Canaries in a coal mine: using globular clusters to place limits on massive black holes in the Galactic halo

We explore the possibility that massive black holes comprise a significant fraction of the dark matter of our Galaxy by studying the dissolution of Galactic globular clusters bombarded by them. In our simulations, we evolve the clusters along a sequence of King models determined by changes of state resulting from collisions with the black holes. We include mass loss in collisions as well as the heating of the remaining bound stars, and determine the role that a finite number of stars plays in the variance of the energy input and mass loss. Several methods are used to determine the range of black hole masses and abundances excluded by survival of Galactic globular clusters: simple order-of-magnitude estimates: collision-by-collision simulations of the energy input and mass loss of a stellar cluster; and a 'smoothed' Monte Carlo calculation of the evolution of cluster energy and mass. The results divide naturally into regimes of 'small' and 'large' black hole mass. 'Small' black holes do not destroy clusters in single collisions: their effect is primarily cumulative, leading to a relation between Mbh and fhalo, the fraction of the halo in black holes of mass Mbh, which is fhaloMbh < constant (up to logarithmic corrections). For fhalo = 1, we find Mbh ≲ 103 M⊙ by requiring survival of the same clusters studied by Moore, who neglected cluster evolution, mass loss, and stochasticity of energy inputs in his estimates, but reached a similar conclusion. 'Large' black holes may not penetrate a cluster without disrupting it; their effect is mainly catastrophic (close collisions), but also partly cumulative (distant collisions). In the large-Mbh limit, fhalo (but not Mbh) can be constrained by computing the probability that a cluster survives a combination of close, destructive encounters and distant, non-destructive encounters. We find that it is unlikely that fhalo ≳ 0.3 by requiring 50 per cent survival probability for Moore's clusters over 1010 yr.