Constraints on binary neutron star merger product from short GRB observations

Binary neutron star (NS) mergers are strong gravitational-wave (GW) sources and the leading candidates to interpret short-duration gamma-ray bursts (SGRBs). Under the assumptions that SGRBs are produced by double neutron star mergers and that the x-ray plateau followed by a steep decay as observed in SGRB x-ray light curves marks the collapse of a supramassive neutron star to a black hole (BH), we use the statistical observational properties of Swift SGRBs and the mass distribution of Galactic double neutron star systems to place constraints on the neutron star equation of state (EoS) and the properties of the post-merger product. We show that current observations already impose the following interesting constraints. (1) A neutron star EoS with a maximum mass close to a parametrization of M-max = 2.37M(circle dot) (1 + 1.58 x 10(-10)P(-2.84)) is favored. (2) The fractions for the several outcomes of NS-NS mergers are as follows: similar to 40% prompt BHs, similar to 30% supramassive NSs that collapse to BHs in a range of delay time scales, and similar to 30% stable NSs that never collapse. (3) The initial spin of the newly born supramassive NSs should be near the breakup limit (P-i similar to 1 ms), which is consistent with the merger scenario. (4) The surface magnetic field of the merger products is typically similar to 10(15) G. (5) The ellipticity of the supramassive NSs is epsilon similar to (0.004 -0.007), so that strong GW radiation is released after the merger. (6) Even though the initial spin energy of the merger product is similar, the final energy output of the merger product that goes into the electromagnetic channel varies in a wide range from several 10(49) to several 10(52) erg, since a good fraction of the spin energy is either released in the form of GWs or falls into the black hole as the supramassive NS collapses.