  Newborn neutron stars surrounded by hyperaccreting and neutrino-cooled disks
may exist in some gamma-ray bursts (GRBs) and/or supernovae (SNe). In this
paper we further study the structure of such a neutron-star disk based on the
two-region (i.e., inner & outer) disk scenario following our previous work, and
calculate the neutrino annihilation luminosity from the disk in various cases.
We investigate the effects of the viscosity parameter, energy parameter
(measuring the neutrino cooling efficiency of the inner disk) and outflow
strength on the structure of the entire disk as well as the effect of emission
from the neutron star surface boundary emission on the total neutrino
annihilation rate. The inner disk satisfies the entropy-conservation or the
advection-dominated self-similar structure depending on the energy parameter.
An outflow from the disk decreases the density and pressure but increases the
thickness of the disk. Moreover, compared with the black-hole disk, the
neutrino annihilation luminosity above the neutron-star disk is higher, and the
neutrino emission from the boundary layer could increase the neutrino
annihilation luminosity by about one order of magnitude higher than the disk
without boundary emission. The neutron-star disk with the advection-dominated
inner disk could produce the highest neutrino luminosity while the disk with an
outflow has the lowest. Although a heavily mass-loaded outflow from the neutron
star surface at early times of neutron star formation prevents the outflow
material from being accelerated to a high bulk Lorentz factor, an energetic
ultrarelativistic jet via neutrino annihilation can be produced above the
stellar polar region at late times if the disk accretion rate and the neutrino
emission luminosity from the surface boundary layer are sufficiently high.
