Neutrino-dominated relativistic shocked accretion flow around rotating black hole: implications for short gamma-ray bursts

TL;DR

This work investigates neutron-star merger-driven central engines for short gamma-ray bursts using shock-enabled, transonic neutrino-dominated accretion flows (NDAFs) around rotating black holes. By solving a set of hydrodynamic equations with an effective Kerr-like potential, including viscous heating and neutrino cooling, the authors obtain global NDAF solutions that can undergo shocks, boosting neutrino annihilation luminosity $L_{\nu\bar{\nu}}$ and GRB energetics. They compare model predictions to observed SGRB luminosities to constrain central-engine parameters $M_{\rm BH}$ and $a_{\rm k}$, incorporating merger-simulated disk masses $M_{\rm disk}$ to bound the spin-disk relationship and find a robust anti-correlation between $a_{\rm k}$ and $M_{\rm disk}$ for fixed BH mass. The results link merger outcomes to GRB energetics, offering a physically motivated route to infer central-engine properties from observational data while noting simplifications like neglecting magnetic fields and degeneracy pressures.$

Abstract

We investigate the physical properties of the central engine powering gamma-ray bursts (GRBs), modelled as a stellar-mass black hole accreting via a neutrino-dominated accretion flow (NDAF). By solving the governing hydrodynamic equations, we obtain global transonic NDAF solutions featuring shock transitions and examine their role in powering GRB energetics. The NDAF solutions are explored over a broad range of black hole parameters, including its mass ($M_{\rm BH}$) and spin ($a_{\rm k}$), and accretion rate ($\dot{M}$). We find that shocked NDAFs can naturally account for the observed diversity in GRB energy output. Incorporating results from numerical simulations of binary neutron star and black hole-neutron star mergers, we estimate the remnant black hole mass and spin parameters for the predicted range of post-merger disk mass ($M_{\rm disk}$). Our analysis reveals that small-mass black holes with relatively low spin values can adequately reproduce the luminosities of short GRBs (SGRBs), whereas identical GRB luminosities can also be achieved for more massive black holes possessing higher spin values. Finally, we uncover a robust correlation between the black hole spin and disk mass such that $M_{\rm disk}$ decreases with increasing $a_{\rm k}$, remaining largely independent of the black hole mass ($M_{\rm BH}$) powering GRBs.

Figures (3)

• Figure 1: Variation of ($\rm a$) Mach number ($M = v/C_{\rm s}$) and ($\rm b$) density ($\rho$) of the NDAF as functions of radial distance ($x$). The corresponding velocity ($v$) and temperature ($T$) profiles are indicated by the color, with the color bars on the right denoting their respective ranges. The flow parameters are chosen as $\mathcal{E}_{\rm in} = 0.0001$, $\lambda_{\rm in} = 1.9880$, $a_{\rm k} = 0.99$, $\dot{m} = 0.01$, $M_{\rm BH} = 3 M_{\odot}$, and $\alpha = 0.001$, respectively. The vertical arrow at $x_{\rm s} = 14.0258$ indicates the location of the shock transition, while the filled circles indicate the location of the inner ($x_{\rm in}$) and outer ($x_{\rm out}$) critical points. See text for the details.
• Figure 2: Parameter space in the $a_{\rm k}–M_{\rm BH}$ plane showing the allowed ranges of black hole spin ($a_{\rm k}$) and mass ($M_{\rm BH}$) yielding the observed $L^{\rm obs}_{\nu {\bar{\nu}}}$. Grey, red, and blue shaded regions denote obtained results for GRB 131001A, GRB 051221A, and GRB 050724, respectively. Here, we choose $M_{\rm disk} = 0.2 M_{\odot}$ and $\alpha = 0.01$. See text for the details.
• Figure 3: Correlation between the black hole spin parameter ($a_{\rm k}$) and the disk mass ($M_{\rm disk}$) for different black hole masses ($M_{\rm BH}$). In each panel, the red and blue shaded regions represent the disk mass ranges corresponding to $M_{\rm BH}=3M_\odot$ and $M_{\rm BH}=7M_\odot$, respectively. The names of the SGRBs are indicated in each panel. See text for the details.