An MAD explanation for the correlation between bulk Lorentz factor and minimum variability time-scale

Abstract

We offer an explanation for the correlation between the minimum variability timescale (MT S) in the prompt emission light curve of gamma-ray bursts (GRBs) and the estimated bulk Lorentz factor of these GRBs, in the context of a magnetically arrested disk (MAD) model. In particular, we show that previously derived limits on the maximum available energy per baryon in a Blandford-Znajek jet leads to a relationship between the characteristic MAD timescale, t M AD , in GRBs and the maximum bulk Lorentz factor: t M AD ∝ Γ −6 , somewhat steeper than (although within the error bars of) the fitted relationship found in the GRB data. Similarly, the MAD model also naturally accounts for the observed anti-correlation between MT S and gamma-ray luminosity L in the GRB data, and we estimate the accretion rates of the GRB disk (given these luminosities) in the context of this model. Both of these correlations (MT S − Γ and MT S − L) are also observed in the AGN data, and we discuss the implications of our results in the context of both GRB and blazar systems.

A Comparison between Radio Loud and Quiet Gamma-Ray Bursts, and Evidence for a Potential Correlation between Intrinsic Duration and Redshift in the Radio Loud Population

“…And indeed active galactic nuclei (AGN), which in many ways can be considered scaled cousins of GRBs (e.g. Nemmen et al (2012); Zhang et al (2013); Wu et al (2016); Lloyd-Ronning et al (2018)), have truly distinct radio loud and quiet sub-populations (Wilson & Colbert 1995;Kellermann et al 2016).…”

Constraints on gamma-ray burst inner engines in a Blandford–Znajek framework

“…The BH-disk system has been shown to be a viable engine for the GRB jet, from the standpoint of the timescales and energetics involved (e.g., consider the energy available from a 20M star accreting 5M at a rate of .01 − 0.1M s −1 ; for more discussion on this, see, for example, Popham et al (1999)). Observationally, we see BH-accretion disks in active galactic nuclei (which can, in many ways, can be considered scaled cousins of GRBs; Nemmen et al (2012); Zhang et al (2013); Wu et al (2016); Lloyd-Ronning et al (2018)), and infer they are behind the relativistic jets observed in these objects.…”

“…In Lloyd-Ronning et al (2018), accretion rates of long GRBs were estimated in the context of the MAD model using…”

New Insights in Extragalactic Magnetic Fields

“…Correlation between Lorentz factor and minimum variability time scale. The minimum variability timescale, MTS, can be anti-correlated with the bulk Lorentz factor in the jet, if the magnetically arrested (MAD) flow is considered (Lloyd-Ronning et al 2018). However, in the MAD mode, the flux accumulated at the BH horizon, and the interchange instability rather than MRI governs the minimum timescale of variability.…”