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

**6.2. Disruption of Stellar Clusters by Halo Objects**

Another type of dynamical effect associated with halo objects would be their
influence on bound groups of stars (in particular, globular clusters and
loose
clusters). Every time a halo object passes near a star cluster, the
object's tidal
field heats up the cluster and thereby reduces its binding energy. Over a
sufficiently large number of fly-bys this could evaporate the cluster
entirely. This process was first discussed by
Spitzer (1958)
for the case in which the disrupting objects are giant molecular clouds.
Carr (1978)
used a similar analysis to argue
that the halo objects must be smaller than 10^{5}
*M*_{} or else
loose clusters would
not survive as long as observed - but this argument neglected the fact
that sufficiently
massive holes will disrupt clusters by single rather than multiple fly-bys.
The correct analysis was given by
Wielen (1985)
for halo objects with the mass of 2 × 10^{6}
*M*_{}
required in the Lacey-Ostriker scenario and by
Sakellariadou (1984)
and Carr & Sakellariadou
(1994)
for halo objects of general mass.
By comparing the expected disruption time for clusters of mass
*m*_{c} and radius
*r*_{c} with the typical cluster lifetime
*t*_{L}, one finds that the local density of halo
holes of mass *M* must satisfy (cf
Ostriker et al 1989)

(6.2) |

Here *V*_{c} ~ (*Gm*_{c} /
*r*_{c})^{1/2} is the velocity dispersion within
the cluster, *V* is the
speed of the halo objects (~ 300 km s^{-1}) and we have
neglected numerical
factors of order unity. The increasing mass regimes correspond to
disruption by
multiple encounters, single encounters, and nonimpulsive encounters,
respectively.
Any lower limit on *t*_{L} therefore places an upper limit on
_{B}.
The crucial
point is that the limit is independent of *M* in the
single-encounter regime, so
that the limit bottoms out at a density of order
(_{c} /
*Gt*^{2}_{L})^{1/2}. The constraint is
therefore uninteresting if this exceeds the observed halo density
_{h}.
In particular,
if the clusters survive for the lifetime of the Galaxy, which is essentially
the age of the Universe *t*_{0}, the limiting density is
just
(_{c}
_{0})^{1/2}, where
_{0} is the
mean cosmological density. If *t*_{L} is much larger, than
*t*_{0}, the fraction of clusters
disrupted within *t*_{0} is *f*_{c} ~
*t*_{0} / *t*_{L} and so the limiting density
is reduced by the factor *f*_{c}.

The strongest limit is associated with globular clusters, for which we take
*m*_{c} = 10^{5}
*M*_{},
*r*_{c} = 10 pc, *V*_{c} = 10 km
s^{-1}, and *t*_{L} > 10^{10}y. We also
assume
that the holes have a speed *V* = 300 km s^{-1}. Rather
remarkably, due to the
"coincidence" that the halo density is the geometric mean of the
cosmological
density and the globular cluster density, the upper limit on
_{B} is
comparable to
the actual halo density; this suggests that halo objects might actually
*determine* the characteristics of surviving globular clusters (cf
Fall & Rees 1977).
Numerical calculations for the disruption of globular clusters by
Moore (1993)
confirm the general qualitative features indicated above: gradual mass
loss for small
halo objects and sudden disruption for larger ones. However, using data for
nine particular globular clusters, Moore infers an upper limit of
10^{3}
*M*_{}. This
is in the multiple-encounter regime and considerably stronger than the limit
implied by Equation (6.2) with *t*_{L} =
*t*_{0}, presumably because his clusters are
very diffuse. Because of the uncertainties, the line corresponding to
Moore's result is only shown dotted in
Figure 3.