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The observations of compact star inspirals from LIGO/Virgo provide a valuabletool to study the highly uncertain equation of state (EOS) of dense matter atthe densities in which the compact stars reside. It is not clear whether themerging stars are neutron stars or quark stars containing self-bound quarkmatter. In this work, we explore the allowed bag-model-like EOSs by assumingthe merging stars are strange quark stars (SQSs) from a Bayesian analysisemploying the tidal deformability observational data of the GW170817 andGW190425 binary mergers. We consider two extreme states of strange quarkmatter, either in nonsuperfluid or color-flavor locked (CFL) and find theresults in these two cases essentially reconcile. In particular, our resultsindicate that the sound speed in the SQS matter is approximately a constantclose to the conformal limit of $c/\sqrt{3}$. The universal relations betweenthe mass, the tidal deformability and the compactness are provided for theSQSs. The most probable values of the maximum mass are found to be $M_{\rmTOV}=2.10_{-0.12}^{+0.12}~(2.15_{-0.14}^{+0.16})\,M_{\odot}$ for normal (CFL)SQSs at a $90\%$ confidence level. The corresponding radius and tidaldeformability for a $1.4\,M_{\odot}$ star are $R_{\rm 1.4}=11.50_{-0.55}^{+0.52}~({11.42}_{-0.44}^{+0.52})~\rm km$ and $\Lambda_{1.4}={650}_{-190}^{+230}~({630}_{-150}^{+220})$, respectively. We also investigatethe possibility of GW190814's secondary component $m_2$ of mass$2.59_{-0.09}^{+0.08}\,M_{\odot}$ being an SQS, and find that it could be a CFLSQS with the pairing gap $\Delta$ larger than $244~\rm MeV$ and the effectivebag parameter $B_{\rm eff}^{1/4}$ in the range of $170$ to $192$ MeV, at a$90\%$ confidence level.

Bayesian inference of strange star equation of state using the GW170817 and GW190425 data