Strange quark star and the parameter space of the quasi-particle model

The properties of strange quark stars are studied within the quasi-particle model. Taking into account chemical equilibrium and charge neutrality, the equation of state (EOS) of $(2+1)$-flavor quark matter is obtained. We illustrate the parameter spaces with constraints from two aspects: one is based on the astronomical results of PSR ${\rm{J}}0740+6620$ and GW 170 817 , and the other is based on the constraints proposed from the theoretical study of a compact star that the EOS must ensure the tidal deformability ${{\rm{\Lambda }}}_{1.4}={190}_{-120}^{+390}$ and support a maximum mass above $1.97\,{M}_{\odot }$. It is found that neither type of constraints can restrict the parameter space of the quasi-particle model in a reliable region and thus we conclude that the low mass compact star cannot be a strange quark star.