We present a first simulation of the post-merger evolution of a black
hole-neutron star binary in full general relativity using an energy-integrated
general relativistic truncated moment formalism for neutrino transport. We
describe our implementation of the moment formalism and important tests of our
code, before studying the formation phase of a disk after a black hole-neutron
star merger. We use as initial data an existing general relativistic simulation
of the merger of a neutron star of 1.4 solar mass with a black hole of 7 solar
mass and dimensionless spin a/M=0.8. Comparing with a simpler leakage scheme
for the treatment of the neutrinos, we find noticeable differences in the
neutron to proton ratio in and around the disk, and in the neutrino luminosity.
We find that the electron neutrino luminosity is much lower in the transport
simulations, and that the remnant is less neutron-rich. The spatial
distribution of the neutrinos is significantly affected by relativistic
effects. Over the short timescale evolved, we do not observe purely
neutrino-driven outflows. However, a small amount of material (3e-4Msun) is
ejected in the polar region during the circularization of the disk. Most of
that material is ejected early in the formation of the disk, and is fairly
neutron rich. Through r-process nucleosynthesis, that material should produce
high-opacity lanthanides in the polar region, and could thus affect the
lightcurve of radioactively powered electromagnetic transients. We also show
that by the end of the simulation, while the bulk of the disk is neutron-rich,
its outer layers have a higher electron fraction. As that material would be the
first to be unbound by disk outflows on longer timescales, the changes in Ye
experienced during the formation of the disk could have an impact on the
nucleosynthesis outputs from neutrino-driven and viscously-driven outflows.
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