We investigate the deposition of energy due to the annihilations of neutrinos
and antineutrinos on the rotation axis of rotating neutron and quark stars,
respectively. The source of the neutrinos is assumed to be a neutrino-cooled
accretion disk around the compact object. Under the assumption of the
separability of the neutrino null geodesic equation of motion we obtain the
general relativistic expression of the energy deposition rate for arbitrary
stationary and axisymmetric space-times. The neutrino trajectories are obtained
by using a ray tracing algorithm, based on numerically solving the
Hamilton-Jacobi equation for neutrinos by reversing the proper time evolution.
We obtain the energy deposition rates for several classes of rotating neutron
stars, described by different equations of state of the neutron matter, and for
quark stars, described by the MIT bag model equation of state and in the CFL
(Color-Flavor-Locked) phase, respectively. The electron-positron energy
deposition rate on the rotation axis of rotating neutron and quark stars is
studied for two accretion disk models (isothermal disk and accretion disk in
thermodynamical equilibrium). Rotation and general relativistic effects modify
the total annihilation rate of the neutrino-antineutrino pairs on the rotation
axis of compact stellar, as measured by an observer at infinity. The
differences in the equations of state for neutron and quark matter also have
important effects on the spatial distribution of the energy deposition rate by
neutrino-antineutrino annihilation.Comment: 38 pages, 9 figures, accepted for publication in MNRA
