Constraining the Nuclear Equation of State of a Neutron Star via High-frequency Quasi-periodic Oscillation in Short Gamma-Ray Bursts

Abstract The determination of the equation of state (EOS) of a neutron star (NS) and its maximum mass is very important for understanding the formation and properties of NSs under extreme conditions, but they remain open questions. Short-duration gamma-ray bursts (GRBs) are believed to originate from the merger of binary NSs or giant flares (GFs) of soft gamma repeaters (SGRs). Recently, the high-frequency quasi-periodic oscillations (QPOs) have been claimed to be identified from two short GRBs (GRB 931101B and GRB 910711). In this paper, we propose that the observed high-frequency QPOs in these two short GRBs result from torsional oscillations in the GFs of SGRs associated with cold NSs, or from radial oscillations of hypermassive NSs as the hot remnants of binary NS mergers, and then to constrain the EOS of NSs. For torsional oscillations, the six selected EOSs (TM1, NL3, APR, SLy4, DDME2, and GM1) of NSs suitable for the zero-temperature condition exhibit significant overlap in mass ranges, suggesting that we cannot constrain the EOS of NSs. For radial oscillations, the six selected EOSs (IUF, TM1, TMA, FSG, BHBLp, and NL3) of NSs suitable for the high-temperature condition cannot be ruled out when redshift is considered. However, it is found that the EOS can only be constrained if the redshift and temperature of the remnant can be measured.