7.2. Properties of merged galaxies
Motivated by the near coincidence of the expected number of merged remnants with the total number of elliptical galaxies in the NGC catalogue and the expectation that the merging of spiral discs would probably lead to "spheroidal heaps of stars," Toomre speculated that elliptical galaxies form from mergers. This idea has received some observational support. Schweizer (1982, 1983) has studied the merger remnant NGC 7252. The two long tails seen in this galaxy indicate a merger between two disc galaxies of about equal masses. The mean surface brightness profile, however, follows the de Vaucouleurs r1/4 law quite closely. This result suggests that merging has rearranged the disc material into something resembling an elliptical galaxy. Malind and Carter (1980) have observed shell-like structure around many elliptical galaxies. Quinn (1982, 1983) has shown that merging a cold disc with a more massive elliptical galaxy results in shells. In addition, merging can also account for the observed pattern between the radial spacings of the shells which other mechanisms, such as galactic winds (Fabian, Nulsen and Steward, 1980) could probably not explain.
Although the idea that many elliptical galaxies have formed from the merging of discs is still highly controversial (Ostriker, 1980; Tremaine, 1981), the suggestion has stimulated several theoretical investigations into the properties of merged remnants. In most cases the studies have been highly idealized, e.g. collisions between purely stellar systems of comparable masses. Even so, some very interesting results have emerged.
7.2.1. Density profiles
White (1978, 1979b) has studied the merging of equal mass spheroidal stellar systems using Aarseth's N-body program. The models are quite crude since each "galaxy" is represented by only 250 particles. This reduces the effective dynamic range because a large softening length must be used in the gravitational potential in order to reduce the effects of two-body relaxation (cf. Section 6.2). White has found that the merger remnants all have similar density profiles with (r) r-3 independent of the initial density profiles of the progenitors. It is almost certain that this result is due to merging rather than two-body relaxation since White finds that "galaxies" evolved in isolation maintain density profiles that are quite different than the r-3 behaviour of the merger remnants. Although encouraging, the results are not applicable to the formation of ellipticals from spirals since the N-body calculations start with spheroidal systems.
The much harder problem of disc mergers has only been tackled recently (Gerhard, 1981; Farouki and Shapiro, 1982; Quinn, 1982; Negroponte, 1982; Negroponte and White, 1983). Much of the problem of simulating encounters between disc galaxies stems from their instability towards forming bars (Ostriker and Peebles, 1973). There are several ways of suppressing the bar instability. The discs may be set up with large random motions, ~ vrot (where vrot is the rotational velocity) but this conflicts with the kinematics of stars in the solar neighbourhood where vrot 250 km sec-1 and ~ 40 km sec-1 (Toomre, 1974, and references therein). The bar instability may be suppressed by using a very large softening parameter in the gravitational potential (Erickson, 1974; Quinn, 1982) but this is artificial and significantly limits the resolution of the models. Alternatively, one can adopt the method advocated by Ostriker and Peebles and include a hot halo component. Using a halo has the disadvantage that the already meagre number of particles used in the simulations must be shared between the halo and the disc components. There is also the additional problem of two-body relaxation in the disc component (Rybicki, 1971). These problems have still not been fully resolved and it is clear that more work needs to be done. Nevertheless, the results from numerical simulations show that both the halo and "luminous" components acquire Hubble-type density profiles after merging. A numerical simulation of a merger between two disc-halo systems is shown in Figure 7.2 (Negroponte and White, 1983).
Figure 7.2. Numerical simulation of a merger between two disc halo systems. The upper block of pictures shows the halo particles and the lower block shows disc particles. In each block, the upper panel shows a projection looking down onto the orbital plane and the lower panel shows a projection in the orbital plane (from Negroponte and White, 1982, with permission).
An important objection to the idea that ellipticals form from merging spirals has been discussed by Ostriker (1980). In a somewhat modified form the argument runs as follows. Consider a cold self-gravitating exponential disc with scale length -1 and mass MD. Its total energy is ED = - 0.15GMD2 (Fall, 1979b, Eq. 6.24). Now, as indicated by the merger experiments, if two such identical discs merge, the resulting object should be spheroidal with a density profile close to the de Vaucouleurs r1/4 law. Thus the total internal energy of the merged remnant is EE - 0.17GME2 / RE. During the merger, the total energy and mass are fairly well conserved, so if the discs merge with orbital energy E0,
Equation (7.4a) may be written in terms of the peak projected velocity dispersion of the remnant p,
where vm is the peak rotational velocity of the exponential disc. The orbital energy E0 is usually negligible in Eq. (7.4b), hence in order to obtain a giant elliptical with a velocity dispersion of 300 km/sec one requires vm 400 km/sec which is a higher rotational velocity than is seen in any spiral. Inclusion of heavy halos may modify the above argument. However, the results of Gerhard's simulations give p vm / 21/2 in good agreement with Eq. (7.4b). It is possible that dissipative effects can help resolve this problem. The numerical simulations of Negroponte and White (1983) include a "gas" component and they find that a substantial fraction of the gas falls to the central regions during a merger.