Neutron Star Mass across Binary Pulsar Subpopulations: Mass-Spin Correlation, Mass Distributions, and Moment of Inertia Effects

We present a hierarchical Bayesian analysis of the joint mass, spin, and orbital properties of about 50 Galactic binary radio pulsars with measured neutron star masses, classified by binary type into pulsar-white dwarf (PSR-WD) and double neutron star (DNS) systems. We find moderate evidence for an anti-correlation between neutron star mass and spin period in the pooled recycled population (correlation coefficient rho = -0.26, with 96% of the posterior probability at rho<0; the 90% credible interval excludes zero), robust to the treatment of candidate DNSs and to a radio-detectability selection correction. Although consistent with accretion-driven recycling, the correlation cannot statistically distinguish an accretion origin from a moment of inertia-driven spin-up mechanism, because the neutron star moment of inertia is nearly linear in mass over the observed range. The DNS systems alone instead lean to the positive side expected from the moment-of-inertia mechanism (rho=+0.13), though with only ten systems this is not statistically conclusive. Mass shows no significant correlation with orbital period or inclination, and only a weak one with eccentricity. As a secondary result, neutron stars with helium white dwarf companions are marginally more massive than those with carbon-oxygen/oxygen-neon white dwarf companions (0.06,M), consistent with more extensive accretion in the helium white dwarf channel. We confirm, in a hierarchical framework, the previously reported correlation between companion mass and orbital eccentricity in double neutron stars (rho=+0.82). We interpret these results within a two-channel picture -- accretion-grown PSR-WD versus birth-mass-dominated DNS.