Neutron stars (NSs), which may contain exotic degrees of freedom in their cores, and self-bound quark stars (QSs), composed entirely of absolutely stable deconfined quark matter, remain the two primary candidates for the compact objects observed as pulsars and in gravitational-wave (GW) events from binary mergers. Using a physics-agnostic equation of state (EOS) for compact star (CS) matter constructed via nonparametric Gaussian process regression, we perform Bayesian inference of the properties of NSs and QSs by analyzing multimessenger observations from GW170817, PSR $\mathrm{J}0740+6620$, PSR $\mathrm{J}0030+0451$, PSR $\mathrm{J}0437-4715$, and PSR $\mathrm{J}0614-3329$ together with ab initio calculations from perturbative quantum chromodynamics and chiral effective field theory. We consider competing cases arising from three scenarios: the NS scenario, in which all CSs are NSs; the udQS scenario, in which all CSs are up-down QSs; and the two-family scenario, in which NSs and strange QSs (SQSs) coexist. Our results based on systematic Bayesian model selection indicate that the most favored case belongs to the two-family scenario, with a Bayes factor of 6.1 relative to the udQS case, corresponding to moderate evidence. In this case, PSR $\mathrm{J}0740+6620$ is favored as an SQS, while the other five CSs, including the two in GW170817, are favored as NSs, although the favored classification of PSR $\mathrm{J}0030+0451$ further depends on the hot-spot model adopted in the NICER analysis. The corresponding maximum mass of a static CS is $M_{\mathrm{TOV}}=1.72_{-0.16}^{+0.18}{M}_{\odot }$ for NSs and $M_{\mathrm{TOV}}=2.63_{-0.31}^{+0.36}{M}_{\odot }$ for SQSs at the 68% confidence interval. Moreover, the inferred sound speed in both NS and QS matter increases monotonically and saturates at high densities, whereas a pronounced peak structure is found in the NS scenario. Our work provides a new framework for identifying the nature of individual CSs and constraining the properties of dense matter in both NSs and QSs. In particular, the most favored case provides potential astrophysical support for the absolute stability of strange quark matter according to the Witten hypothesis.

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• Nuclear matter in neutron stars
• Neutron stars & pulsars