Spherical accretion in a uniformly expanding medium

We consider spherically symmetric accretion of material from an initially homogeneous, uniformly expanding medium onto a Newtonian point mass M. The gas is assumed to evolve adiabatically with a constant adiabatic index Gamma, which we vary over the range Gamma is an element of [1, 5/3]. We use a one-dimensional Lagrangian code to follow the spherical infall of material as a function of time. Outflowing shells gravitationally bound to the point mass fall back, giving rise to a inflow rate that, after a rapid rise, declines as a power law in time. If there were no outflow initially, Bondi accretion would result, with a characteristic accretion timescale t(alpha,0). For gas initially expanding at a uniform rate, with a radial velocity U = R/t(0) at radius R, the behavior of the flow at all subsequent times is determined by t(alpha,0)/t(0). If t(alpha,0)/t(0) much greater than 1, the gas has no time to respond to pressure forces, so the fluid motion is nearly collisionless. In this case, only loosely bound shells are influenced by pressure gradients and are pushed outward. The late-time evolution of the mass accretion rate M over dot is close to the result for pure dust, and we develop a semianalytic model that accurately accounts for the small effect of pressure gradients in this limit. In the opposite regime, t(alpha,0)/t(0) much less than 1, pressure forces significantly affect the motion of the gas. At sufficiently early times, t less than or similar to t(tr), the flow evolved along a sequence of quasi-stationary, Bondi-like states, with a time-dependent M over dot determined by the slowly varying gas density at large distances. However, at later times, t greater than or similar to t(tr), the fluid flow enters a dustlike regime; t(tr) is the time when the instantaneous Bondi accretion radius reaches the marginally bound radius. The transition time t(tr) depends sensitively on t(alpha,0)/t(0) for a given Gamma and can greatly exceed t(0). We show that there exists a critical value Gamma = 11/9, below which the transition from fluid to ballistic motion disappears. As one application of our calculations, we consider the fallback of initally outflowing gas onto the compact remnant in the core of a Type II supernova. The results have important implications for determining whether the remnant in SN 1987A is a neutron star or a black hole. We demonstrate that the outcome of fallback depends sensitively on initial conditions, principally on the sound speed of the material at the onset of infall. If the sound speed is small initially, c(s) less than or similar to 300-400 km s(-1), then the mass accretion rate remains super-Eddington for many years after the explosion, and the total mass accreted is substantial, perhaps enough to drive collapse of the neutron star to a black hole for a sufficiently soft equation of state. On the other hand, if the sound speed is considerably larger at the onset of infall, c(s) similar to 10(4) km s(-1) or so, both the mass accretion rate and the total mass accreted may be small enough that a neutron star could lie at the core of SN 1987A.