Is There a Relation between Duration and E_iso in Gamma-Ray Bursts?

The system of accretion disk and black hole is usually considered as the central engine of Gamma-ray Bursts (GRBs). It is usually thought that the disk in the central engine of GRBs is the advection-dominated accretion disk, which is developed from a massive (mass M_disk) torus at radius r_disk. We find a positive correlation between the isotropic gamma-ray energy E_iso and duration (so-called T_90) for GRBs. We interpret this correlation within the advection-dominated accretion disk model, associating E_iso and T_90 with M_ disk and viscous timescale respectively.
Comment: 2 pages, 3 figures. Feeding compact objects: Accretion on all scales. Proceedings IAU Symp. No. 290, 2012