# Constraints on Gamma-ray Burst Inner Engines in a Blandford-Znajek Framework

## TL;DR

This paper constrains the magnetic fields and black hole properties needed to power gamma-ray bursts via the Blandford-Znajek mechanism, analyzing progenitor systems and jet formation conditions.

## Contribution

It provides quantitative limits on magnetic fields and BH parameters for GRBs and explores progenitor magnetic fields and angular momentum retention for jet production.

## Key findings

- Magnetic fields of 5x10^{14} to 10^{17} G are required to power observed GRBs.
- Progenitor stars need magnetic fields around 10^{6} G, while neutron star mergers require ~10^{15} G.
- Conditions for progenitors to retain enough angular momentum for BZ jet formation are discussed.

## Abstract

Under the assumption that a Gamma-ray Burst (GRB) is ultimately produced by a Blandford-Znajek (BZ) jet from a highly spinning black hole BH, we put limits on the magnetic field and BH mass needed to power observed long and short GRBs. For BHs in the range of $2-10 M_{\odot}$ (for long GRBs) and $0.5-4 M_{\odot}$ (for short GRBs), we find magnetic fields in the range of $5x10^{14} \lesssim B \lesssim 10^{17}$ G are needed to power the observed GRBs. Under the simple assumption of flux conservation, we estimate the magnetic fields of the progenitor systems for both long and short GRBs, finding that single massive star progenitors require fields $\sim 10^{6}$ G and NS merger systems require fields $\sim 10^{15}$ G. We also discuss the implications and consequences of high magnetic fields in GRB BH-disk systems, in terms of MRI field growth and magnetically arrested disks. Finally, we examine the conditions under which the progenitor systems can retain enough angular momentum to create BHs spinning rapidly enough to power BZ jets.