A paper recently came out in Nature simulating the evolution of the $\sim10^4M_{\odot}$ globular cluster Palomar 4 (Gieles et al. 2021, arXiv link). The authors argue that in ~1 billion years, a combination of low density, tidal stripping and a large initial black hole population mean that the cluster will become entirely composed of black holes. I was curious as to whether an object similar to the end product would be detectable - in other words, whether we could determine not just that there are a couple of black holes serendipitously in an area, but that they're actually part of a single structure, albeit diffuse.

My first thought was microlensing. The paper suggests that the quasars would be a good source but that the current lensing rate of $\sim10^{-8}\;\text{yr}^{-1}$ is too low to say much about the black hole population. This would probably increase as the black hole fraction grows, but I suspect not by much, given that ~20% of the cluster is believed to already be in the form of black holes. On the other hand, this lensing rate was computed for the region of the sky in and around Palomar 5, which is not necessarily optimal.

Assuming a cluster of black holes of a few thousand solar masses orbiting in the Galactic halo roughly 25 kpc from Earth, could we detect it? Would microlensing be possible, and if not, is there a better method I'm overlooking?


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