**7.2.2. Rotational properties**

Consider the merger of two non-rotating systems, with impact parameter
*r*_{p}
2*r*_{h}, and orbital energy
*E*_{0}
0. From the cross-section of
Figure 7.1 the
total orbital angular momentum will be approximately
*J*_{0}
*mr*_{p}(*Gm* / *r*_{p})^{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
*E*_{0}
0 and a flat distribution of impact parameters between
0 *r*_{p}
2*r*_{h}.
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.