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The stability and equation of state of quark matter are studied within bothtwo-flavor and (2+1)-flavor Nambu-Jona-Lasinio (NJL) models including thevector interactions. With a free parameter $\alpha$, the Lagrangian isconstructed by two parts, the original NJL Lagrangian and the Fierztransformation of it, as $L=(1-\alpha) L_{\rm{NJL}}+\alpha L_{\rm{Fierz}}$. Wefind that there is a possibility for both $ud$ nonstrange and $uds$ strangematter being absolute stable, depending on the interplay of the confinementwith quark vector interaction and the exchange interaction channels. Thecalculated quark star properties can reconcile with the recently measuredmasses and radii of PSR J0030+0451 and PSR J0740+6620, as well as the tidaldeformability of GW170817. Furthermore, the more strongly-interacting quarkmatter in the nonstrange stars allows a stiffer equation of state andconsequently a higher maximum mass ($\sim2.7\, M_{\odot}$) than the strangeones ($\sim2.1\, M_{\odot}$). The sound velocities in strange and nonstrangequark star matter are briefly discussed compared to those of neutron starmatter.

Interacting $ud$ and $uds$ quark matter at finite densities and quark stars