Constraints from gamma-ray burst phenomenology on the hypothesis of quark stars as the central engine of gamma-ray bursts

The existence of a strange quark star (QS) predicted in the Bodmer-Witten hypothesis has been a matter of debate. The combustion from a neutron star to a strange QS in its accreted process in a low-mass X-ray binary is proposed to be a scenario that generates gamma-ray bursts (GRBs); the baryon contamination of the outflow is very low and mainly from the masses of crusts (${M}_{\text{crust}}$) of QSs. A special subset of GRBs detected in the past 16 years is collected and used to estimate ${M}_{\text{crust}}$ under this assumption of QSs as central engines. Correspondingly, ${M}_{\text{crust}}$ is calculated in the frameworks of several models for cold dense quark matter (MIT bag model and Nambu-Jona-Lasino model with or without the impacts from the formation of color superconducting condensates being considered) for comparison with the observation. In conclusion, we find that the GRB samples have so far failed to provide positive support for this hypothesis, and the Nambu-Jona-Lasino model in which the existence of hybrid stars is allowed might be more consistent with the observation.