Formation of twin compact stars in low-mass X-ray binaries

Context. Millisecond pulsars (MSPs) are laboratories for stellar evolution, strong gravity, and ultra-dense matter. Although MSPs are thought to originate in low-mass X-ray binaries (LMXBs), approximately 27% do not have a binary companion, and others are found in systems with large orbital eccentricities. Understanding how these systems form may provide insight into the internal properties of neutron stars (NSs). Aims. We studied the formation of a twin compact star through rapid first-order phase transitions in NS cores due to mass accretion in LMXBs. We investigated whether this mechanism, possibly coupled with secondary kick mechanisms such as neutrino or electromagnetic rocket effects, leaves an observable long-lasting imprint on the orbit. Methods. We simulated mass accretion in LMXBs consisting of a NS and a low-mass main-sequence companion and followed the evolution of the NS mass, radius, and spin until a strong phase transition is triggered. For the internal NS structure, we assumed a multi-polytrope equation of state that allows a sharp phase transition from hadronic to quark matter and satisfies observational constraints. Results. We find that in compact binary systems with relatively short pre-Roche lobe overflow orbital periods, an accretion-induced phase transition can occur during the LMXB phase. In contrast, in binary systems with wider orbits, this transition can take place during the spin-down phase, leading to the formation of an eccentric binary MSP. If the transition is accompanied by a secondary kick with a magnitude > 20 km s−1, then the binary has a high probability of being disrupted, thereby forming an isolated MSP, or being reconfigured into an ultra-wide orbit. Conclusions. Our findings suggest that accretion in LMXBs provides a viable path for the formation of twin compact stars that could leave a long-lived and thus observable imprint on the orbit. The eccentricity distribution of binary MSPs with long orbital periods (> 50 d) can provide stringent constraints on first-order phase transitions in dense nuclear matter.