What can we learn about GRB from the variability timescale related correlations?

Abstract: Recently, two empirical correlations related to the minimum variability timescale ($\rm MTS$) of the lightcures are discovered in gamma-ray bursts (GRBs). One is the anti-correlation between $\rm MTS$ and Lorentz factor $\Gamma$, the other is the anti-correlation between the $\rm MTS$ and gamma-ray luminosity $L_\gamma$. Both the two correlations might be used to explore the activity of the central engine of GRBs. In this paper we try to understand these empirical correlations by combining two popular black hole (BH) central engine models (namely, Blandford & Znajek mechanism and neutrino-dominated accretion flow). By taking the $\rm MTS$ as the timescale of viscous instability of the neutrino-dominated accretion flow (NDAF), we find that these correlations favor the scenario in which the jet is driven by Blandford-Znajek (BZ) mechanism.