Hidden Twin-star Solutions from an Agnostic Speed-of-sound Model: XTE J1814–338 and GW170817 as a Multimessenger Differentiator

The twin star configuration, where two neutron stars share the same mass but exhibit different radii, can arise from a strong first-order phase transition in the dense-matter equation of state (EoS). This first-order phase transition behavior can be naturally mimicked by flexible agnostic EoS models, including the polytropic (PP) and speed-of-sound (CS) parameterizations, by appropriate choices of model parameters. Here, we systematically map an underexplored twin-star subspace of a widely used CS model and perform a Bayesian inference using mass–radius (MR) constraints from X-ray observations of rotation-powered millisecond pulsars. The inferred compact twin-star branch, at M ≃ 1–1.2 M _⊙ and R ≃ 7 km, overlaps the MR ranges reported for the accreting millisecond X-ray pulsar XTE J1814–338 (J1814), motivating a hybrid twin-star interpretation of its extreme compactness. Including the J1814 inference further selects an extreme phase transition pressure ${P}_{\,\rm{trans}\,}=108.{9}_{-4.85}^{+6.46}$ MeV fm ^–3 , a transition density ${\varepsilon }_{\,\rm{trans}\,}/{\varepsilon }_{0}=4.84{7}_{-0.134}^{+0.271}$ (with ε _0 the nuclear saturation energy density), and an energy density jump ${\rm{\Delta }}\varepsilon =558.{7}_{-278.7}^{+303.6}$ MeV fm ^–3 , corresponding to ${\rm{\Delta }}\varepsilon /{\varepsilon }_{0}=3.71{6}_{-1.854}^{+2.020}$ . To satisfy the full set of astrophysical constraints in this setting, the hybrid-core sound speed is driven close to the causal limit ( ${c}_{s}^{2}/{c}^{2}\gt 0.9$ ), suggesting strongly interacting exotic matter. We then include the GW170817 tidal-deformability constraint and find that it acts as a key differentiator: the J1814-compatible compact twin-star branch is strongly suppressed, and the Bayesian evidence drops markedly (from $\mathrm{ln}Z\sim -37.7$ to $\mathrm{ln}Z\sim -497.1$ in our implementation), implying that a twin-star explanation of J1814 is viable under X-ray MR constraints alone but becomes tightly constrained or effectively excluded once GW170817 is enforced.