Electron-positron energy deposition rate from neutrino pair annihilation on the rotation axis of neutron and quark stars

Abstract

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 disc 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 colour-flavourlocked phase, respectively. The electron-positron energy deposition rate on the rotation axis of rotating neutron and quark stars is studied for two accretion disc models (isothermal disc and accretion disc 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 general relativistic objects, 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.

General relativistic ray-tracing algorithm for the determination of the electron-positron energy deposition rate from neutrino pair annihilation around rotating neutron and quark stars

“…Similar plots can be found in Birkl et al (2007), where the EMDR distribution near the black holes was determined for different kinds of neutrino tori and disc models under the assumption of non‐isotropic neutrino–antineutrino scattering. Our results are also consistent with the previous works presenting the EMDR calculations along the rotational axis and the equatorial plane of the same neutron and quark star models (Kovács et al 2010, 2011).…”

“…In Figs 3 and 4 we present the EMDR derived at 10 4 observers in the zx plane above the accretion disc for the rotating neutron and quark star models with the same total mass M and angular frequency Ω, when the neutrino temperature of the disc is set to the constant T (3 r g ). As in Kovács et al (2010, 2011), we consider the configurations for M = 1.8 M ⊙ and Ω= 5000 s −1 for each EOS. The physical parameters for these stellar models are presented in Table A1 ().…”

“…For black holes the area of the effective source of the radiation is proportional to the spin parameter, and a rapidly rotating black hole can enhance the energy–momentum deposition in its vicinity from neutrino–antineutrino annihilation (Asano & Fukuyama 2001; Miller et al 2003). In Kovács et al (2010, 2011) it was shown that this relation between the EDMR and a * will break down in the case of some stellar models, where the surface of the strongly deformed star in the equatorial plane not only prevents the radiant area of the disc from the further increase, but also reduces this area by forcing the inner edge of the disc to locate at higher and higher radii. Although the higher spin indeed enhances the deposition rate even for the rapidly rotating stars with DH, BBBParis, BBBAV14 and APR type EOSs, the stiff RMF and the STOS0 models, together with the quark stars, do not follow this relation.…”

“…For EMDR due to the annihilation of pairs emitted from a thin accretion disc rotating around a compact star, the most efficient configurations are those in which the central body has a moderate spin ( a * ≤ 0.4). In this domain a * is high enough to produce more rotational energy, which is converted into the disc radiation, but at the same time it is still low enough to prevent the stellar surface from occupying a location where it would reduce the effective radiant area of the disc (Kovács et al 2010, 2011).…”

“…In most of the previous investigations of the neutrino annihilation processes the central compact object was assumed to be a black hole. A comparative study of the neutrino annihilation process from neutrinos emitted by accretions discs around neutron and quark stars was initiated in Kovács, Cheng & Harko (2010), and further developed in Kovács, Cheng & Harko (2011). In these studies the electron–positron energy deposition rate was obtained in the equatorial plane and along the rotation axis of neutron and quark stars, described by several equations of state.…”