Accretion of Primordial Black Holes in Stellar Interiors

Abstract

We study spherical accretion onto primordial black holes (PBHs) embedded in the core of a solar-type star. We compute the radiative efficiency self-consistently for the first time across the optically thin range ($10^{-16.5}$-$10^{-10}M_\odot$) with time-dependent simulations, and follow the growth up to $10^{-2}M_\odot$ using an analytical photon-trapping prescription above $5\times 10^{-13}M_\odot$. Near the Schwarzschild radius ($r_{\rm S}\sim 10^{-11}$cm for a $10^{-16}M_\odot$ PBH), gas compressed to $T\sim 10^{11}$K radiates through microphysical processes that fundamentally alter the classical adiabatic Bondi solution. We solve the time-dependent spherical Euler equations with an implicit cooling source term, determining $\dot M$, $\eta = L/\dot M c^2$, and the flow structure self-consistently. We identify three regimes for spherical accretion: a Hot Bondi regime ($M_{\rm BH}\lesssim 10^{-14}M_\odot$) in which bremsstrahlung cooling is dynamically negligible; a bremsstrahlung-cooling regime ($10^{-14}$-$5\times 10^{-13}M_\odot$) driving the flow toward isothermal with $\eta\approx 10^{-2}$; and a photon-trapping regime above $5\times 10^{-13}M_\odot$, in which the Bondi sphere is optically thick and the accretion rate remains close to the Bondi value. Cooling enhances $\dot M$ by a factor of $\sim$2-7, keeping growth super-exponential throughout the spherical regime. The radiative efficiency is an order of magnitude lower than previously assumed, and the critical initial PBH mass required to consume a solar-mass star within a Hubble time is $M_{\rm 0,crit}\sim 10^{-16}M_\odot$.