We present an extensive study of accretion onto neutron stars in which
the velocity of the neutron star and structure of the surrounding med
ium is such that the Bondi-Hoyle accretion exceeds 10(-4) M. yr(-1). T
wo types of initial conditions are considered for a range of entropies
and chemical compositions: an atmosphere in pressure equilibrium abov
e the neutron star, and a freely falling inflow of matter from infinit
y (also parameterized by the infall rate). We then evolve the system w
ith one- and two-dimensional hydrodynamic codes to determine the outco
me. For most cases, hypercritical (also termed ''super Eddington'') ac
cretion caused by rapid neutrino cooling allows the neutron star to ac
crete above the Bondi-Hoyle rate as previously pointed out by Chevalie
r. However, for a subset of simulations which corresponds to evolution
arily common events, convection driven by neutrino heating can lead to
explosions by a mechanism similar to that found in core-collapse supe
rnovae. Armed with the results from our calculations, we are in a posi
tion to predict the fate of a range of rapid-infall neutron star accre
tors present in certain low-mass X-ray binaries, common envelope syste
ms, supernova fallbacks, and Thorne-Zytkow objects (TZOs). A majority
of the common envelope systems that we considered led to explosions ex
pelling the envelope, halting the neutron star's inward spiral, and al
lowing the formation of close binary systems. As a result, the smother
ed neutron stars produced in the collisions studied by Davies & Benz m
ay also explode, probably preventing them from forming millisecond pul
sars. For the most massive supernovae, in which the fallback of materi
al toward the neutron star after a successful explosion is large, we f
ind that a black hole is formed in a few seconds. Finally, we argue th
at the current set of TZO formation scenarios is inadequate and leads
instead to hypercritical accretion and black hole formation. Moreover,
it appears that many of the current TZ models have structures ill sui
ted for modeling by mixing-length convection. This has prompted us to
develop a simple test to determine the viability of this approximation
for a variety of convective systems.