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3.1. Dynamical Friction

When two galaxies start orbiting around each other, the first long-range process that drives their evolution is dynamical friction. When one object (e.g., the stellar body of a galaxy) flies through another mass distribution (e.g., the dark matter halo of the other galaxy), the gravitational forces will unavoidably create a mass accumulation from the latter system along the wake of the first object. This will in turn induce braking forces. This process also acts on non-overlapping systems, although it is much weaker then. Dynamical friction is what drives the merger of interacting galaxies into single, more massive objects. In the process a small fraction of the mass is expulsed and becomes unbound, carrying away a substantial fraction of the initial energy at high velocity, so that the merger remnant is a lower-energy, usually more compact system.

3.2. Violent Relaxation

The typical merger timescale for a pair of massive galaxies is about a billion year, although large variations are possible for small impact parameters or high encounter velocities. This is barely larger than the rotation period of the outer disk of a spiral galaxy. Thus, stars (or gas clouds or dark matter particles) in an interacting and merging system undergo a variation in the mass distribution/gravitational potential that is relatively rapid compared to their own dynamical timescale. In such conditions stellar orbits do not follow a slow secular evolution anymore, but can be completely redistributed. For a given star, the average energy along its final post-merger orbit can be quite different from the initial average energy along the initial pre-merger orbit: this large difference arise because of the rapid change in the mass/potential distribution and defines the violent relaxation. Some stars (or gas clouds or dark matter particles) will then undergo large decrease of their average energy, which implies that they sink towards the central regions: the central regions of galaxies thus become denser and more compact in a merger. Other stars will gain energy and increase their orbit semi-major axis - some even escape: a more extended outer envelope in the mass distribution results.

When one writes the projected radial surface density profile of a galaxy as a Sersic profile log(Sigma) ~ µ ~ e-(r - a)1/n / b), where n is the Sersic index, spiral galaxies have exponential disks with n appeq 1. A merger remnant will have a steeper central profile and a more extended outer envelope, which corresponds to n > 1. The high Sersic indices of elliptical galaxies (say, 2 < n < 6) are thus consistent with the common idea that they are the end-product of spiral-spiral mergers.

3.3. Gas response and tidal torques

The tidal field    A first driver of the gas response in galaxy interaction is the tidal field. Typically, the tidal field of a single galaxy is disruptive at large radius and outside its own disk, but can be compressive in the inner regions if the mass distribution has a low Sersic index. During a distant interaction or the early stages of a merger, a given galaxy is then mostly affected by a disruptive tidal field from its distant companion. More advanced mergers can have compressive tidal field over large regions, when the galaxies begin to overlap (e.g., Renaud et al. 2008 for the Antennae).

While a disruptive tidal field naturally tends to expel material from disk galaxies, it is not the only mechanism responsible for the formation of long tidal tails, and it cannot explain central gas inflows: this is in fact mostly driven by gravity torques.

Gravity torques, inflows and outflows    The tidal field from a companion breaks the symmetry of the gravitational potential. This induces a response of the disk material, in particular its cold gas, which is more pronounced for prograde 2 interactions. The gas can form an interaction-driven pair of grand-design spiral arms, like modeled in detail for instance for M51 by Dobbs et al. (2010) - note though that grand-designs spiral do not require an interaction to form (Elmegreen & Thomasson 1993), and are not connected to interactions in observations (van den Bergh 2002). The gas response is often more complex than a pair of spiral arms, but a general feature remains: inside the corotation radius 3, the gas preferentially concentrates on the leading side of the valley of potential; outside of the corotation it concentrates on the trailing side. A similar but better-known gas response is found in barred galaxies, where the disk symmetry is broken about the same way by the barred pattern (Combes & Gerin 1985, Athanassoula 1992). A corotation does not always exist and can move with time, but is in general located at a few kpc of radius in the disk. The subsequent process is illustrated on Figure 3: inside the corotation, the gas undergoes negative gravity torques, and loose angular momentum in a rapid central gas inflow towards the central kpc or less. In the outer disk, gas would gain angular momentum and fly out to larger radii in long tidal tails.

Figure 3

Figure 3. Simplified description of the gas response in a galaxy interaction. Inside the corotation radius, gas concentrates on the leading side of the valley of potential and undergoes negative gravity torques, which drives a central gas inflow. At the opposite, positive gravity torques dominate outside the corotation, which drives lot of the outer disk material in the so-called "tidal" tails. In detail the gas response is more complex because the system evolves rapidly in a non-equilibrium configuration, but the main response is the one shown here. The same response occurs in barred galaxies in a weaker but more directly observable way (see Figure 4).

Figure 4

Figure 4. In a barred galaxy, the valley of potential along the bar induces the same gas response as in an interaction (but at a weaker degree). The gaseous arms on the leading side of the bar inside the corotation radius, attested by two sharp dust lanes on this optical image, are more visible as the system evolves in a steady state.

It is worth noting that:

Collisional ring galaxies form through a different dynamical process. The central impact of a companion onto the disk triggers large epicyclic motions around the initial orbits of stars and gas clouds. The superposition of motions and the variation of the epicyclic frequency with radius result in an expanding wave of material. This process is thoroughly reviewed by Appleton & Struck-Marcell (1996). The ring wave is initially an unbound feature, like the spiral waves in an isolated disk, but the ring can become self-gravitating, bound, when enough mass is gathered in the ring (e.g., Bournaud et al. 2007). While the initial process differs, collisional rings and are relatively similar to tidal tails in terms of substructure formation, so they will hereafter be treated as the same kind of "tidal" structures.

2 in which the orbit and disk rotations have similar orientations. Back.

3 The corotation radius is the radius at which the rotation speed of the studied disk equals the orbital speed of the companion. Back.

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