The Growth of the Central Black Holes in Quasi-stars

Observations by JWST have confirmed the presence of supermassive black holes (BHs) at redshifts z ≳ 10, lending support to scenarios in which BHs experience rapid growth through intense gas accretion. Here we investigate the growth of a BH embedded at the center of a quasi-star, a theoretically predicted object formed via direct collapse. In a quasi-star, the central BH accretes at a highly super-Eddington rate, while the excess energy is transported outward by convection and radiated at approximately the Eddington luminosity of the entire star. We employ the open-source stellar evolution code MESA to construct quasi-star models and follow the time-dependent growth of the central BH under different prescriptions for the accretion rate at the inner boundary R_i, and further considering the effect of winds. For the case R_i = NR_B, where N is a constant and R_B is the Bondi radius corresponding to the mass of the BH and the gas infalling onto it, our models terminate when the BH mass reaches a critical value M_crit (N) = c_s³_,i/(12 √N³G³ πр_i ) (where c_s,i and ρ_i are the sound speed and density at R_i, respectively), a limit we also derive analytically. Models that feature an inner convective region matched to an outer adiabatic envelope exhibit BH growth up to approximately M_BH/M_★ ≃ 0.33, largely independent of the stellar mass M_★ itself. This ratio is approximately preserved even in the presence of mass loss, as several properties of the model are independent of the quasi-star’s total mass.