Gas depletion in primordial globular clusters due to accretion onto stellar-mass black holes

Abstract

(abridged) We consider the effect of stellar remnants on the interstellar medium of a massive star cluster following the initial burst of star formation. We argue that accretion onto stellar-mass black holes (BHs) is an effective mechanism for rapid gas depletion in clusters of all masses, as long as they contain progenitor stars more massive than \gtrsim 50\msun. This scenario is attractive for the progenitor systems of present-day massive globular clusters (GCs) which likely had masses M \gtrsim 10^7\msun. In such clusters, supernovae and stellar winds cannot provide a plausible explanation for the sudden removal of the primordial gas reservoir that is required to explain their complex chemical enrichment history. In order to consider different regimes in the gas accretion rate onto stellar-mass BHs, we consider both the Bondi-Hoyle and Eddington approximations. For either model, our results show that the gas can be significantly depleted within only a few tens of Myrs. This process will affect the distribution of BH masses, and may accelerate the dynamical decoupling of the BH population and, ultimately, their dynamical ejection. Moreover, the timescales for gas depletion are sufficiently short that the accreting BHs could significantly affect the chemistry of subsequent star formation episodes. The gas depletion times and final mass in BHs are sensitive to the assumed model for the accretion rate, and to the initial mass of the most massive BH which, in turn, is determined by the upper mass cut-off of the stellar IMF. Our results imply that the remnant accretion history can have an important bearing on the observed present-day cluster mass-to-light ratio. In particular, we show that an increase of the upper mass cut-off with decreasing metallicity could contribute to the observed anti-correlation between the mass-to-light ratio and the metallicity of GCs.