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A supramassive, strongly-magnetized millisecond neutron star (NS) has beenproposed to be the candidate central engine of at least some short gamma-raybursts (SGRBs), based on the "internal plateau" commonly observed in the earlyX-ray afterglow. While a previous analysis shows a qualitative consistencybetween this suggestion and the Swift SGRB data, the distribution of observedbreak time $t_b$ is much narrower than the distribution of the collapse time ofsupramassive NSs for the several NS equations-of-state (EoSs) investigated. Inthis paper, we study four recently-constructed "unified" NS EoSs, as well asthree developed strange quark star (QS) EoSs within the new confinementdensity-dependent mass model. All the EoSs chosen here satisfy the recentobservational constraints of the two massive pulsars whose masses are preciselymeasured. We construct sequences of rigidly rotating NS/QS configurations withincreasing spinning frequency $f$, from non-rotating ($f = 0$) to the Keplerianfrequency ($f = f_{\rm K}$), and provide convenient analytical parametrizationsof the results. Assuming that the cosmological NS-NS merger systems have thesame mass distribution as the Galactic NS-NS systems, we demonstrate that allexcept the BCPM NS EoS can reproduce the current $22\%$ supramassive NS/QSfraction constraint as derived from the SGRB data. We simultaneously simulatethe observed quantities (the break time $t_b$, the break time luminosity $L_b$and the total energy in the electromagnetic channel $E_{\rm total}$) 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 post-merger product ofNS-NS mergers might be fast-rotating supramassive QSs rather than NSs.

Internal X-ray plateau in short GRBs: Signature of supramassive fast-rotating quark stars?