7.2.2. Rotational properties
Consider the merger of two non-rotating systems, with impact parameter rp 2rh, and orbital energy E0 0. From the cross-section of Figure 7.1 the total orbital angular momentum will be approximately J0 mrp(Gm / rp)1/2. The final merged remnant will then have a spin parameter, max = J| E|1/2 G-1 M-5/2 0.14 which is about twice the value appropriate to giant elliptical galaxies ( 0.07). This difficulty was first discussed by White (1979a) who pointed out that the problem could only be resolved if merging occurred from bound, nearly linear orbits.
Recently, cosmological N-body simulations which include galaxy merging have been studied by several authors (Jones and Efstathiou, 1979; Aarseth and Fall, 1980; Roos, 1981; Findlay, 1983). These authors find that the merged remnants rotate slowly. In particular, the experiments of Aarseth and Fall show that most mergers occur with E0 0 and a flat distribution of impact parameters between 0 rp 2rh. Thus the median value of expected of merged remnants will be 0.07, in good agreement with observations. Inclusion of internal spins is also straightforward in such calculations. For large galaxies, which undergo several mergers, the inclusion of internal spins (i = 0.43, appropriate for a self-gravitating exponential) makes little difference to the final values of . For small galaxies, including internal spins increases the final value of (Findlay, 1983). This result is in qualitative agreement with observations which show that faint ellipticals generally have higher values of than bright ellipticals (Davies et al., 1983). The cancellation of internal spins is easy to understand. If the initial spins are randomly oriented and mergers occur with negligible orbital energy, the contribution to due to the internal spins will decrease as N-3/2 i, where N is the number of merged systems, assumed, to be identical and with initial spin parameter i. Hence roughly N 3 suffices to reduce from 0.43 to 0.07 (Fall, 1979b). These results are interesting since they illustrate how slowly rotating galaxies and rapidly rotating discs could both form without the need for varying amounts of dissipation or a bimodal distribution of angular momenta (Efstathiou and Jones, 1980). It must be emphasized, however, that the cosmological simulations do not satisfactorily model the behaviour of the dark matter, and this may influence the results on rotation in a complicated way (e.g., Silk and Norman, 1981; Kashlinsky, 1983).
The models of White (1978, 1979b), Villumsen (1982) and Gerhard (1981) also show that merging will redistribute the orbital angular momentum to produce a fairly flat rotation curve and that off-centre collisions will lead to an oblate, or triaxial, configuration whose short axis lies parallel to the initial orbital angular momentum vector, the flattening being partly due to velocity anisotropy. Nearly head-on collisions result in prolate configurations with the long axis parallel to the initial trajectory.