What Can We Learn about GRB from the Variability Timescale Related Correlations?

Recently, two empirical correlations related to the minimum variability timescale (MTS) of the light curves are discovered in gamma-ray bursts (GRBs). One is the anti-correlation between MTS and Lorentz factor Γ, and the other is the anti-correlation between the MTS and gamma-ray luminosity L _γ. Both of 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 central engine models (namely, the Blandford and Znajek mechanism (BZ) and the neutrino-dominated accretion flow (NDAF)). By taking the MTS as the timescale of viscous instability of the NDAF, we find that these correlations favor the scenario in which the jet is driven by the BZ mechanism.