  We explore low angular momentum accretion flows onto black holes formed after
the collapse of massive stellar cores. In particular, we consider the state of
the gas falling quasi-spherically onto stellar-mass black holes in the
hypercritical regime, where the accretion rates are in the range 0.001 - 0.5
solar masses per second and neutrinos dominate the cooling. Previous studies
have assumed that in order to have a black hole switch to a luminous state, the
condition l >> r_g c, where l is the specific orbital angular momentum of the
infalling gas and r_g is the Schwarszchild radius, needs to be fulfilled. We
argue that flows in hyperaccreting, stellar mass disks around black holes are
likely to transition to a highly radiative state when their angular momentum is
just above the threshold for disk formation, l ~ 2 r_g c. In a range where l
lies between r_g c and 2 r_g c, a dwarf disk forms in which gas spirals rapidly
into the black hole due to general relativistic effects, without any help from
horizontal viscous stresses. For high rotation rates with l greater than 2 r_g
c, the luminosity is supplied by large, hot equatorial bubbles around the black
hole. The highest neutrino luminosities are obtained for l ~ 2 r_g c, and this
value of angular momentum also produces the most energetic neutrinos, and thus
also the highest energy deposition rates. Given the range of l explored in this
work, we argue that, as long as l is greater than 2 r_g c, low angular momentum
cores may in fact be better suited for producing neutrino--driven explosions
following core collapse in supernovae and gamma ray bursts.
