SPHERICAL ACCRETION IN A UNIFORMLY EXPANDING MEDIUM

We consider spherically symmetric accretion of material from an initia lly homogeneous, uniformly expanding medium onto a Newtonian point mas s M. The gas is assumed to evolve adiabatically with a constant adiaba tic 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 spheri cal infall of material as a function of time. Outflowing shells gravit ationally bound to the point mass fall back, giving rise to a inflow r ate that, after a rapid rise, declines as a power law in time. If ther e were no outflow initially, Bondi accretion would result, with a char acteristic 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 collision less. In this case, only loosely bound shells are influenced by pressu re gradients and are pushed outward. The late-time evolution of the ma ss accretion rate M over dot is close to the result for pure dust, and we develop a semianalytic model that accurately accounts for the smal l 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 si milar 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 time s, t greater than or similar to t(tr), the fluid flow enters a dustlik e regime; t(tr) is the time when the instantaneous Bondi accretion rad ius reaches the marginally bound radius. The transition time t(tr) dep ends 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 in itally outflowing gas onto the compact remnant in the core of a Type I I supernova. The results have important implications for determining w hether the remnant in SN 1987A is a neutron star or a black hole. We d emonstrate that the outcome of fallback depends sensitively on initial conditions, principally on the sound speed of the material at the ons et 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 sup er-Eddington for many years after the explosion, and the total mass ac creted is substantial, perhaps enough to drive collapse of the neutron star to a black hole for a sufficiently soft equation of state. On th e other hand, if the sound speed is considerably larger at the onset o f infall, c(s) similar to 10(4) km s(-1) or so, both the mass accretio n rate and the total mass accreted may be small enough that a neutron star could lie at the core of SN 1987A.