Annu. Rev. Astron. Astrophys. 1994. 32: 531-590 Copyright © 1994 by Annual Reviews. All rights reserved

6.5. Constraints on Dark Objects Outside Halos

Dynamical constraints on dark objects in the Galactic disk are generally stronger than the halo limits. In particular, Bahcall et al (1985) have argued that the disk dark matter could not comprise objects larger than 2 M or else they would disrupt the wide binaries observed by Latham et al (1984). [This limit can be deduced from Equation (6.2) by identifying m_c and r_c with the total mass and separation of the binary.] This is an important constraint because, if correct, it rules out disk dark matter comprising stellar black holes. However, the Bahcall et al conclusion has been disputed by Wasserman & Weinberg (1987) on the grounds that there is no sharp cut-off in the distribution of binary separations above 0.1 pc. The limit is therefore weakened (somewhat arbitrarily) to 10 M in Figure 3.

Dynamical constraints on dark objects in clusters of galaxies are weaker than the halo limits. For example, one does not get an interesting constraint by applying Equation (6.2) to the disruption of cluster galaxies by cluster black holes because the upper limit on _B exceeds the cluster density. However, one does get an interesting constraint from upper limits on the fraction of galaxies f_g with unexplained tidal distortions. Equation (6.2) can also be applied in this case, except that the limits are weakened by a factor f^-1_g, where the parameter (~ 2) represents the difference between distortion and disruption. Van den Bergh (1969) applied this argument to the Virgo cluster and inferred that black holes binding the cluster could not be bigger than 10⁹ M. If we assume that Virgo is typical, we obtain the limit indicated in Figure 3. We also show the limit corresponding to the requirement that there be at least one black hole of mass M within the cluster.

The dynamical constraints on intergalactic black holes are even weaker. The most interesting one comes from the fact that, if there were a population of huge intergalactic black holes, each galaxy would have a peculiar velocity due to its gravitational interaction with the nearest one (Carr 1978). If the holes were smoothly distributed and had a number density n, one would expect every galaxy to have a peculiar velocity of order GMn^2/3 t_g. Since the CMB dipole anisotropy shows that the peculiar velocity of our own Galaxy is only 600 km s^-1, one infers a limit _B < (M / 10¹⁶ M)^-1/2 and this is also shown in Figure 3. The limit on the bottom right corresponds to the requirement that there be at least one object of mass M within the current particle horizon.