Bondi accretion in the early universe

This paper presents a study of quasi-steady spherical accretion in the early Universe, before the formation of the first stars and galaxies. The main motivation is to derive the basic formulas that will be used in a companion paper to calculate the accretion luminosity of primordial black holes and their effect on the cosmic ionization history. The following cosmological effects are investigated: the coupling of the gas to the CMB photon fluid (i.e., Compton drag), Hubble expansion, and the growth of the dark matter halo seeded by the gravitational potential of the central point mass. The gas equations of motion are solved assuming either a polytropic or an isothermal equation of state. We consider the cases in which the accreting object is a point mass or a spherical dark matter halo with power-law density profile, as predicted by the theory of "secondary infall''. Analytical solutions for the sonic radius and fitting formulas for the accretion rate are provided. Different accretion regimes exist depending on the mass of the accreting object. If the black hole mass is smaller than 50-100 Msun, gas accretion is unaffected by Compton drag. A point mass and an extended dark halo of equal mass accrete at the same rate if M>5000 Msun, while smaller mass dark halos accrete less efficiently than the equivalent point mass. For masses M>3 x 10^4 Msun, the viscous term due to the Hubble expansion becomes important and the assumption of quasi-steady flow fails. Hence, the steady Bondi solutions transition to the time-dependent self-similar solutions for "cold cosmological infall".