Allowed regions of the parameter space of the masses of two coalescing neutron stars that leads to a short-duration gamma-ray burst. For simplicity, the second neutron star is assumed to be larger than the first neutron star. The left panel shows the result when the maximum mass of a non-spinning neutron star is equal to M _max = 1.8  M _☉ and the right panel shows the result for a maximum mass of 2.1  M _☉. In the right panel, the blue line corresponds to a total mass of M ₁ + M ₂ = 1.2  M _max, below which a neutron star rotating as a solid body can be supported against collapse by centrifugal forces. In both panels, the red line corresponds to a total mass of M ₁ + M ₂ = 1.4  M _max, above which a neutron star cannot be supported against collapse, even if it is rotating differentially. The green line corresponds to a mass ratio of M ₂/ M ₁ = 4/3, above which the initial outcome of the collision is a black hole surrounded by a massive torus. Short-duration gamma ray bursts can be generated when the outcome of the collision is either the delayed collapse of a supermassive neutron star into a black hole, or the prompt collapse of the two stars into a black hole surrounded by a massive torus. The allowed region of the parameter space for M _max = 1.8  M _☉ is marginal but increases rapidly as M _max exceeds 2  M _☉.