[Paper Review] Hot tori around black holes as sources of gamma ray bursts

M. Jaroszyński|ArXiv.org|Jun 8, 1995

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper investigates hot, dense tori orbiting stellar-mass Kerr black holes as potential energy sources for cosmological gamma-ray bursts. Using models based on neutron star mergers and failed supernovae, it finds that merger remnants lack sufficient energy unless extreme viscosity and entropy are assumed, while high-angular-momentum systems—especially around near-maximal black holes (a ≈ 1)—remain viable candidates, particularly those from rapidly rotating Wolf-Rayet star collapses.

ABSTRACT

We investigate the configurations consisting of massive, dense and hot tori around stellar mass Kerr black holes as possible sources of energy for the gamma ray bursts in cosmological hypothesis of their origin. We limit parameters of our models to the values resulting from neutron stars merger calculations or suggested in the ``failed supernova'' scenario. We investigate models with different angular momentum distributions and different specific entropies. We construct also approximate evolutionary tracks of our systems postulating some viscosity mechanism to be present. We find, that models resulting from a merger of two neutron stars give too little energy to be likely sources of gamma ray bursts. This conclusion remains true despite the artificially high values of specific entropy and viscosity, which we use in our calculations. The promising models should contain a high angular momentum black hole ($a \sim 1$) and/or a torus with almost constant specific angular momentum. The configurations resulting from a collapse of rapidly rotating WR stars are not excluded as sources of the bursts due to a greater freedom in choosing their initial parameters.

Motivation & Objective

• To evaluate whether hot, massive tori around stellar-mass Kerr black holes can supply enough energy for cosmological gamma-ray bursts.
• To assess the viability of torus configurations formed by neutron star mergers or failed supernovae as burst sources.
• To explore how angular momentum distribution and specific entropy affect energy output and evolution.
• To model the evolutionary tracks of such systems under assumed viscosity mechanisms.
• To determine whether initial conditions from known astrophysical scenarios can produce observable gamma-ray burst energies.

Proposed method

• Constructs equilibrium models of hot, dense tori with varying specific angular momentum and entropy distributions.
• Applies constraints from neutron star merger simulations and the 'failed supernova' scenario to set realistic initial parameters.
• Imposes a viscosity mechanism (e.g., α-viscosity) to model angular momentum transport and torus evolution.
• Calculates total available energy in the torus and compares it to observed gamma-ray burst energetics.
• Generates approximate evolutionary tracks to assess energy release over time.
• Uses relativistic hydrodynamics principles to model equilibrium configurations around Kerr black holes.

Experimental results

Research questions

• RQ1 Can tori formed by neutron star mergers produce sufficient energy to power observed gamma-ray bursts?
• RQ2 How do variations in specific entropy and angular momentum distribution affect the total energy output of a torus?
• RQ3 What role does the black hole's spin (a ≈ 1) play in enhancing energy availability for bursts?
• RQ4 Are configurations from rapidly rotating Wolf-Rayet star collapses viable as gamma-ray burst sources?
• RQ5 How do viscosity and angular momentum transport influence the evolution and energy release of the torus?

Key findings

• Models from neutron star mergers fail to produce enough energy to power typical gamma-ray bursts, even with artificially high entropy and viscosity.
• Tori with near-constant specific angular momentum and high black hole spin (a ≈ 1) show significantly greater energy potential.
• The configuration resulting from the collapse of a rapidly rotating Wolf-Rayet star remains a viable candidate due to greater initial parameter freedom.
• Energy output is highly sensitive to angular momentum distribution and black hole spin, with maximal spin maximizing available energy.
• The inclusion of viscosity does not rescue low-energy merger models, indicating fundamental energy limitations in such scenarios.
• High-angular-momentum tori around near-maximal Kerr black holes emerge as the most promising source candidates in the model framework.