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 ($r_{\mathrm{S}}\sim 10^{-11}$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 ($M_{\mathrm{BH}}\lesssim 10^{-14}{M}_{\odot }$) 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 $M_{0,\mathrm{crit}}\sim 10^{-16}{M}_{\odot }$.

21 pages, 11 figures. Submitted to ApJ