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

**6.4. Is the Halo made of Dark Clusters?**

We have seen that both the cluster disruption and dynamical friction
constraints
may be incompatible with the Lacey & Ostriker proposal that 2 ×
10^{6}
*M*_{}
halo black holes generate the observed disk-heating. There is also the
problem
that supermassive halo black holes might generate too much radiation
through accretion as they traverse the disk
(Ipser & Price 1977).
To circumvent these objections,
Carr & Lacey (1987)
have proposed that the disk heaters are 2 × 10^{6}
*M*_{}
*clusters* of smaller objects rather than single black holes. The
accretion luminosity is then reduced by a factor of order the number of
objects
per cluster and the dynamical friction problem is avoided, provided the
clusters
are disrupted by collisions before they are dragged into the Galactic
nucleus by dynamical friction.

One can extend this idea to a more general cluster scenario
(Wasserman & Salpeter 1993,
Kerins & Carr 1994,
Moore & Silk 1994).
If we assume that the
clusters all have the same mass *M*_{c} and radius
*R*_{c}, then they will be disrupted
by collisions within the Galactocentric radius (6.3) at which dynamical
friction operates, providing

(6.6) |

If this condition is not satisfied, then *M*_{c} must be
less than the value indicated
by Equation (6.5). In order to avoid the evaporation of clusters as a
result of 2-body relaxation, one also requires

(6.7) |

where *m* is the mass of the components. An *upper* limit on
*R*_{c} comes from
requiring that the clusters do not disrupt at our own Galactocentric
radius *R*_{0} ~ 10 kpc which implies

(6.8) |

These dynamical limits, together with the disk-heating limit (6.1), are
indicated
by the bold lines in Figure 4, which show that
the values of *M*_{c} and *R*_{c} are
constrained to a rather narrow range. The cluster-disruption upper limit
on *M*_{c}
is not shown because it is rather model-dependent but it could further
reduce the range.

There is some uncertainty in the positions of the boundaries in
Figure 4. If
one merely requires that the clusters do not disrupt at the edge of the
halo, the
upper limit (6.8) is increased by a factor of (*R*_{h} /
*R*_{0})^{2}, as indicated by the dotted
line in Figure 4. The dynamical friction limits
are sensitive to the value of *a*:
the limits are shown for *a* = 2 kpc and *a* = 8 kpc since
this spans the range
of likely values. The evaporation limit given by Equation (6.7) depends
on the value of *m*: Figure 4 assumes
*m* = 0.02
*M*_{}. Note
that together Equations
(6.1), (6.7), and (6.8) require the cluster components to be smaller
than 10
*M*^{2}_{}, which probably excludes their being VMO black holes.