Bayesian inference of strangeon matter using the measurements of PSR J0437-4715 and GW190814

The observations of compact star inspirals from LIGO/Virgo combined with mass and radius measurements from NICER provide a valuable tool to study the highly uncertain equation of state (EOS) of dense matter at the densities characteristic of compact stars. In this work, we constrain the solid states of strange-cluster matter, called strangeon matter, as the putative basic units of the ground state of bulk strong matter using a Bayesian statistical method, incorporating the mass and radius measurements of PSR J0030+0451, PSR J0740+6620, and the recent data for the $1.4\ M_{\odot}$ pulsar PSR J0437-4715. We also include constraints from gravitational wave events GW170817 and GW190814. Under the prior assumption of a finite number of quarks in a strangeon, $N_{\rm q}$, our analysis reveals that current mass-radius measurements favor a larger $N_{\rm q}$. Specifically, the results support the scenario where a strangeon forms a stable bound state with $N_{\rm q}=18$, symmetric in color, flavor, and spin spaces, compared to the minimum $N_{\rm q}$ prior. The comparative analyses of the posterior EOS parameter spaces derived from three-parameter model and two-parameter model demonstrate a consistent prediction under identical observational constraints. In particular, our results indicate that the most probable values of the maximum mass are found to be $3.58^{+0.16}_{-0.12}\ M_{\odot}$ ($3.65^{+0.18}_{-0.16}\ M_{\odot}$) at $90\%$ confidence level for three-parameter (two-parameter) EOS considering the constraints of GW190814. The corresponding radii for $1.4\ M_{\odot}$ and $2.1\ M_{\odot}$ stars are $12.04^{+0.27}_{-0.31}~\rm km$ ($12.16^{+0.26}_{-0.31}~\rm km$) and $13.43^{+0.31}_{-0.32}~\rm km$ ($13.60^{+0.29}_{-0.34}~\rm km$), respectively. This result may impact interestingly on the research of multiquark states, which could improve our understanding of the nonperturbative strong force.