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 use a Bayesian statistical method to constrain the solid states of strange-cluster matter, called strangeon matter, as the putative basic units of the ground state of bulk strong matter, incorporating the mass and radius measurements of PSR J0030+0451, PSR J0740+6620, and the recent data for the 1. 4M_ 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, Nₐ, our analysis reveals that current mass-radius measurements favor a larger Nₐ. Specifically, the results support the scenario where a strangeon forms a stable bound state with Nₐ=18, symmetric in color, flavor, and spin spaces, with a relatively strong Bayesian evidence. The comparative analyses of the posterior EOS parameter spaces derived from the three-parameter model and two-parameter model demonstrate a consistent prediction under identical observational constraints. In particular, our results reveal that the most probable values of the maximum mass are found to be 3. 58-₀. ₁₂^+0. 16M_ (3. 65-₀. ₁₆^+0. 18M_) at the 90% confidence level for three-parameter (two-parameter) EOS, based on the joint analysis of PSR J0030+0451, PSR J0740+6620, PSR J0437-4715, GW170817, and GW190814. Correspondingly, the radii for 1. 4M_ and 2. 1M_ stars are 12. 04-₀. ₃₁^+0. 27 km (12. 16-₀. ₃₁^+0. 26 km), and 13. 43-₀. ₃₂^+0. 31 km (13. 60-₀. ₃₄^+0. 29 km), respectively. The tidal deformability ₁. ₄ for a 1. 4M_ star is 205-₃₂. ₅₃^+32. 49 (212. 36-₃₂. ₆₆^+53. 71). These results may impact the research of multiquark states, which could potentially improve our understanding of the nonperturbative strong interaction.