Disk mass after a binary neutron star merger as a constraining parameter for short gamma-ray bursts

Context. The coincident detection of GW170817 and gamma-ray burst GRB170817A marked a milestone for the connection between binary neutron star (BNS) mergers and short gamma-ray bursts (sGRBs). These mergers can lead to the formation of a black hole that is surrounded by a disk and to the generation of a powerful jet. It spends energy to break free from the merger ejecta, and then a portion of it is dissipated to produce observable emissions. Aims. Our primary goal is to enhance our comprehension of BNS mergers by constraining the disk mass for a selection of sGRBs. To do this, we used the isotropic gamma-ray luminosity and corresponding emission times as key indicators. Methods. We leveraged data from GW170817 to estimate the disk mass surrounding the BNS merger remnant, and we subsequently inferred the efficiency of the accretion onto the jet. We then statistically examined other sGRB observations to estimate whether they might have been induced by BNS mergers Results. Our findings suggest that when similar physical parameters are employed as in the only observed BNS-powered GRB event, GRB170817A, a substantial fraction of sGRBs would need an unrealistically massive disk remnant. Conclusions. This observation raises the possibility that either a different mechanism powered those events or that the post-collapse disk efficiency varies significantly in different BNS merger scenarios.