The Kick Velocities of Neutron Stars in Binary Systems

Abstract: Neutron stars (NSs) receive natal kicks on their formation in supernovae (SNe). We consider constraints placed on the natal kick magnitudes by NSs in different kinds of binary systems. We compare observed systems to predictions from the COMPAS rapid population synthesis code, where we apply kick models with varied natal kick prescriptions. Specifically, we compare binary orbits (i.e., periods and eccentricities) and systemic kick estimates of (1) Gaia observations of NS-harboring binaries (Gaia NSs), (2) NS low-mass X-ray binaries (LMXBs), (3) NS-white dwarf binaries (NSWDs), (4) NS high-mass X-ray binaries (HMXBs) and in particular Be X-ray binaries (BeXBs), and (5) double NSs (DNSs). In this comparison, we find that we can reproduce most of the observed properties of the Gaia NSs, LMXBs, and NSWDs with natal kicks calibrated to the velocities of young isolated pulsars, although we need "rocket" kicks to explain the Gaia NS eccentricities. The HMXBs and DNSs, in contrast, show evidence of significantly reduced NS natal kicks. In particular, we find that an apparent correlation between eccentricity and systemic kick for DNSs can be explained by Blaauw kicks, if the natal kicks are ${\lesssim}\,10\,$km$\,$s$<sup>{-1}$. Although our model does not align well with low-metallicity Gaia NSs, high-eccentricity BeXBs, and DNS mass estimates, we provide alternative hypothetical explanations for these systems. We conclude that a model in which NSs that are formed in binaries with high-mass companions receive significantly reduced natal kicks can provide a relatively consistent explanation for the observed NSs in binary systems.

• The paper systematically compares natal-kick models with five observed binary populations, using analytical supernova-orbit calculations and population synthesis to test eccentricities, periods, and systemic velocities.
• Neutron stars formed with low-mass companions require kicks comparable to isolated pulsars, around 630 km/s, while Be X-ray binaries and double neutron stars are best explained by kicks of 10 km/s or less.
• The results suggest Blaauw recoil from asymmetric mass loss dominates many double-neutron-star systems, but common-envelope physics, remnant-mass prescriptions, and the physical origin of the kick dichotomy remain unresolved.

Disberg, Mandel, and Hirai present a systematic comparison between neutron star (NS) natal kick models and observations of NS-harboring binaries across five distinct populations: Gaia NS candidates, NS low-mass X-ray binaries (LMXBs), NS–white dwarf systems (NSWDs), high-mass X-ray binaries (HMXBs) with emphasis on Be X-ray binaries (BeXBs), and double neutron stars (DNSs) (2608.19690). The central result is a bifurcated picture: NSs formed with low-mass companions appear to receive natal kicks calibrated to isolated pulsars (with $v_{\text{SN}}=630\,\text{km}\,\text{s}^{-1}$), whereas NSs formed with high-mass companions—in BeXBs and DNSs—require significantly reduced kicks of ${\lesssim}10\,\text{km}\,\text{s}^{-1}$.

Kick model and analytical framework

The authors extend the classical formalism of Brandt & Podsiadlowski to eccentric pre-supernova orbits, deriving post-SN semi-major axes, eccentricities, orbital-plane inclinations, and systemic kicks for arbitrary kick direction and orbital phase. They also implement "rocket" kicks—asymmetric spin-down radiation that secularly accelerates the NS along its spin axis—using the formalism of Hirai et al., which induces eccentricity oscillations at fixed semi-major axis. An appendix derives the maximum rocket kick before periastron contact induces a merger.

Natal kick magnitudes follow the Mandel & Müller prescription, in which the kick is drawn from a normal distribution whose mean scales with $(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$. The parameters are calibrated to the lognormal kick distribution of young isolated pulsars ($\mu=5.60$, $\sigma=0.68$), yielding $$v_{\text{NS}}=(630\pm100)\,\text{km}\,\text{s}^{-1}$$ and $f_{\text{NS}}=0.45\pm0.20$. The authors separately distinguish stripped supernovae (SSNe), with an adjustable parameter $v_{\text{SSN}}$, from envelope-retaining SNe. Notably, they demonstrate that binary-origin scatter ($v_{\text{orb}}/v_{\text{kick}}\sim1\%$ median for unbound systems) is roughly an order of magnitude smaller than observational uncertainties in isolated-pulsar kick estimates, validating the use of isolated pulsars as a calibration sample. Five kick models are explored: full kicks isotropic or polar, reduced SSN kicks ($v_{\text{SSN}}=5\,\text{km}\,\text{s}^{-1}$), and combinations with ${\lesssim}10\,\text{km}\,\text{s}^{-1}$0 rocket kicks.

Gaia neutron star binaries

For the 21 wide binaries with NS candidates identified by El-Badry et al., models with full natal kicks produce overly eccentric systems unless supplemented by rocket kicks; the combination of ${\lesssim}10\,\text{km}\,\text{s}^{-1}$1 and ${\lesssim}10\,\text{km}\,\text{s}^{-1}$2 reproduces both the observed periods (${\lesssim}10\,\text{km}\,\text{s}^{-1}$3 d) and moderate eccentricities (${\lesssim}10\,\text{km}\,\text{s}^{-1}$4–0.8). However, this conclusion is fragile: adopting the two-stage common-envelope formalism of Hirai & Mandel makes Blaauw kicks alone sufficient to populate the Gaia detection range even with low natal kicks, rendering the orbits nearly uninformative about kick magnitude.

The systemic velocities sharpen the discrimination. Kinematically constrained kick estimates for non-halo Gaia NSs yield a lognormal with ${\lesssim}10\,\text{km}\,\text{s}^{-1}$5, ${\lesssim}10\,\text{km}\,\text{s}^{-1}$6 (median 65 km s${\lesssim}10\,\text{km}\,\text{s}^{-1}$7), consistent with the CE-subset predictions of the high-kick models but difficult to reconcile with low-kick models without invoking dynamical heating. Three low-metallicity systems on halo-like Galactic orbits—with inferred kicks of 380–710 km s${\lesssim}10\,\text{km}\,\text{s}^{-1}$8—are excluded on the grounds that they likely formed in an accreted metal-poor dwarf galaxy rather than the thin disc, an assumption the authors state plainly.

LMXBs and NSWDs

The 19 NS LMXBs of O'Doherty et al. show systemic kicks described by ${\lesssim}10\,\text{km}\,\text{s}^{-1}$9, $(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$0 (median 136 km s$(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$1). High-natal-kick models match this distribution well after correcting for kinematic bias, while the reduced-kick model falls systematically short—a discrepancy the authors judge larger than plausible model uncertainties. This constitutes one of the strongest constraints in the paper: LMXB systemic velocities require natal kicks comparable to those of isolated pulsars.

For 41 recycled millisecond pulsars with He WD (33 systems) or CO WD (8 systems) companions selected from the ATNF catalog, the high-kick model again provides a consistent fit (observed He WD fits: $(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$2, $(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$3). The CO WD subsample is better described by a Maxwellian with scale $(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$4. The authors note a population mismatch—roughly 85% of simulated systems have CO WD companions versus a majority of observed He WD companions—whose origin (observational bias or COMPAS tension) remains unresolved. Even under high kicks, ~10% of predicted systemic kicks fall below 25 km s$(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$5, compatible with observed low-velocity MSPs.

Be X-ray binaries

The BeXB analysis yields the sharpest contradiction with high-kick models. Among the 23 BeXBs of Valli et al., the low-eccentricity group ($(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$6) is well reproduced by the reduced-kick model, whereas the high-eccentricity group exhibits a tight period–eccentricity relation that neither full-isotropic nor polar nor rocket-kick variants can reproduce: drawing 12 objects from the high-kick model, the probability of obtaining a relation as tight as observed is negligibly small.

The authors challenge the assumption underlying Valli et al.'s polar-kick interpretation—that BeXB progenitors have circular pre-SN orbits. Compiling progenitor-like systems (Be+sdO, O+WR, B+stripped-star binaries), they find several eccentric systems within the observable BeXB periastron range ($(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$7–$(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$8) that align with the BeXB period–eccentricity relation, all clustering near periastron distances of $(M_{\text{CO}}-M_{\text{NS}})/M_{\text{NS}}$9. They propose a merger-in-a-triple scenario, analogous to $\mu=5.60$0 Carinae, to explain pre-SN eccentricity, and show in an appendix that a tight period–eccentricity relation survives the SN essentially intact when natal kicks are small, because massive companions render orbits robust against Blaauw kicks. Systemic velocity estimates from Fortin et al. show no evidence of the steep period dependence expected if the high-eccentricity BeXBs lost $\mu=5.60$1 in the SN, though the small sample prevents a decisive rejection of that model.

Double neutron stars

For DNSs, the reduced-kick model reproduces the observed period–eccentricity distribution through bimodal Blaauw kicks arising from the non-monotonic Mandel & Müller remnant mass prescription (a jump in expelled mass at $\mu=5.60$2). Full-kick models scatter DNSs broadly across parameter space and fail to match the observations. Critically, the authors identify an apparent correlation between eccentricity and systemic kick among short-period DNSs that emerges naturally when Blaauw kicks dominate; the observed DNSs of Disberg et al.—supplemented here by a new estimate for J2150+3427 of $\mu=5.60$3—follow this correlation, providing tentative evidence that DNS systemic kicks are dominated by mass loss rather than natal kicks.

A further consequence concerns short gamma-ray burst offsets: under the reduced-kick model, systemic kicks lie almost entirely in the pre-SN orbital plane, hence perpendicular to the post-SN angular momentum, implying that projected SGRB offsets approximate true offsets. The authors also verify that the maximum-offset scaling of Mandel et al. holds for low-kick populations.

Two tensions remain. First, the observed Galactic DNS total masses, tightly concentrated between $\mu=5.60$4 and $\mu=5.60$5, exceed model predictions by $\mu=5.60$6–$\mu=5.60$7, though the observed masses do qualitatively follow the predicted trend of higher mass with higher systemic kick under low kicks. Second, the spin-orbit misalignments of B1913+16 (~20°) and B1534+12 (~25°) sit awkwardly with a purely in-plane Blaauw-kick picture, a caveat inherited from Grichener et al.

Limitations and open questions

The paper concedes several structural limitations. The kinematic method for inferring systemic kicks assumes formation on circular thin-disc trajectories in a static, smooth Galactic potential and neglects dynamical heating, which most affects precisely the low-kick models it is used to test. Radial velocities estimated under isotropy skew posteriors toward high values, partially mitigated by lognormal likelihood fitting. The conclusions depend on the default COMPAS evolutionary prescriptions—the CE formalism being the dominant uncertainty—and on the Mandel & Müller remnant mass map, for which alternatives such as the Schneider et al. two-range prescription could alter the DNS results. A notable inconsistency is that COMPAS supernova-type labels do not correlate with the empirically required kick bifurcation: the SNe producing Gaia NSs, LMXBs, and NSWDs are mostly labeled USSNe despite requiring high kicks, while BeXB-forming CCSNe require low kicks, leaving the physical mechanism behind the bifurcation unidentified. Rocket kicks remain detectable only in the Gaia NSs; the difficulty of explaining low-eccentricity BeXBs with rockets hints at either a natal-kick–rocket-kick correlation or an alternative mechanism for reducing Gaia NS eccentricities.

Conclusion

This work consolidates observational constraints on NS natal kicks into a coherent, if not fully explained, dichotomy: kicks calibrated to young isolated pulsars suffice for NSs born alongside low-mass companions (Gaia NSs, LMXBs, NSWDs), while NSs born with high-mass companions (BeXBs, DNSs) require kicks suppressed to $\mu=5.60$8, with DNS dynamics dominated by Blaauw recoil. The open questions the paper leaves—what binary property suppresses the kick, why COMPAS SN-type labels fail to track it, and how the high-eccentricity BeXBs and DNS masses should be interpreted—define the immediate agenda for this field.