Physical origin of the ultralow and polar-aligned neutron-star natal-kick modes inferred from Be X-ray binary orbits

Neutron stars receive natal kicks at formation, but the physical origin of these kicks remains debated. A hierarchical Bayesian analysis of the orbits of 23 Galactic Be X-ray binaries (Valli et al. 2025) identified two distinct low-kick modes: an ultralow mode with nearly isotropic kicks below about 10 km/s in low-eccentricity systems, and a polar mode with kicks near 100 km/s, small velocity spread, and directions confined within about 5 degrees of the progenitor's spin axis in high-eccentricity systems. Neither mode is reproduced by current three-dimensional core-collapse supernova simulations, and the leading alternative, asymmetric spin-down radiation, requires neutron-star birth spin periods near 1 ms, in tension with observations. The open problem is to identify the core-collapse physics that produces both modes, determine which explosion channels and progenitor properties generate them, and corroborate or refute the inferred kick-direction structure with additional spin-orbit tilt measurements, systemic velocities, and larger samples that exclude biases from tertiary companions, residual pre-supernova eccentricity, and long-term orbital evolution.

Background

Neutron stars (NSs), the compact remnants of massive stars, are observed as radio pulsars moving with space velocities of hundreds of $\mathrm{km\,s^{-1}}$; a standard description fits the velocities of young pulsars with a single Maxwellian distribution of width $\sigma \simeq 265\,\mathrm{km\,s^{-1}}$ (Hobbs et al. 2005). This 'natal kick' is thought to arise from asymmetries in the core-collapse supernova explosion: gravitational acceleration of the newly formed proto-NS by anisotropic ejecta (the 'tug-boat' effect), recoil from anisotropic neutrino emission, or magnetohydrodynamic processes — for instance, magnetorotational simulations with asymmetric magnetic fields produce kicks up to roughly $500\,\mathrm{km\,s^{-1}}$ (Kondratyev et al. 2024). No mechanism is settled.

Be X-ray binaries (BeXRBs) provide a laboratory for natal kicks. They contain an NS accreting intermittently from the equatorial decretion disc of a Be star — a hot, rapidly rotating massive star — in an eccentric orbit. Because the post-supernova orbital period and eccentricity depend sensitively on the kick magnitude and its direction relative to the pre-supernova orbit, while the Be star's spin axis preserves the direction of the pre-supernova orbital axis, the observed population encodes the kick distribution. Earlier work had already inferred two populations of X-ray pulsars tied to two supernova types — electron-capture supernovae (weak, nearly symmetric explosions triggered by electron capture in an O-Ne-Mg core) versus iron-core-collapse supernovae (Knigge et al. 2011) — and ultra-stripped supernovae (explosions of nearly naked helium cores stripped by binary mass transfer) have been invoked to explain very low kicks in NS binaries.

Valli et al. (2025) analyzed 23 BeXRBs with well-determined orbits, which separate into a low-eccentricity group and a high-eccentricity sequence in the period–eccentricity plane. Their inference yields two distinct low-kick modes. The low-eccentricity group is best explained by nearly isotropic kicks with a mean of about $7\,\mathrm{km\,s^{-1}}$ (ultralow, $\lesssim 10\,\mathrm{km\,s^{-1}}$), with progenitors of median current mass $\sim 2.3\,M_\odot$ (birth mass $\sim 10\,M_\odot$). The high-eccentricity sequence requires kicks tightly clustered around $\sim 100\,\mathrm{km\,s^{-1}}$ with small velocity spread, confined within $\sim 5^\circ$ of the progenitor's spin (and pre-supernova orbital) axis, with progenitors of median current mass $\sim 4.9\,M_\odot$ (birth mass $\sim 15\,M_\odot$). The $\sim 100\,\mathrm{km\,s^{-1}}$ component matches the low-velocity mode of isolated pulsars, so together with the classical high-velocity component it suggests three distinct kick modes in NS formation. The only direct spin–orbit misalignment measurement in a BeXRB — the tilt $\theta = 35^\circ \pm 7^\circ$ of PSR B1259-63, obtained by modelling the relativistic (geodetic) precession of the pulsar's spin axis about the orbital angular momentum over 23 years of timing (Shannon et al. 2014) — agrees with the polar-kick prediction.

The result poses an unresolved theoretical and observational problem. Producing $\lesssim 10\,\mathrm{km\,s^{-1}}$ kicks requires suppressing both hydrodynamical asymmetries and anisotropic neutrino emission beyond what three-dimensional core-collapse simulations routinely produce, and current simulations also do not reproduce narrowly directed, narrowly distributed polar kicks. An alternative — kicks imparted by asymmetric spin-down radiation of the young NS — would require birth spin periods near $1\,\mathrm{ms}$, in tension with spin estimates from models and observations.

Problem Statement

Identify the physical mechanism, rooted in core-collapse (or alternative compact-object-formation) physics, that produces the two low-kick natal-kick modes inferred from Be X-ray binary orbits, and establish its correspondence with explosion channel and progenitor properties. Concretely, the problem comprises three linked facets serving one objective — a validated physical explanation of the natal-kick structure of neutron stars born in Be X-ray binaries.

(1) Mechanism. Provide a quantitative physical account — analytic or simulation-based — that reproduces, for the relevant progenitor classes, (a) ultralow ($\lesssim 10\,\mathrm{km\,s^{-1}}$), nearly isotropic natal kicks in systems descending from progenitors of birth mass near $10\,M_\odot$, and (b) kicks clustered near $\sim 100\,\mathrm{km\,s^{-1}}$ with small velocity spread, directed within $\sim 5^\circ$ of the progenitor's spin axis, in systems descending from progenitors of birth mass near $15\,M_\odot$. The account must be consistent with independent constraints, including neutron-star birth spin periods (which disfavor asymmetric spin-down radiation unless spins near $1\,\mathrm{ms}$ are admitted) and the observed period–eccentricity distributions of both Be X-ray binary eccentricity groups.

(2) Explosion-channel mapping. Determine which explosion channels — electron-capture versus iron-core collapse, magnetorotational explosions, and the roles of progenitor core rotation and magnetic fields — generate each mode, as a function of progenitor mass, metallicity, and binary history.

(3) Observational corroboration. Test the inferred kick-direction structure against observables beyond orbital periods and eccentricities — additional direct spin–orbit tilt measurements (PSR B1259-63 is currently the only one), systemic velocities, and enlarged samples including well-characterized extragalactic analogs — at a level that rules out, or quantifies, the bias channels acknowledged in the source: tertiary companions, subtle long-term orbital evolution, and residual pre-supernova eccentricity.

Facet (1) is the core of the problem; facets (2) and (3) are the channels through which the mechanism is confirmed or refuted. Facet (3) is an analysis-and-design task — identifying and justifying the observations and tests that would discriminate the two modes, and quantifying the acknowledged bias channels — rather than a requirement to collect new data.

References

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