Minimum gas mass accreted by spinning intermediate-mass black holes in stellar clusters

The spin of intermediate-mass black holes (IMBHs) growing through repeated black hole mergers in stellar clusters statistically asymptotes to zero. Putative observations of IMBHs with dimensionless spin parameter χ≳0.6χ≳0.6 would require a phase of coherent gas accretion to spin up the black hole. We estimate the amount of gas necessary to produce a given IMBH spin. If the observed IMBH mass and spin are greater than 1000 solar masses and 0.6, respectively, the IMBH must have coherently accreted at least 100 solar masses of gas. In this scenario, as long as the spin is not maximal, the IMBH can only accrete half of its mass at most. Our estimates can constrain the relative contribution of accretion and mergers to the growth of IMBHs in dense stellar environments.