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

Abstract

We present a full general relativistic numerical code for estimating the energy–momentum deposition rate (EMDR) from neutrino pair annihilation (). The source of the neutrinos is assumed to be a neutrino‐cooled accretion disc around neutron and quark stars. We calculate the neutrino trajectories by using a ray‐tracing algorithm with the general relativistic Hamilton's equations for neutrinos and derive the spatial distribution of the EMDR due to the annihilations of neutrinos and antineutrinos around rotating neutron and quark stars. We obtain the EMDR for several classes of rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the Massachusetts Institute of Technology (MIT) bag model equation of state and in the colour–flavour‐locked (CFL) phase. The distribution of the total annihilation rate of the neutrino–antineutrino pairs around rotating neutron and quark stars is studied for isothermal discs and accretion discs in thermodynamical equilibrium. We demonstrate both the differences in the equations of state for neutron and quark matter and rotation with the general relativistic effects significantly modify the EMDR of the electrons and positrons generated by the neutrino–antineutrino pair annihilation around compact stellar objects, as measured at infinity.

Can Black Hole Neutrino-Cooled Disks Power Short Gamma-Ray Bursts?

“…Thus the main problem is how to precisely calculate the neutrino annihilation processes. Birkl et al (2007), Kovács et al (2011a), and Kovács & Harko (2011b) analyzed the influence of general relativistic effects on the neutrino annihilation efficiency, which has a prominent increase compared with the Newtonian calculations. Based on the geodesic-tracing method, Zalamea & Beloborodov (2011) also studied annihilations via tracing the neutrino track.…”

Relativistic Global Solutions of Neutrino-Dominated Accretion Flows

“…2007; Kovács et al 2011a;Kovács & Harko 2011b). Even, it may be also attractive if we can combine the pair creation with the other magnetic mechanisms (e.g.…”

Elastic scattering in general relativistic ray tracing for neutrinos

“…To test the algorithm, we integrate the ray tracing equations (Eqns. [34][35][36][37][38] for various observers in the following configurations. This suite of configurations defines a hierarchy of increasing physical realism: beginning with a homogeneous medium of effectively infinite extent (i.e.…”

“…Several ray tracing formulations for radiation transport already exist. Most formulations assume an analytic spacetime metric [30,31,37,38]. And many make the simplifying assumption of blackbody emission from a neutrinosurface [30,37,38], limiting them to equilibrium, optically-thick configurations.…”

“…Most formulations assume an analytic spacetime metric [30,31,37,38]. And many make the simplifying assumption of blackbody emission from a neutrinosurface [30,37,38], limiting them to equilibrium, optically-thick configurations. Current state-of-the-art ray tracing formulations avoid the assumption of blackbody spectra by integrating a local emissivity along each geodesic (e.g.…”