drive a large fraction of the it close to the center of each galaxy. One - but not the only - way this can happen is for the perturbed stellar disk to form a bar (e.g. Noguchi 1987); gravitational torques between the bar and the shocked gas rob the latter of its angular momentum and so allow it to flow inward (Barnes & Hernquist 1991; see also Noguchi 1988; Combes et al. 1990). If the encounter is a close one, the shocks generated are extremely strong and a substantial fraction of the gas in the disk can flow inwards on a dynamical time-scale. This inward-driven gas typically collects in a rotating ring or ``blob'' with dimensions, scaling the models back to reality, of ltapprox 1 kpc (e.g. Barnes & Hernquist 1991).

Only when two galaxies undergo a final, nearly head-on collision will hydrodynamic forces between these newly-built gas blobs come into play. Such ``final encounters'' result from orbital decay in bound pairs of galaxies. In the present context, the central gas blobs lose orbital angular momentum to the surrounding stellar stuff. Their eventual coalescence cancels out much of their residual spin about different axes. Thus experimental merger remnants are often left with massive central gas clouds containing gtapprox 50% of the gas initially spread throughout the victim disks. The linear dimensions of these clouds, corresponding to a few hundred pc, are comparable to the spatial resolution of the calculations; more detailed simulations are needed to model the structure of these central concentrations.

The ultimate fate of gas in merging galaxies will be still more difficult to predict. Observations discussed in the next section imply that compression in large-scale shocks and in the dense gas clouds may convert a substantial fraction of the gas to stars on a ~ 108 yr time-scale (e.g. Larson 1987). It seems likely that energy released by stellar or non-thermal activity could blow out most of the remaining gas, producing the ``super-winds'' seen in some IR-luminous galaxies (e.g. Baan et al. 1989; Heckman et al. 1990). Such outflows may well strip merger remnants of their cool interstellar gas, create the x-ray coronae around some ellipticals (e.g. Forman et al. 1985; Fabbiano 1989), or even transport metals back to the intercluster medium. However, these possibilities have not been convincingly demonstrated in numerical simulations.

If the time-scale for star-formation significantly exceeds the remnant's central dynamical time-scale, the gas may settle into a relatively thin central disk like the one in NGC 7252 (Schweizer 1982). A similar disk has been reported in a numerical model of merging spiral galaxies (Hernquist & Barnes 1991). Because the gas must lose so much angular momentum to arrive where we find it, the small amount of spin it retains may not be well-correlated with the rotation of the merger remnant as a whole. Indeed, both NGC 7252 and the above-mentioned model contain counter-rotating gas disks, spinning in the opposite direction from the rest of the remnant. Subsequent star formation would leave a compact stellar disk (e.g. Schweizer 1990) with kinematics unlike the rest of the galaxy, perhaps resembling the ``kinematically decoupled'' cores found in elliptical galaxies (e.g. Bender 1990a and references therein). Counter-rotating systems can be produced by purely stellar-dynamical mergers (Kormendy 1984; Balcells & Quinn 1990), and apparent counter-rotation may also result from projection effects in triaxial systems with streaming motions (Statler 1991). However, the line-profiles of some systems indicate that their disks are dynamically ``cold'' (e.g. Bender 1990b; Rix & White 1992); such disks were probably assembled in gaseous form as described here.

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