  The merger of compact binaries, especially black holes and neutron stars, is
frequently invoked to explain gamma-ray bursts (GRB's). In this paper, we
present three dimensional hydrodynamical simulations of the relatively
neglected mergers of white dwarfs and black holes. During the merger, the white
dwarf is tidally disrupted and sheared into an accretion disk. Nuclear
reactions are followed and the energy release is negligible. Peak accretion
rates are ~0.05 Msun/s (less for lower mass white dwarfs) lasting for
approximately a minute. Many of the disk parameters can be explained by a
simple analytic model which we derive and compare to our simulations. This
model can be used to predict accretion rates for white dwarf and black hole (or
neutron star) masses which are not simulated in this paper. Although the
mergers studied here create disks with larger radii, and longer accretion times
than those from the merger of double neutron stars, a larger fraction of the
merging star's mass becomes part of the disk. Thus the merger of a white dwarf
and a black hole could produce a long duration GRB. The event rate of these
mergers may be as high as 1/Myr per galaxy.
