This is a fun IMBH story we worked out when Kostas and Luca were visiting last summer from JHU. What if (one day, who knows) we observe a highly spinning intermediate-mass black hole? If that happens, is going to be puzzling because IMBH that grow in clusters by mergers of smaller black holes tend to spin down, not up. This is a funny property of black holes, namely that extracting spins is easier than putting it in, so on average black holes slow down after they have merged many times. So if we see an IMBH with large spins, the spin must come from somewhere else. Where? Maybe gas. The argument then is that one can actually convert an IMBH spin measurement into the minimum amount of gas that must have been accreted to get that spin.

Konstantinos Kritos, Luca Reali, Davide Gerosa, Emanuele Berti.
arXiv:2409.13011 [astro-ph.HE].