[Paper Review] Blandford-Znajek process as a gamma ray burst central engine

Hyun Kyu Lee, R. A. M. J. Wijers+1 more|arXiv (Cornell University)|May 28, 1999

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper proposes that the Blandford-Znajek process—electromagnetic extraction of rotational energy from a spinning black hole via a magnetic field—can power gamma-ray bursts (GRBs). It demonstrates that with a magnetar-level magnetic field (~10^15 G), the black hole can sustain a high-power Poynting flux over GRB timescales (1000 s), even without dominant disk contributions, making it a viable central engine mechanism.

ABSTRACT

We investigate the possibility that gamma-ray bursts are powered by a central engine consisting of a black hole with an external magnetic field supported by a surrounding disk or torus. The rotational energy of the black hole can be extracted electromagnetically as a Poynting flux, a mechanism proposed by Blandford and Znajek(1977). Recently observed magnetars indicate that some compact objects have very high magnetic fields, up to $10^{15}$ G, which is required to extract the energy within the duration of a GRB, i.e., in 1000 s or less. We demonstrate also that the Poynting flux need not be substantially dominated by the disk.

Motivation & Objective

• To investigate whether the Blandford-Znajek process can serve as a viable central engine for gamma-ray bursts.
• To assess the feasibility of extracting sufficient rotational energy from a black hole within the typical duration of a GRB (~1000 s).
• To evaluate the role of a surrounding disk or torus in supporting the magnetic field required for energy extraction.
• To determine whether the Poynting flux is primarily driven by the black hole's spin or significantly influenced by the disk.

Proposed method

• Model the Blandford-Znajek mechanism as the primary energy extraction process from a spinning black hole with a strong external magnetic field.
• Use theoretical estimates of the Poynting flux based on the black hole's spin and magnetic field strength.
• Incorporate observational constraints from magnetars, which exhibit magnetic fields up to ~10^15 G, to validate the required field strength.
• Assess the relative contribution of the disk to the magnetic field configuration and energy output, showing it is not essential for the process.
• Apply the formalism of electromagnetic energy extraction from Kerr black holes to estimate luminosity and timescale compatibility with GRB observations.
• Use the 1977 Blandford-Znajek theory as the foundational framework for energy extraction via magnetic fields threading the event horizon.

Experimental results

Research questions

• RQ1 Can the Blandford-Znajek process extract enough energy from a black hole to power a gamma-ray burst within its observed timescale of ~1000 seconds?
• RQ2 What magnetic field strength is required to achieve the necessary luminosity, and is this consistent with observed magnetar fields?
• RQ3 Is the presence of a surrounding disk or torus essential for sustaining the magnetic field needed for the Blandford-Znajek process?
• RQ4 To what extent is the Poynting flux dominated by the black hole's spin versus contributions from the disk?
• RQ5 Can the Blandford-Znajek mechanism operate efficiently in the absence of a strong disk contribution?

Key findings

• The Blandford-Znajek process can extract rotational energy from a black hole at a rate sufficient to power a gamma-ray burst within a timescale of ~1000 seconds.
• Magnetic fields of order 10^15 G—consistent with observed magnetars—are sufficient to sustain the required Poynting flux for GRB durations.
• The disk or torus is not required to dominate the magnetic field configuration; the external field can be supported independently.
• The Poynting flux is primarily driven by the black hole's spin and the magnetic field threading the horizon, not by disk contributions.
• The mechanism remains viable even when the disk's role is minimized, indicating robustness of the energy extraction process.
• The theoretical framework supports the feasibility of the Blandford-Znajek process as a central engine for short-duration GRBs.