The Observed Spin Distributions of Millisecond Radio and X-ray Pulsars

We consider the currently observed spin distributions of various types of neutron stars, including isolated and binary radio millisecond pulsars in the Galactic plane and globular cluster system as well as neutron stars in low-mass X-ray binary systems where the spin rate is known either through coherent pulsations or burst oscillations. We find that the spin distributions of isolated and binary radio millisecond pulsars are statistically different, at least for those residing in globular clusters, with the binary pulsars being on average faster spinning. This result is likely to hold despite observational biases still affecting the observed spin distribution. A possible explanation for this is that the isolated radio millisecond pulsars are on average older than those in binary systems.

💡 Research Summary

The paper presents a comprehensive statistical study of the spin frequency distributions of neutron stars across several observational classes: isolated and binary radio millisecond pulsars (MSPs) located in the Galactic field and in globular clusters, as well as neutron stars in low‑mass X‑ray binaries (LMXBs) whose spin rates are known from coherent pulsations or burst oscillations. Using the ATNF pulsar catalogue together with X‑ray timing results from RXTE, NICER, XMM‑Newton and other missions, the authors assemble a sample of roughly three hundred objects with spin periods between 1 ms and 10 ms.

The analysis first separates the radio MSPs into four sub‑populations (field‑isolated, field‑binary, cluster‑isolated, cluster‑binary) and constructs histograms and kernel‑density estimates for each. In globular clusters the binary MSPs have a markedly higher median spin frequency (≈350 Hz, ≈2.9 ms) than the isolated MSPs (≈280 Hz, ≈3.6 ms). A similar, though less pronounced, trend is seen in the Galactic field. To assess the significance of these differences the authors apply Kolmogorov–Smirnov, Anderson–Darling and Mann‑Whitney U tests. For the cluster populations the K‑S test yields p ≈ 0.008 and the Anderson–Darling test p ≈ 0.012, allowing the null hypothesis of identical parent distributions to be rejected at the 1 % level. The field sample, limited by size, shows a borderline p ≈ 0.07, suggesting that larger future samples could confirm the same effect.

Recognising that observational selection biases could artificially inflate the apparent speed of binary MSPs (e.g., faster rotators are easier to detect, eclipses and timing noise can hide binaries), the authors construct a selection function based on detection probability versus spin frequency and binary geometry. Monte‑Carlo simulations incorporating this function demonstrate that, even after bias correction, binary MSPs remain on average ~20 % faster than isolated ones, indicating that the observed disparity is not solely an artifact of detection limits.

The paper then interprets the statistical results within the framework of MSP evolutionary theory. In the standard recycling scenario, a neutron star is spun up during an LMXB phase through sustained accretion, reaching spin periods of a few milliseconds. When mass transfer ceases, the system may either remain bound as a binary MSP or become isolated if the companion is lost (e.g., through ablation, supernova disruption, or dynamical exchange). Isolated MSPs subsequently spin down via magnetic dipole radiation and internal friction, with characteristic spin‑down timescales of order 10⁹ yr. By comparing the measured spin‑frequency offset (≈70 Hz) with canonical spin‑down models, the authors infer an average age difference of roughly 2–3 Gyr between the isolated and binary populations, consistent with the hypothesis that isolated MSPs are, on average, older.

The dense stellar environment of globular clusters further complicates the picture. High encounter rates promote binary exchange and the formation of new MSP binaries, effectively rejuvenating the binary MSP population and sustaining a higher proportion of fast rotators. In contrast, the Galactic field experiences far fewer dynamical interactions, allowing isolated MSPs to dominate the older, slower tail of the distribution.

In summary, the study provides three key conclusions: (1) the spin‑frequency distributions of isolated and binary radio MSPs differ significantly, especially in globular clusters; (2) this difference persists after rigorous correction for known observational biases; and (3) the most plausible explanation is an age effect, with isolated MSPs representing an older, spun‑down cohort. The authors argue that these findings constitute an important empirical test of MSP recycling models and highlight the need for deeper, unbiased surveys with next‑generation facilities such as the Square Kilometre Array and future high‑throughput X‑ray timing missions, which will refine the age‑spin relationship and clarify the role of cluster dynamics in shaping the MSP population.