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 χ0.6 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 M1000M and χ0.6, respectively, the IMBH must have coherently accreted at least ∼100M of gas. In this scenario, as long as the spin is not maximal, the IMBH can only accrete at most half of its mass. Our estimates can constrain the relative contribution of accretion and mergers to the growth of IMBHs in dense stellar environments.