Ultra-relativistic, neutrino driven flows in GRBs: A double transonic flow solution in Schwarzschild spacetime

TL;DR

This paper models a double transonic flow driven by neutrino annihilation near a Schwarzschild black hole, revealing how energy deposition profiles influence outflow efficiency and entropy, with implications for gamma-ray burst emissions.

Contribution

It provides a new solution for neutrino-driven transonic flows in Schwarzschild spacetime, linking energy deposition profiles to outflow power and entropy generation.

Findings

Over 50% of deposited energy can produce relativistic outflows.

Outflow efficiency is higher for shallower energy deposition profiles.

Large entropy generated affects GRB photospheric emission.

Abstract

The structure of a hydrodynamic, double transonic flow driven by neutrino annihilation in the polar region of a Schwarzschild black hole is computed for different energy deposition profiles. The requirement that both, the inflow into the black hole and the outflow to infinity pass smoothly through their sonic points fixes the stagnation radius and stagnation pressure. The asymptotic power of the outflow is shown to be the integral of the energy deposition rate above the stagnation radius. The outflow production efficiency depends on the energy deposition profile, and is generally higher for shallower profiles. Using recent calculations of the neutrino annihilation rate, we estimate that over 50 percents of the total energy deposited above the horizon can emerge in the form of a relativistic outflow at infinity. The continuous creation of plasma during the expansion of the outflow leads to generation of a large specific entropy. This has important implications for the prompt photospheric emission in GRBs.