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Potential Kick Velocity distribution of black hole X-ray binaries and implications for natal kicks

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Using VLBI and Gaia astrometry for 16 black hole X-ray binaries, the paper finds about 75% have potential kick velocities above 70 km/s and fits a unimodal Gaussian kick distribution with mean 107±16 km/s, implying most black holes…

desk verdict A useful population-level compilation of BHXB kick constraints, but the headline 107 km/s mean rests on an unstated choice for four systems' radial velocities, and one proper-motion entry disagrees with the body text. read the letter →

arxiv 1908.07199 v2 pith:V6LXLFTR submitted 2019-08-20 astro-ph.HE

P. Atri , J. C. A. Miller-Jones , A. Bahramian , R. M. Plotkin , P. G. Jonker , G. Nelemans , T. J. Maccarone , G. R. Sivakoff
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A. T. Deller S. Chaty M. A. P. Torres S. Horiuchi J. McCallum T. Natusch C. J. Phillips J. Stevens S. Weston
This is my paper · ORCID
classification astro-ph.HE
keywords blackholeX-raybinariesnatalkickspropermotionsVLBIastrometryGaiaDR2potentialkickvelocityGalacticorbitsspin-orbitmisalignment
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to turn black hole X-ray binaries (BHXBs) into tracers of how black holes are born. Since a black hole's birth kick pushes the binary out of the Galactic plane, the authors use VLBI and Gaia proper motions, distances, and radial velocities for 16 systems to reconstruct each binary's past orbit and read off its velocity at every Galactic plane crossing, which they call the potential kick velocity (PKV). They find that about 75% of the systems have PKVs above 70 km/s, and that the population is well described by a unimodal Gaussian with mean 107±16 km/s. If correct, this implies strong natal kicks are common, favouring supernova or asymmetric-fallback birth over quiet direct collapse for most black holes, and it would make spin-orbit misalignment common in BHXBs.

What carries the argument

The central object is the potential kick velocity (PKV): the peculiar velocity a binary has at the moment its Galactocentric orbit crosses the Galactic plane, computed by Monte Carlo realization of about 5000 orbits per system integrated backwards 10 Gyr in the galpy MWPotential2014 Galactic potential. Uncertainties in proper motion, distance (from Gaia DR2 parallaxes with a Milky Way prior or from literature estimates), and systemic radial velocity are propagated by drawing inputs from Gaussian or uniform distributions. The resulting PKV probability distributions for all 16 systems are then combined with a Bayesian hierarchical unimodal/bimodal Gaussian model, with model comparison via the corrected Akaike information criterion.

What would settle it

A calculation that reconstructs the true natal kick for a system such as GX 339-4 from its binary parameters and a supernova model, yielding a kick below 50 km/s while its PKV is about 200 km/s, would falsify the claim that PKV is a reliable proxy for natal kick.

Watch

Extended reading notes

Core claim

The central claim is that black hole X-ray binaries as a population received substantial natal kicks at birth, much larger than the recoil expected from symmetric mass loss in a supernova, which is limited to a few tens of km/s. Using the best available astrometry for 16 systems, the paper estimates the peculiar velocity at Galactic plane crossing (PKV) for each and finds that 75% exceed 70 km/s. A Bayesian hierarchical fit to the population favours a unimodal Gaussian with mean 107±16 km/s and standard deviation about 56±14 km/s, while a bimodal model with peaks near 41 and 136 km/s is possible but not preferred. The paper also reports no significant correlation between black hole mass and PKV, and notes that the BHXB PKV distribution sits a factor of 3–4 below the pulsar kick velocity distribution, suggesting black holes receive weaker kicks than neutron stars.

Load-bearing premise

The entire analysis assumes that the velocity a binary has when it crosses the Galactic plane is a faithful stand-in for the kick it received at birth, which requires that the black hole formed near the plane (not in a globular cluster or the bulge) and that 10 Gyr of Galactic orbits have not erased the kick signal.

Editorial extensions

If this is right

  • Most BHXBs would have been born in supernovae or supernova-fallback events rather than by direct collapse, with only a minority (Cyg X-1, 1A 0620-00, V404 Cyg, GRS 1915+105) looking like low-kick systems.
  • Strong kicks imply spin-orbit misalignment should be common in BHXBs, which is consistent with the prevalence of low-frequency quasi-periodic oscillations, and suggests caution when assuming spin-orbit alignment in black hole spin measurements.
  • If such kicks are typical, many black holes would be ejected from globular clusters, lowering the retention fraction and changing predictions for BH-BH merger rates in dense stellar environments.
  • The lack of correlation between black hole mass and PKV supports formation models in which there is no clean mass threshold separating direct collapse from supernova birth.
  • Gravitational-wave mergers of black hole binaries should frequently show misaligned spins and be displaced from their birth sites if the natal kick distribution extends to these binaries.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same PKV distribution applies to the wider black hole population and not just to binaries that stayed bound, the true natal kick distribution may be even stronger, since binaries disrupted by very large kicks are missing from this sample.
  • The hint of bimodality in the PKV distribution could be sharpened with future Gaia data releases and additional VLBI astrometry of quiescent BHXBs; if confirmed, it would map directly onto the two birth channels discussed in the paper.
  • A direct test of the PKV-as-kick assumption would be to reconstruct the actual natal kick for a system like GX 339-4 from its binary parameters and a supernova model; if the reconstructed kick is far below its ~200 km/s PKV, the proxy would be called into question.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reports new VLBI proper-motion measurements for three black hole X-ray binaries (GX 339–4, GRS 1716–249, Swift J1753.5–0127), compiles astrometric, distance, and systemic radial-velocity constraints for 16 BHXBs, and integrates their Galactocentric orbits backward in time to derive probability distributions for the peculiar velocity at each Galactic-plane crossing, which the authors call the potential kick velocity (PKV). A Monte Carlo code propagates measurement uncertainties, and a Bayesian hierarchical fit is used to model the PKV distribution of the population. The headline result is a unimodal Gaussian PKV distribution with mean 107±16 km/s, along with the statement that 75% of the systems have median PKVs above 70 km/s, which is interpreted as evidence for strong natal kicks and spin-orbit misalignment. The paper also compares the PKV distribution with pulsar kick velocities, discusses implications for globular-cluster retention and BH-BH merger rates, and finds no significant correlation between BH mass and PKV.

Significance. If the central result holds, this is a valuable observational constraint on the natal kick distribution of stellar-mass black holes, with implications for BH formation pathways, spin-orbit misalignment in X-ray binaries, globular-cluster BH retention, and rates of BH-BH mergers. The paper's strengths are the careful VLBI astrometric reduction, the transparent Monte Carlo propagation of measurement uncertainties, the public code, and the explicit enumeration of caveats in Section 7.2. The hierarchical population analysis is a sensible way to combine heterogeneous posterior distributions, and the comparison with pulsar kick velocities is informative. The main concern is not the quality of the astrometry but whether the population-fit result is uniquely determined by the data, given the treatment of four systems with unmeasured systemic radial velocities.

major comments (3)
  1. [Section 7.1 and Table 5] The hierarchical population fit in Section 7.1 is run on 'all the BHXB systems' (16 systems), but the manuscript never states which of the five systemic radial-velocity hypotheses defined in Section 5.2 was used for the four systems without measured γ (GRS 1716–249, Swift J1753.5–0127, MAXI J1820+070, VLA J2130+12), nor whether the uncertainty in γ was marginalized over. Table 5 shows that the PKV distributions for these systems differ substantially across the five hypotheses; for example, the PKV median for MAXI J1820+070 ranges from 84 to 153 km/s and for GRS 1716–249 from 67 to 100 km/s. Since one-eighth to one-quarter of the sample is affected, the quoted population mean of 107±16 km/s is not uniquely determined by the reported input choices. Please specify exactly which PKV distribution was entered for each of these four systems, and ideally run the population fit with a prior over the five γ hypotheses to test whether the inferred mean and its uncertainty are robust.
  2. [Section 4.2 and Table 5] There is an internal inconsistency in the adopted proper motion for GRS 1716–249. Equation (2) reports µα cosδ = −3.83 ± 1.25 mas/yr, but Table 5 lists µα cosδ = −1.7 ± 1.25 mas/yr for the same source. The difference is more than 1.6σ and directly affects the computed PKV distribution and hence the population fit. This must be corrected or explained, because the table is the input used for the quantitative claims of the paper.
  3. [Sections 1.3, 6, and 7.2] The central interpretation throughout the abstract, Section 7.3, Section 7.7, and Section 7.9 is that the PKV distribution is a natal kick distribution, but Section 7.2 correctly notes that PKV is only a proxy and that the interpretation assumes birth in the Galactic plane, no globular-cluster origin, and no secular orbital evolution beyond the adopted Milky-Way potential. These caveats are acknowledged but not propagated into the headline claims; for instance, Cyg X-1 is included despite the statement that it has never crossed the Galactic plane in its lifetime, and a GC-ejection origin for objects such as XTE J1118+480 is mentioned as a plausible alternative. Please either soften the natal-kick language to 'potential kick' throughout the abstract and conclusions, or provide quantitative robustness tests (for example, re-running the hierarchical fit excluding Cyg X-1 and high-latitude systems that may be GC escapees) to show that the inferred mean of ~107 km/s is not driven by systems for which the proxy assumption is least secure.
minor comments (5)
  1. [Section 6.1.1] There is a typo: 'median of 200 km s−1 snd' should read 'median of 200 km s−1 and'.
  2. [Section 1] The name 'Blauuw' in the first paragraph of Section 1 should be 'Blaauw' for the Blaauw kick.
  3. [Section 7.1] The source list 'GS 1352–64' appears to be a typo for 'GS 1354–64'.
  4. [Figure 8] The x-axis label in Figure 8 reads 'Natal kick velocity', but the plotted quantity is the potential kick velocity; relabeling would avoid overclaiming.
  5. [Abstract and Section 8] The statement that '75% of our systems have potential kicks >70 km/s' is based on the median of each system's PKV distribution, not on a direct measurement; the wording should make this distinction explicit.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the PKV distributions are computed from astrometry, distances, and a Galactic potential, and the hierarchical Gaussian fit uses these distributions as data rather than imposing them.

full rationale

The central derivation is self-contained. Individual PKV distributions are produced by Monte Carlo orbit integrations (Section 6) from measured proper motions, parallax-based or literature distances, systemic radial velocities, and the galpy MWPotential2014. The population-level unimodal Gaussian with mean 107±16 km/s is then fit to these PKV distributions using a Bayesian hierarchical model with uninformative priors (Section 7.1), so the Gaussian is an output of the fit, not an input that constructs the PKVs. The paper explicitly states that PKV is only a proxy for the natal kick (Section 7.2: 'The potential kick velocity (PKV) that we estimate here is not the actual natal kick'), which is an acknowledged modeling assumption rather than a circular definition. The GC-origin assumption is also stated as an assumption. The handling of four systems without measured systemic radial velocities, via five ad hoc gamma hypotheses in Section 5.2, is under-specified for the 16-system hierarchical fit and is a legitimate reproducibility/robustness concern, but it does not reduce any prediction to its inputs by construction. No load-bearing self-citation chain or fitted-parameter-renamed-as-prediction is present.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim depends on these assumptions; the most important is the plane-crossing proxy, which is a derived statistic rather than a directly measured kick.

free parameters (2)
  • Assumed systemic radial velocities for 4 systems = GRS 1716-249: -10 km/s; Swift J1753.5-0127: 93 km/s; MAXI J1820+070: 33 km/s; VLA J2130+12: 10 km/s (each with 50 km/s…
    These systems lack measured gamma; the values are the expected Galactic rotation velocities at their positions, with five scenarios tested. The central value is adopted for the reported PKV in Table 7.
  • Assumed BH mass for systems without dynamical masses = 8 +/- 3 M_sun (Kreidberg et al. 2012)
    Used for the BH mass-PKV correlation test for GS 1354-64, MAXI J1836-194, GRS 1716-249, MAXI J1820+070 and VLA J2130+12.
assumptions (4)
  • domain assumption GR02 LMXB spatial density prior for parallax-to-distance inversion
    Section 5.1; the prior is derived for LMXBs including NS systems and is used to convert Gaia parallaxes to distances.
  • domain assumption MWPotential2014 Galactic potential for orbit integration
    Section 6; standard galpy model, but potential uncertainties affect plane-crossing velocities.
  • domain assumption BHXBs are born in the Galactic plane and not in globular clusters
    Section 7.2; stated explicitly; if a system formed in a GC or outside the plane, the PKV is not a natal kick proxy.
  • ad hoc to paper The peculiar velocity at every Galactic plane crossing is a valid kick proxy over 10 Gyr
    Section 1.3 and Section 6; the code assigns the plane-crossing velocity to kick potential, ignoring dynamical heating and the unknown age of the system.

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Cite this review

Pith. "Pith review of Potential Kick Velocity distribution of black hole X-ray binaries and implications for natal kicks." pith.science (2026). https://pith.science/paper/V6LXLFTR

@misc{pith2026190807199,
  author       = {Pith},
  title        = {Pith review of: Potential Kick Velocity distribution of black hole X-ray binaries and implications for natal kicks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V6LXLFTR}},
  note         = {Machine review of arXiv:1908.07199}
}
abstract

We use Very Long Baseline Interferometry to measure the proper motions of three black hole X-ray binaries (BHXBs). Using these results together with data from the literature and Gaia-DR2 to collate the best available constraints on proper motion, parallax, distance and systemic radial velocity of 16 BHXBs, we determined their three dimensional Galactocentric orbits. We extended this analysis to estimate the probability distribution for the potential kick velocity (PKV) a BHXB system could have received on formation. Constraining the kicks imparted to BHXBs provides insight into the birth mechanism of black holes (BHs). Kicks also have a significant effect on BH-BH merger rates, merger sites, and binary evolution, and can be responsible for spin-orbit misalignment in BH binary systems. $75\%$ of our systems have potential kicks $>70\,\rm{km~s^{-1}}$. This suggests that strong kicks and hence spin-orbit misalignment might be common among BHXBs, in agreement with the observed quasi-periodic X-ray variability in their power density spectra. We used a Bayesian hierarchical methodology to analyse the PKV distribution of the BHXB population, and suggest that a unimodal Gaussian model with a mean of $107\pm16\,\rm{km~s^{-1}}$ is a statistically favourable fit. Such relatively high PKVs would also reduce the number of BHs likely to be retained in globular clusters. We found no significant correlation between the BH mass and PKV, suggesting a lack of correlation between BH mass and the BH birth mechanism. Our Python code allows the estimation of the PKV for any system with sufficient observational constraints.

Figures

Figures reproduced from arXiv: 1908.07199 by the authors.

Figure 1
Figure 1. Proper motion fit for GX 339–4. GX 339–4 was tracked for three epochs over three different outbursts. Top panel: Offset of measured positions relative to the first epoch in Right Ascen￾sion. Bottom panel: Offset of measured positions in Declination relative to the first epoch. 57800 57850 57900 57950 58000 0.0 −0.5 −1.0 −1.5 RA offset (mas) −2.0 57800 57850 57900 57950 58000 MJD 0 −5 −10 −15 Dec offset (mas) −20 16-… view at source ↗
Figure 2
Figure 2. Proper motion fits for GRS 1716–249. GRS 1716–249 was tracked for three epochs over one outburst using the LBA, with positions shown with respect to the first LBA epoch. Top panel: fits by considering position measurements of two epochs at a time in RA and Dec - epoch 1 and 2 (dashed line); epoch 2 and 3 (dotted line); epoch 1 and 3 (dotted dashed line). The three declination measurements do not lie on a straight li… view at source ↗
Figure 2
Figure 2. Measured declinations in these epochs do not ap [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figures from the paper (8 more)
Figure 3
Figure 3. Figure 3: shows a linear fit to the measured positions of Swift J1753.5–0127 over a span of 4 years. Although we used a different calibration scheme for the VLBA and EVN 55200 55400 55600 55800 56000 56200 56400 56600 0 1 2 3 4 RA offset (mas) µα cos δ = 0.84 ± 0.06 mas/yr 55200…
Figure 4
Figure 4. Figure 4: Potential kick velocity probability distribution of GX 339–4 with a median of 200 km s−1 (dashed line) and a 5t h and 95t h percentile of 122 km s−1 and 258 km s−1 (in dotted lines), respectively. 6.1.1 GX 339–4 Gaia could not make a parallax measurement for GX 339–4. …
Figure 5
Figure 5. Figure 5: Left panel: PKV probability distribution of GRS 1716–249 using Gaussian systemic radial velocity (γ¯) distributions with means of −110 km s−1 , -60 km s−1 , -10 km s−1 , 40 km s−1 and 90 km s−1 all with a 1σ of 50 km s−1 . The medians of all the PKV distributions are t…
Figure 6
Figure 6. Figure 6: Left panel: Posterior distribution function for the distance to Swift J1753.5–0127, constructed from the Gaia-DR2 parallax measurement using the Milky Way LMXB distribution prior (see Section 5.1 for details). The mode of the distribution is at 7.7 kpc. The 5t h, 50t h…
Figure 7
Figure 7. Figure 7: Realisations of the inferred unimodal (top) and bi￾modal (bottom) distributions for potential kick velocities (v), in￾ferred from the data (d). The blue lines represent the model cor￾responding to the median values from the posterior sample for data from all the system…
Figure 8
Figure 8. Figure 8: PKV probability distributions of the 16 BHXBs in our sample. It can be seen that no single system is responsible for either of the two most prominent peaks in the aggregated natal kick distribution. tem, the direction of the kick and the mass ejected in the SN explosio…
Figure 9
Figure 9. Figure 9: Comparison of best fit unimodal and bimodal BHXB PKV distributions to the best pulsar kick velocity distribution. The BHXB PKV unimodal distribution is represented by the solid line and has a median of 107 km s−1 . The BHXB PKV bimodal distribution is represented by th…
Figure 10
Figure 10. Figure 10: Left: the variation of PKV with the current height of the system above the Galactic plane. There are five systems with a PKV below 100 km s−1 are within 500 pc of the Galactic plane. There are two systems that are within 500 pc but have PKVs >100 km s−1 . Right: the v…

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    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.