Bayesian Inference of Dense-Matter Equations of State from Small-Radius Compact Stars with Twin-Star Scenarios

We investigate dense-matter equations of state (EOSs) within a Bayesian framework, with particular emphasis on whether recent small-radius compact-star candidates can be accommodated in a twin-star scenario. For the hadronic sector, we adopt a meta-modeling EOS constrained by the NICER mass–radius measurements of PSR J0030$+$0451, PSR J0437$-$4715, PSR J0614$-$3329, and the massive pulsar PSR J0740$+$6620. The hadronic inference indicates that PSR J0614$-$3329 favors a somewhat softer EOS than the other two $\sim 1.4M_{\odot }$ pulsars, while the $\sim 2M_{\odot }$ constraint prevents the EOS from becoming too soft. We then introduce a strong first-order phase transition through a constant-speed-of-sound quark-matter segment. Using HESS J1731$-$347 and XTE J1814$-$338 to constrain the phase-transition parameters, we find a preferred transition density of $n_{\mathrm{t}}\sim 2.7\text{–}2.8n_0$, a sizable energy-density jump of $600\text{–}700$ MeV, and a relatively large post-transition sound speed of $c_s^2\mathrm{/}{c}^2\sim 0.85$. Such a phase transition generates a disconnected hybrid branch with radii of about $6\text{–}7$ km at masses around $1.2\text{–}1.4M_{\odot }$, and strongly suppresses the dimensionless tidal deformability relative to the purely hadronic branch. This pronounced change in tidal deformability is a characteristic signature of the twin-star mechanism and may provide an important observational tool for identifying phase transitions in neutron-star matter in future multimessenger measurements. These results show that small-radius compact stars can provide direct constraints on both the strength of a first-order phase transition and the stiffness of the post-transition phase in dense matter.