A supramassive, strongly magnetized millisecond neutron star (NS) has been proposed to be the candidate central engine of at least some short gamma-ray bursts (SGRBs), based on the “internal plateau” commonly observed in the early x-ray afterglow. While a previous analysis shows a qualitative consistency between this suggestion and the Swift SGRB data, the distribution of observed break time $t_b$ is much narrower than the distribution of the collapse time of supramassive NSs for the several NS equations-of-state (EoSs) investigated. In this paper, we study four recently constructed “unified” NS EoSs (BCPM, BSk20, BSk21, and Shen) as well as three developed strange quark star (QS) EoSs within the new confinement density-dependent mass (CDDM) model, labelled as CIDDM, CDDM1, and CDDM2. All the EoSs chosen here satisfy the recent observational constraints of the two massive pulsars of which the masses are precisely measured. We construct sequences of rigidly rotating NS/QS configurations with increasing spinning frequency $f$, from nonrotating ($f=0$) to the Keplerian frequency ($f=f_{\mathrm{K}}$), and provide convenient analytical parametrizations of the results. Assuming that the cosmological NS-NS merger systems have the same mass distribution as the Galactic NS-NS systems, we demonstrate that all except the BCPM NS EoS can reproduce the current 22% supramassive NS/QS fraction constraint as derived from the SGRB data. We simultaneously simulate the observed quantities (the break time $t_b$, the break time luminosity $L_b$, and the total energy in the electromagnetic channel $E_{\text{total}}$) of SGRBs and find that, while equally well reproducing other observational constraints, QS EoSs predict a much narrower $t_b$ distribution than that of the NS EoSs, better matching the data. We therefore suggest that the postmerger product of NS-NS mergers might be fast-rotating supramassive QSs rather than NSs.

• Received 17 June 2016
• Corrected 21 July 2020

DOI:https://doi.org/10.1103/PhysRevD.94.083010