Xieyuan Dong, Hong Shen, Jinniu Hu, Ying Zhang

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 \(\sim1.4\,M_\odot\) pulsars, while the \(\sim2\,M_\odot\) 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 \(n_\mathrm{t}\sim2.7\text{--}2.8\,n_0\), a sizable energy-density jump of \(600\text{--}700\) MeV, and a relatively large post-transition sound speed of \(c_s^2/c^2\sim0.85\). Such a phase transition generates a disconnected hybrid branch with radii of about \(6\text{--}7\) km at masses around \(1.2\text{--}1.4\,M_\odot\), 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.