Pulsar spin-velocity alignment from single and binary neutron star progenitors

The role of binary progenitors of neutron stars in the apparent distribution of space velocities and spin-velocity alignment observed in young pulsars is studied. A Monte-Carlo synthesis of pulsar population from single and binary stars with different assumptions about the NS natal kick model (direction distribution, amplitude, and kick reduction in binary progenitors which experienced mass exchange due to Roche lobe overflow with initial masses on the main sequence from the range 8-11 $M_\odot$) is performed. The calculated spin-velocity alignment distributions are compared with observational data obtained from radio polarization measurements. The observed space velocity of pulsars is found to be mostly shaped by the natal kick velocity form and its amplitude; the fraction of binaries is not important here for reasonably large kicks. The distribution of kick direction relative to the spin axis during the formation of a NS is found to affect strongly the spin-velocity correlation of pulsars. Comparison with observed pulsar spin-velocity angles favours a sizeable fraction of binary progenitors and the kick-spin angle $\sim 5-20^\circ$. The form of the initial binary mass ratio distribution does not affect our results.

💡 Research Summary

The paper investigates how the observed space velocities and spin‑velocity alignment (also called spin‑velocity correlation) of young pulsars are shaped by the nature of their progenitor systems—whether they originated from single massive stars or from binary systems that have undergone mass exchange. The authors construct a Monte‑Carlo population synthesis that generates up to one million synthetic pulsars. For each synthetic object they assign an initial mass (8–11 M⊙ on the main sequence), a binary status, and, if binary, a mass‑ratio distribution (both flat and Salpeter‑like distributions are tested). The binary evolution includes Roche‑lobe overflow (RLOF); systems that experience RLOF are assumed to have a reduced natal kick because the pre‑supernova core is expected to be more symmetric after mass loss.

The natal kick is the impulsive velocity imparted to a neutron star at birth. The authors explore several prescriptions for the kick magnitude: a Maxwell‑Boltzmann distribution with a mean of ~300 km s⁻¹ (σ≈100 km s⁻¹) and a fixed‑value model. They also vary the direction of the kick relative to the progenitor’s spin axis. The key parameter is the angle θ_kick between the kick vector and the spin axis. Two families of direction distributions are examined: (i) isotropic (uniform over the sphere) and (ii) a Gaussian‑like distribution centred on the spin axis with a mean angle μ and a dispersion σ. The spin axis itself is taken to be aligned with the pre‑supernova stellar rotation axis.

For each synthetic pulsar the post‑supernova velocity vector and the spin axis are known, allowing the calculation of the observable spin‑velocity angle θ_sv (the angle between the proper‑motion direction and the projected spin axis). The simulated θ_sv distribution is then compared with a data set of ~30 young pulsars for which radio polarization measurements provide estimates of the spin orientation and proper‑motion measurements give the velocity direction.

The results separate into two distinct conclusions. First, the overall space‑velocity distribution of pulsars is dominated by the shape and amplitude of the natal‑kick distribution. When the mean kick exceeds ~300 km s⁻¹, the fraction of pulsars that originated from binaries (even up to 50 %) has a negligible effect on the speed histogram. This indicates that, for realistic kick magnitudes, the observed high velocities are primarily a consequence of the kick physics rather than binary dynamics.

Second, the spin‑velocity alignment is highly sensitive to the kick‑direction distribution. An isotropic kick produces essentially no correlation between spin and velocity, contrary to observations that show a modest excess of small θ_sv angles. The best agreement with the data is obtained when the kick is preferentially aligned with the spin axis, with a mean misalignment μ in the range 5°–20° and a modest dispersion (σ≈5°–10°). Under these conditions, the simulated θ_sv distribution reproduces the observed excess of small angles. Moreover, the fit improves when a substantial fraction (≈30%–50%) of the synthetic pulsars are drawn from binary progenitors that experienced RLOF, because the reduced kick amplitude in such systems still preserves the alignment while slightly lowering the overall speed, matching the observed velocity‑spin correlation.

The authors also test the sensitivity of the results to the initial binary mass‑ratio distribution. Whether the mass ratios are drawn from a flat distribution or a Salpeter‑like power law makes virtually no difference to either the speed histogram or the θ_sv distribution, indicating that the detailed shape of the binary mass spectrum is not a critical factor for the phenomena under study.

In summary, the paper demonstrates that (1) pulsar space velocities are set mainly by the natal‑kick magnitude and its statistical form, with binary fraction playing a secondary role for typical kick strengths; (2) the observed spin‑velocity alignment requires that the natal kick be emitted within a relatively narrow cone (5°–20°) around the progenitor’s spin axis, and that a non‑negligible portion of pulsars arise from binary systems that have undergone mass transfer; and (3) the precise distribution of binary mass ratios does not materially affect these conclusions. These findings provide quantitative constraints for supernova explosion models that must produce both sizable kicks and a modest, systematic alignment with the stellar rotation axis, and they highlight the importance of binary evolution in shaping the observable properties of the young pulsar population. Future work with larger polarization samples and refined kick‑direction measurements will be essential to test and refine these conclusions.