Mergers of double neutron stars are considered the most likely progenitorsfor short gamma-ray bursts. Indeed such a merger can produce a black hole witha transient accreting torus of nuclear matter (Lee & Ramirez-Ruiz 2007,Oechslin & Janka 2006), and the conversion of a fraction of the torusmass-energy to radiation can power a gamma-ray burst (Nakar 2006). Usingavailable binary pulsar observations supported by our extensive evolutionarycalculations of double neutron star formation, we demonstrate that the fractionof mergers that can form a black hole -- torus system depends very sensitivelyon the (largely unknown) maximum neutron star mass. We show that the availableobservations and models put a very stringent constraint on this maximum massunder the assumption that a black hole formation is required to produce a shortgamma-ray burst in a double neutron star merger. Specifically, we find that themaximum neutron star mass must be within 2 - 2.5 Msun. Moreover, a singleunambiguous measurement of a neutron star mass above 2.5 Msun would exclude ablack hole -- torus central engine model of short gamma-ray bursts in doubleneutron star mergers. Such an observation would also indicate that if in factshort gamma-ray bursts are connected to neutron star mergers, the gamma-rayburst engine is best explained by the lesser known model invoking a highlymagnetized massive neutron star (e.g., Usov 1992; Kluzniak & Ruderman 1998; Daiet al. 2006; Metzger, Quataert & Thompson 2007).
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