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Mixed origins: strong natal kicks for some black holes and none for others

T0 review · 3 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Black holes are born with a mix of strong and weak natal kicks, and the observed split matches a mixed-origin scenario of direct collapse and supernova kicks.

desk verdict A useful and mostly sensible re-analysis of BH natal kicks whose qualitative mixed-origin conclusion is probably right, but the quantitative thresholds have an equation/table mismatch and a real age-matching weakness that need fixing before publication. read the letter →

arxiv 2411.16847 v2 pith:EHHLM6O7 submitted 2024-11-25 astro-ph.GA astro-ph.HEastro-ph.SR

Pranav Nagarajan , Kareem El-Badry This is my paper · ORCID
classification astro-ph.GAastro-ph.HEastro-ph.SR
keywords blackholenatalkicksstellarkinematicsGaiaDR3X-raybinariesToomrediagramsGalacticorbitsdirectcollapseholessupernova
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

Using Gaia DR3 astrometry and radial velocities, this paper tries to establish whether stellar-mass black holes receive a "natal kick" when they form, and how big such kicks are. For 12 black-hole binaries with well-measured distances, the authors compare each black hole's present-day space velocity and Galactic orbit with the velocity dispersion of its local stellar population, rather than treating its raw peculiar velocity as the kick. They find that half the systems are kinematically hotter than at least 68% of their local stars, four systems are hotter than 90% of local stars (implying kicks $\gtrsim 100$ km s$^{-1}$), and six systems look kinematically ordinary (disfavoring kicks $\gtrsim 50$ km s$^{-1}$). Two systems with independent orbital evidence, V404 Cyg and VFTS 243, require kicks $\lesssim 10$ km s$^{-1}$. The conclusion is that black holes do not all form gently: some are born with strong kicks and some with almost none, a split that matters for how black-hole binaries form and merge.

What carries the argument

The argument is carried by the Toomre diagram: a plot of the non-azimuthal velocity $\sqrt{V_R^2 + V_z^2}$ against the azimuthal velocity $V_\phi$ for the black-hole binary and for several hundred nearby Gaia DR3 stars. Around the comparison sample's median azimuthal velocity the authors draw semicircles that enclose 68%, 90%, and 95% of the local stars; these contours represent how hot the local stellar population is, i.e. how much of a black hole's motion could be ordinary dynamical heating rather than a kick. The minimum kick is the distance from the black hole's velocity to the 68% contour, $V_{\rm kick,min} = \max(0,\, V - V_{68\%})$, with $V=\sqrt{V_R^2+V_z^2+V_\phi^2}$. Galactic orbits integrated backward in time for 1 Gyr serve as a visual cross-check: systems classified as kicked have puffier, more eccentric orbits, while unkicked systems stay near circular orbits close to the disk midplane.

What would settle it

Measure the ages (by asteroseismology, spectroscopy, or Gaia colors) of the local comparison stars around the six systems classified as "no kick" and compare them with the ages of the binaries' companions; if the comparison stars turn out to be systematically much older, then a black hole born in a younger, colder population would look unkicked next to elderly heated giants, and the no-kick classifications would collapse. If age-matched samples reproduce the same split, that would confirm the result.

Watch

Extended reading notes

Core claim

The central claim is that a black hole's raw present-day velocity is a biased measure of its natal kick, because most black-hole binaries are old and their orbits have been dynamically heated by the Galaxy. Once a local comparison sample from Gaia DR3 is used to define 68%, 90%, and 95% velocity-dispersion contours on a Toomre diagram, the minimum kick is $V_{\rm kick,min} = \max(0,\, V - V_{68\%})$. By this metric, half of the 12 disk systems show at least weak kick evidence, one-third exceed the 90th percentile of their local population, and two systems (Swift J1727.8-162 and GRO J1655-40) exceed the 95th percentile, implying birth kicks $\gtrsim 100$ km s$^{-1}$. The other half are consistent with their local populations, so kicks $\gtrsim 50$ km s$^{-1}$ are disfavored for them. The paper therefore argues that it would be wrong to conclude that most black holes form with weak kicks merely because two well-studied systems did, and that the data are consistent with a mixed origin: direct collapse with weak kicks for some black holes, supernova kicks for others.

Load-bearing premise

The load-bearing assumption is that the stars found today within 500 pc of each black hole represent the stellar population in which the black hole's progenitor was born, so that the spread of their velocities is the right baseline for "no kick."

Editorial extensions

If this is right

  • Minimum kicks inferred for most systems are smaller than the raw peculiar velocities quoted in earlier work, so treating present-day velocity alone as the kick overestimates black-hole kicks in old populations.
  • At least four black holes (Swift J1727.8-162, GRO J1655-40, GRS 1124-684, and Gaia BH1) are kinematically hotter than 90% of their local stars, consistent with birth kicks of roughly $\gtrsim 100$ km s$^{-1}$.
  • Six black holes in the sample have kinematics consistent with their local populations, disfavoring kicks $\gtrsim 50$ km s$^{-1}$; V404 Cyg and VFTS 243 independently require kicks of only $\lesssim 5$-$10$ km s$^{-1}$.
  • Binary population synthesis and gravitational-wave merger-rate models that assume all black holes form with negligible kicks are missing a real population of strongly kicked black holes.
  • The sample as a whole is consistent with a mixed-origin scenario, some black holes forming by direct collapse with weak kicks and others in supernovae with strong kicks, though the uncertainties are too large to prove the kick distribution is truly bimodal.

Reading between the lines

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

  • Because binaries that survive strong kicks are preferentially destroyed, the strong-kick cases in this sample likely underrepresent the true fraction of strongly kicked black holes in the field, so the field population may be even more kick-heavy than the 50% found here.
  • Applying the same local-dispersion comparison to neutron-star binaries would give a uniform, apples-to-apples measurement of neutron-star versus black-hole kicks; the paper's appendix suggests neutron-star binaries are more dispersed, but not dramatically.
  • The main caveat is testable: age-dating the comparison stars would let future work replace the implicit same-population assumption with an explicit, age-matched baseline.
  • With more astrometric black-hole binaries from future Gaia releases, the percentile method could map the kick distribution's shape and distinguish a true bimodal distribution from a broad unimodal one.
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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 / 7 minor

Summary. The paper estimates natal kicks for 12 Galactic black-hole binaries by comparing their Gaia-based space velocities and Galactic orbits with local comparison samples drawn from Gaia DR3 (500 pc projected radius, distance-matched, with quality cuts on parallax and velocity errors; the samples are mostly red giants). Using Toomre diagrams, the authors define 68/90/95% velocity thresholds for each local population and classify each BH as showing or not showing evidence of a kick, reporting 'minimum kicks' as the excess over the 68% threshold. They find that 6 of 12 systems lie beyond the 68th percentile, including 4 beyond the 90th (Swift J1727.8-162, GRO J1655-40, GRS 1124-684, Gaia BH1), while 6 lie within it (MAXI J1820+070, MAXI J1305-704, V404 Cyg, 3A 0620-003, Cyg X-1, Gaia BH2). Combining these classifications with independent dynamical constraints on V404 Cyg (kick ≲ 5 km/s from triple stability) and VFTS 243 (≲ 10 km/s from orbital circularity), they argue that the data are consistent with a mixed origin: some BHs form with strong kicks and some with negligible kicks, while cautioning that binary selection biases favor weak kicks and that a bimodal distribution is not directly proven. An appendix compares the kinematics of BH and NS binaries.

Significance. If the central claims hold, the paper makes a useful methodological contribution: it replaces the cold thin-disk birth assumption of earlier kick studies (e.g., Atri et al. 2019; Zhao et al. 2023) with empirically measured local velocity dispersions, yielding more conservative minimum kicks and a population-level dichotomy rather than a unimodal distribution. Strengths worth emphasizing: the no-kick baseline is measured from Gaia DR3 percentiles rather than fitted; the paper is transparent about assumptions (age-match caveat in §3.1 and §4.2.10, arbitrariness of the percentile choice in §3.2, birth-location test in §4.4); it quantifies the binary selection bias toward weak kicks (§4.4); and it checks each system against dedicated literature studies (§4.2). The strong-kick conclusion is robust to the comparison-sample construction (Swift J1727.8-162 and GRO J1655-40 exceed the 95th percentile), and the existence of at least some very-weak-kick BHs rests on independent dynamical evidence (V404 Cyg, VFTS 243), so the mixed-origin conclusion survives even if individual kinematic classifications shift.

major comments (3)
  1. [§3.2, Eqs. (4)–(5), Table 2] The reported minimum kicks cannot be reproduced from the written equations. Equation (4) defines V as the full Galactocentric 3D speed sqrt(V_R^2 + V_z^2 + V_phi^2), which for a thin-disk system is dominated by the azimuthal component V_phi ~ 230 km/s, so max(0, V - V68%) would be roughly 100-200 km/s for every system and could never be zero; yet six rows of Table 2 report V_kick,min = 0. Every row instead satisfies V_kick,min = V_pec,local - V68% within rounding (e.g., GRO J1655-40: 138 - 76 = 62; GRS 1124-684: 115 - 67 = 48; XTE J1118+480: 123 - 87 = 36; Gaia BH1: 79.4 - 50.0 = 29; and the zero rows correspond to V_pec,local < V68%). The intended estimator is evidently the target's excess beyond the 68% Toomre radius in the (V_phi, V_perp) plane, which is well defined, but it is not what Eqs. (4)-(5) state. Please correct the equations or the table, and align the numbers quoted in Sections 4.2.4, 4.2.6, 4.2.7, and 4.2.11 with the corrected definition.
  2. [§3.1, §4.2.10, §4.4] The no-kick baseline rests on an untested age-matching assumption. The comparison samples are dominated by red giants (old, dynamically heated), and the paper states only that it assumes the BH binaries and reference samples probe similar stellar populations; for Cyg X-1 it explicitly acknowledges that most comparison stars are older than the system, yet no age or chemistry selection, and no test of the resulting bias, is provided. Because old giants have a larger V68% than a young thin-disk birth population, the comparison is not conservative for young systems: Cyg X-1's peculiar velocity of 24.2 km/s (18th percentile) could be consistent with a sizable kick if judged against an age-matched sample, and the §4.2.10 statement that the present-day peculiar velocity is a 'reasonable estimate' of the kick is in tension with the concern just raised. The §4.4 disk-crossing test addresses birth location, not birth population. Please quantify the age-mixing bias (e.g., by stratifying the comparison sample by color or isochrone age, or by constructing a young-star comparison sample for Cyg X-1) and revise the claim that six BHs have kinematics that disfavor kicks of ≳50 km/s accordingly.
  3. [§3.1, Table 2, §4.1] The kick/no-kick classification is quoted without propagated uncertainties. The 10,000-sample Monte Carlo described in §3.1 is used only to assign error bars to V_pec,local and V_pec,circ; the velocity percentiles, the V68%/V90%/V95% thresholds, the V_kick,min values, and the counts of systems beyond each contour are all reported as single numbers, even though the peculiar-velocity errors are large enough to move systems across thresholds (e.g., MAXI J1305-704 at 71+41/-28 km/s reaches its V68% = 110 km/s only in the upper error tail, and V404 Cyg at the 60th percentile is eight points inside the 68% contour). The binomial probabilities in §4.1 treat the counts as exact. Please propagate the Monte Carlo samples through the percentile-rank calculation and report, for example, the probability that each system is classified as kicked, and recast the 'at least 4' and 'half' statements with these uncertainties.
minor comments (7)
  1. [Abstract and §4.1] The quoted probabilities (0.098, 0.021, 0.099) are exact-count binomial probabilities, but the appropriate statistics for 'observing six systems beyond the 68% contour' (etc.) are the tail probabilities, which are approximately 0.18 (≥6 of 12 at p=0.32), 0.025 (≥4 of 12 at p=0.10), and 0.12 (≥2 of 12 at p=0.05); the 68% count is therefore not significant at the 90% level, and the text should either state tail probabilities or explicitly say 'exactly'.
  2. [Abstract] The statement that the four systems above the 90th percentile 'were born with kicks of ≳100 km/s' overstates what the adopted thresholds imply: the relevant V90% values for the four systems are 142, 108, 98, and 77 km/s (Gaia BH1), so the ≳100 km/s inference is only directly supported for Swift J1727.8-162 and GRO J1655-40; please tie the statement to the individual V90% thresholds.
  3. [Section 1] 'Blauuw kick' is a typo for 'Blaauw kick' (Blaauw 1961).
  4. [References and §4.2.8] Two distinct Miller-Jones et al. (2009) papers (ApJL 706, L230 and MNRAS 394, 1440) are cited without year-letter disambiguation; please introduce 2009a/2009b in the text and reference list.
  5. [Throughout] The analysis depends entirely on Gaia DR3 queries and Monte Carlo sampling, but no code, catalog of the comparison samples, or query parameters are provided; a reproducibility statement or data release would substantially strengthen the paper.
  6. [§4.2.2] 'A minimum natal kick of > 14 km/s' should read 'of 14 km/s' (or '≥14 km/s') to match the V'_kick,min = 14 entry in Table 3.
  7. [Figure 4 and §4.4] The orbits are integrated for only 1 Gyr although §4.4 describes LMXBs as several Gyr old; a sentence justifying the integration time as illustrative of the present-day orbital structure would prevent confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: BH kicks are tested against externally measured Gaia DR3 comparison samples, and the weak-kick cases rest on independent dynamical constraints.

full rationale

The paper's central derivation compares each BH's space velocity to a local comparison sample drawn from Gaia DR3. The V68/V90/V95 radii are computed from the comparison stars' velocities, not fitted to the BHs, and the minimum-kick estimator Vkick,min = max(0, V - V68%) is a stated lower bound rather than a fitted prediction. The split into kick/no-kick systems is therefore an outlier test against an external benchmark, not a reduction of the conclusion to its inputs. The weak-kick claims for V404 Cyg and VFTS 243 are supported by independent dynamical arguments (hierarchical-triple stability and the circular orbit of a non-tidally-synchronized binary); VFTS 243 is fully external to the authors, and V404 Cyg's constraint is an independently falsifiable dynamical calculation outside this paper's fitted values. The paper explicitly flags the age-matching assumption in Section 3.1 ('An implicit assumption in our analysis is that the BH binary and the reference samples probe similar stellar populations') and again for Cyg X-1 in Section 4.2.10, and tests robustness by repeating the analysis at last disk crossing in Section 4.4. These are acknowledged limitations affecting statistical power and interpretation, not circular constructions: the comparison sample is not derived from the BHs, and the thresholds are not calibrated to produce the kick classifications. No equation is equivalent to its own input by construction, no fitted parameter is renamed as a prediction, and no load-bearing uniqueness theorem or ansatz is imported from the authors' prior work. The presence of author-overlapping citations (Gaia BH1/BH2 discovery papers, V404 Cyg triple paper) does not raise the circularity score because those citations provide real, independently checkable data and dynamical constraints rather than unverified self-support.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The analysis has one hand-chosen threshold and several domain assumptions, but no fitted parameters and no invented physical entities. The main assumption is that local Gaia stars represent the BH birth population.

free parameters (1)
  • 68th percentile threshold V68% = Per-system values 45-123 km/s (Table 2)
    Chosen by hand as the 1-sigma kick evidence threshold; changing it (e.g., to the 50th percentile) changes which systems are classified as kicked, so the central classification depends on this arbitrary choice.
assumptions (4)
  • domain assumption The local comparison sample probes the same kinematic population as the BH binary's birth environment.
    Stated in Section 3.1; if false, the baseline dispersion is wrong and kick classifications shift.
  • ad hoc to paper Subtracting the 68th-percentile Toomre radius from the present-day peculiar velocity yields a lower bound on the natal kick.
    Equation (5) defines Vkick,min this way; it is not derived from binary evolution or supernova theory, and Eq. (4) as printed is inconsistent with the table values.
  • domain assumption The adopted Galactic potential (gala MilkyWayPotential2022) is accurate enough for 1 Gyr orbit integrations.
    Used in Section 3.3; different potentials change Vpec,circ by about 6 km/s for Swift J1727.8-162 (Section 4.2.1).
  • standard math Reported uncertainties are adequately represented by split normal distributions.
    Section 3.1 uses split normals; this assumes error symmetry and independence of astrometric and RV terms beyond published covariances.

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Cite this review

Pith. "Pith review of Mixed origins: strong natal kicks for some black holes and none for others." pith.science (2026). https://pith.science/paper/EHHLM6O7

@misc{pith2026241116847,
  author       = {Pith},
  title        = {Pith review of: Mixed origins: strong natal kicks for some black holes and none for others},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EHHLM6O7}},
  note         = {Machine review of arXiv:2411.16847}
}
abstract

Using stellar kinematic data from Gaia DR3, we revisit constraints on black hole (BH) natal kicks from observed accreting and detached BH binaries. We compare the space velocities and Galactic orbits of a sample of 12 BHs in the Galactic disk with well-constrained distances to their local stellar populations, for which we obtain proper motions and radial velocities from Gaia DR3. Compared to most previous studies, we infer lower minimum kick velocities, because our modeling accounts for the fact that most BH binaries are old and have likely been kinematically heated by processes other than kicks. Nevertheless, we find that half of the BHs have at least weak evidence for a kick, being kinematically hotter than at least 68% of their local stellar populations. At least 4 BHs are kinematically hotter than 90% of their local stellar populations, suggesting they were born with kicks of $\gtrsim 100$ km s$^{-1}$. On the other hand, 6 BHs have kinematics typical of their local populations, disfavoring kicks of $\gtrsim 50$ km s$^{-1}$. For two BHs, V404 Cyg and VFTS 243, there is strong independent evidence for a very weak kick $\lesssim 10$ km s$^{-1}$. Our analysis implies that while some BHs must form with very weak kicks, it would be wrong to conclude that most BHs do, particularly given that selection biases favor weak kicks. Although the uncertainties on most individual BHs' kicks are still too large to assess whether the kick distribution is bimodal, the data are consistent with a scenario where some BHs form by direct collapse and receive weak kicks, and others form in supernovae and receive strong kicks.

Figures

Figures reproduced from arXiv: 2411.16847 by the authors.

Figure 1
Figure 1. Top: Distribution of binaries hosting dynamically confirmed BHs with luminous companions in a face-on artist’s rendition of the Milky Way disk (Credit: NASA/JPL-Caltech/ESO/R. Hurt). The right panel shows an inset zoomed in on the solar neighborhood. Error bars correspond to uncertainties on distance measurements. Systems without reliable proper motions or distances are not included, resulting in most BHs in the Gal… view at source ↗
Figure 2
Figure 2. Toomre diagrams for systems hosting BHs that show evidence for a natal kick. The azimuthal and non-azimuthal components of the spatial velocities of the targets are compared to those of a local comparison sample of stars from Gaia DR3. The median of the comparison sample is marked with a gold star. Semi-circles centered on the median Vϕ that contain 68%, 90%, and 95% of the comparison sample are plotted in cyan, dar… view at source ↗
Figure 3
Figure 3. Same as [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Galactic orbits of all binaries in our final sample. The orbits are integrated back in time by 1 Gyr based on current location and spatial velocity. The solar orbit is shown for reference. In the left two columns, we show the integrated orbits for systems hosting BHs t…
Figure 5
Figure 5. Figure 5: Toomre diagram comparing kinematics of luminous companions to BHs (blue) and NSs (orange), respectively. We show both the BHs considered in this work and NSs from Zhao et al. (2023) with low-mass companions that have robust 6D measurements and are not in the Galactic h…

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Forward citations

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Reference graph

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