The Evolutionary Path of Millisecond X-ray Pulsars: Co-evolution of Binary Systems and Neutron Stars

This article conducts a comprehensive numerical simulation of the evolution of accreting millisecond X-ray pulsar (AMXPs) binary systems using the MESA code, revealing that the initial orbital period is the most critical parameter shaping binary evolution. The study connects the evolutionary path from low-mass X-ray binaries (LMXBs) to millisecond pulsars, providing a self-consistent theoretical framework for understanding the evolution of extreme celestial bodies and laying the foundation for observational predictions and verification.

Low-mass X-ray binaries (LMXBs) consist of a compact object (mostly a neutron star) and a low-mass companion star. Material from the companion star falls onto the compact object via an accretion disk, releasing X-rays. The transition from LMXBs to millisecond pulsars involves four stages: companion star expansion, accretion-driven spin-up, magnetic field decay, and accretion termination. Accreting millisecond X-ray pulsars (AMXPs), as an intermediate link, have about 20 known cases to date, providing key observational constraints for evolutionary theories.

Using the open-source MESA stellar evolution code, the simulations cover three trajectories: solar-like companion stars, low-mass companion stars, and white dwarf companion stars. Key physical processes include magnetic braking, gravitational wave radiation, mass transfer, and neutron star accretion; the neutron star spin model can explain the torque-luminosity relationship and the 'pulse absence' problem where most LMXBs lack X-ray pulses.

Parameter scans show that the initial orbital period is the most influential parameter, with greater importance than the magnetic braking index. Its significance lies in: predicting evolutionary paths, inferring initial conditions from current orbital periods, and providing clues to the formation mechanism of LMXBs. Magnetic braking only affects the speed of evolution, not the path.

Simulation results are highly consistent with AMXP observations: spin periods of 1-10 ms, orbital period distribution, and mass functions all match; the model explains the pulse absence problem (no periodic beams in specific accretion rate ranges). Evolutionary timescales: the mass transfer phase lasts millions to billions of years, and the spin-up phase is on the order of millions of years; detectability depends on X-ray luminosity, accretion rate range, and radio emission conditions.

Significance: Improving the theory of millisecond pulsar formation, providing observational predictions (e.g., spin distributions corresponding to specific orbital periods), and supporting gravitational wave source research. Limitations: One-dimensional approximation, simplified neutron star model, and incomplete coverage of parameter space. Future directions: Multi-dimensional magnetohydrodynamic simulations, research on the equation of state of neutron stars, population synthesis, and comparison with more observational samples.