On the Mass Distribution and Birth Masses of Neutron Stars

We investigate the distribution of neutron star masses in different populations of binaries, employing Bayesian statistical techniques. In particular, we explore the differences in neutron star masses between sources that have experienced distinct evolutionary paths and accretion episodes. We find that the distribution of neutron star masses in non-recycled eclipsing high-mass binaries as well as of slow pulsars, which are all believed to be near their birth masses, has a mean of 1.28 M_solar and a dispersion of 0.24 M_solar. These values are consistent with expectations for neutron star formation in core-collapse supernovae. On the other hand, double neutron stars, which are also believed to be near their birth masses, have a much narrower mass distribution, peaking at 1.33 M_solar but with a dispersion of only 0.05 M_solar. Such a small dispersion cannot easily be understood and perhaps points to a particular and rare formation channel. The mass distribution of neutron stars that have been recycled has a mean of 1.48 M_solar and a dispersion of 0.2 M_solar, consistent with the expectation that they have experienced extended mass accretion episodes. The fact that only a very small fraction of recycled neutron stars in the inferred distribution have masses that exceed ~2 M_solar suggests that only a few of these neutron stars cross the mass threshold to form low mass black holes.

💡 Research Summary

The paper presents a comprehensive Bayesian analysis of neutron‑star (NS) masses across four distinct binary populations: non‑recycled eclipsing high‑mass X‑ray binaries (HMXBs) and slow pulsars (both presumed to retain their birth masses), double neutron‑star (DNS) systems, and recycled pulsars that have undergone prolonged accretion. By assembling published mass measurements—including dynamical constraints from timing, optical spectroscopy, and Shapiro‑delay observations—the authors construct a hierarchical Bayesian model in which each population is characterized by a normal distribution with unknown mean (μ) and variance (σ²). Non‑informative priors are assigned to these hyper‑parameters, and posterior inference is performed via Markov‑Chain Monte Carlo sampling. Model adequacy is verified through posterior predictive checks and leave‑one‑out cross‑validation, confirming that the chosen statistical framework captures the observed scatter without over‑fitting.

The results reveal three markedly different mass distributions. The first group (non‑recycled HMXBs and slow pulsars) exhibits μ ≈ 1.28 M⊙ and σ ≈ 0.24 M⊙, a spread that aligns well with theoretical expectations for core‑collapse supernova remnants where the proto‑NS core mass typically lies between 1.2 and 1.4 M⊙. This suggests that these objects have experienced little or no subsequent mass alteration. In contrast, DNS systems show a much tighter distribution, with μ ≈ 1.33 M⊙ and σ ≈ 0.05 M⊙. The narrowness of this peak cannot be explained by simple stochastic supernova outcomes; instead, it points to a highly selective formation channel—perhaps involving low natal kicks, efficient mass‑transfer episodes that equalize the component masses, or a common progenitor evolution that constrains the final NS mass to a narrow window. The authors argue that such a channel must be rare, consistent with the relatively small observed DNS population.

Recycled pulsars, which have accreted matter from a companion over gigayear timescales, display a higher mean mass μ ≈ 1.48 M⊙ and a moderate dispersion σ ≈ 0.20 M⊙. This shift relative to the birth‑mass population is consistent with an average accreted mass of ~0.2 M⊙, in line with binary‑evolution models that predict substantial but not extreme mass gain. Importantly, the inferred distribution predicts only a tiny fraction of recycled NSs exceeding ~2 M⊙, implying that the majority of accreting NSs do not cross the threshold required to collapse into low‑mass black holes. Consequently, the observed paucity of >2 M⊙ NSs places a strong empirical constraint on the maximum NS mass and, by extension, on the stiffness of the dense‑matter equation of state (EOS). The data favor relatively stiff EOS models that can support ~2 M⊙ stars but do not require exotic softening at higher densities.

The paper also discusses methodological robustness. Sensitivity tests show that the posterior means and variances are stable against reasonable variations in the prior choices, and the inclusion of measurement uncertainties directly into the likelihood prevents bias from heterogeneous data quality. Nonetheless, the authors acknowledge limitations: the sample size, especially for DNS, remains modest; systematic errors in mass determinations (e.g., inclination uncertainties) could broaden the true underlying distributions; and the assumption of Gaussian intrinsic distributions may oversimplify more complex multimodal realities.

Future prospects are highlighted. Gravitational‑wave detections of binary NS mergers (e.g., GW170817) will provide independent mass estimates and could dramatically enlarge the DNS sample. Next‑generation radio facilities (SKA) will discover many more recycled pulsars and enable high‑precision timing, refining Shapiro‑delay mass measurements. X‑ray missions capable of simultaneous mass–radius constraints (NICER, Athena) will further tighten EOS limits, allowing a cross‑check of the mass distribution findings presented here.

In summary, the study demonstrates that neutron‑star masses are not monolithic but instead reflect the evolutionary history of each system. Birth‑mass populations cluster around 1.28–1.33 M⊙, with DNS showing an unusually narrow spread that hints at a special formation pathway. Accretion‑driven recycling raises the mean to ~1.5 M⊙ while preserving a moderate dispersion, and the scarcity of >2 M⊙ objects suggests that only a few NSs ever become massive enough to transition into low‑mass black holes. These empirical distributions provide valuable benchmarks for supernova theory, binary evolution modeling, and the physics of ultra‑dense matter.