Constraints on binary neutron star merger product from short GRB observations

Abstract

Binary neutron star 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 supra-massive neutron star to a black hole (BH), we use the statistical observational properties of {\em 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 put following interesting constraints: 1) A neutron star EoS with a maximum mass close to a parameterization of $M_{\rm max} = 2.37\,M_\odot (1+1.58\times10^{-10} P^{-2.84})$ is favored; 2) The fractions for the several outcomes of NS-NS mergers are as follows: $\sim40\%$ prompt BHs, $\sim30\%$ supra-massive NSs that collapse to BHs in a range of delay time scales, and $\sim30\%$ stable NSs that never collapse; 3) The initial spin of the newly born supra-massive NSs should be near the breakup limit ($P_i\sim1 {\rm ms}$), which is consistent with the merger scenario; 4) The surface magnetic field of the merger products is typically $\sim 10^{15}$ G; 5) The ellipticity of the supra-massive NSs is $\epsilon \sim (0.004 - 0.007)$, so that strong GW radiation is released post 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 $10^{49}$ erg to several $10^{52}$ erg, since a good fraction of spin energy is either released in the form of GW or falls into the black hole as the supra-massive NS collapses.