Constraints on binary neutron star merger product from short GRB observations

Abstract

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 Mmax=2.37M<inf>⊙</inf>(1+1.58×10-10P-2.84) is favored. (2) The fractions for the several outcomes of NS-NS mergers are as follows: ∼40% prompt BHs, ∼30% supramassive NSs that collapse to BHs in a range of delay time scales, and ∼30% stable NSs that never collapse. (3) The initial spin of the newly born supramassive NSs should be near the breakup limit (Pi∼1 ms), which is consistent with the merger scenario. (4) The surface magnetic field of the merger products is typically ∼1015 G. (5) The ellipticity of the supramassive NSs is ε∼(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 1049 to several 1052 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.