A MAD Explanation for the Correlation between Bulk Lorentz Factor and Minimum Variability Timescale

Abstract

We offer an explanation for the anti-correlation between the minimum variability timescale ($MTS$) 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, $t_{MAD}$, in GRBs and the maximum bulk Lorentz factor: $t_{MAD}\propto {\Gamma }^{-6}$, 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 $MTS$ and gamma-ray luminosity $L$ in the GRB data, and we estimate the accretion rates of the GRB disks (given these luminosities) in the context of this model. Both of these correlations ($MTS-\Gamma$ and $MTS-L$) are also observed in the AGN data, and we discuss the implications of our results in the context of both GRB and blazar systems.

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• Giant X-ray and optical Bump in GRBs: evidence for fall-back accretion model
• Radio Loud vs. Radio Quiet Gamma-ray Bursts: the Role of Binary Progenitors
• Constraints on Gamma-ray Burst Inner Engines in a Blandford-Znajek Framework
• Variability of magnetically-dominated jets from accreting black holes
• Accretion into black hole, and formation of magnetically arrested accretion disks