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REVIEW 2 major objections 4 minor 298 references

Roughly 170 million black holes have formed in the Milky Way; about 91 percent are now isolated, and the most massive sit closest to the Galactic plane because heavy black holes are born with weak kicks.

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2026-08-01 04:23 UTC pith:RJT5XCAC

load-bearing objection A careful, reproducible forward-model census of the Milky Way BH population; the headline mass–location correlation is conditional on the fallback-scaled kick prescription, and the abstract should say so. the 2 major comments →

arxiv 2607.22814 v1 pith:RJT5XCAC submitted 2026-07-24 astro-ph.GA astro-ph.HEastro-ph.SR

Charting the Galactic Underworld I: Comprehensive simulations of the kinematics, rates, and demographics of Milky Way black holes

Tom Wagg , Katelyn Breivik , Adrian M. Price-Whelan , Mathieu Renzo , Julianne J. Dalcanton , Natasha S. Abrams This is my paper
classification astro-ph.GA astro-ph.HEastro-ph.SR
keywords black hole demographicsnatal kicksfallback mass fractionbinary population synthesisGalactic potentialscale heightmicrolensingremnant mass prescriptions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish the intrinsic census of Milky Way black holes: how many exist, where they sit, how fast they move, and which ones have companions. The headline numbers are roughly 170 million black holes formed over the Galaxy's history, about 91 percent now isolated, about 3 percent escaped, and a vertical scale height roughly 2.5 times that of visible stars. The deeper claim is that present-day position encodes the birth event: heavy black holes form with more of the supernova material falling back, which damps their kicks, so the most massive black holes hug the Galactic plane while light ones are flung to high altitudes and sometimes out of the Galaxy. If the paper is right, this mass–location correlation becomes a direct observational lever on supernova kick physics, and the simulated population becomes the reference intrinsic catalog against which future microlensing, astrometric, and X-ray detections will be interpreted. The predictions are sharp and therefore testable: several trends reverse or disappear under alternative kick and remnant-mass models.

Core claim

The paper's discovery is a self-consistent, present-day map of the Milky Way's black holes. In the fiducial run, 1.7×10^8 have formed; 91% are isolated, 3% escape, and the bound scale height is 786 pc versus 306 pc for stars. The load-bearing correlation couples mass to location: because natal kicks are scaled by fallback, black holes above about 14 solar masses receive almost no kick, stay near the plane, and keep their companions, while light black holes are flung to high altitudes, disrupting their binaries. The correlation is absent at formation and emerges only by present day. BH-star binaries split into tight, low-mass post-common-envelope systems and wide, high-mass non-interacting on

What carries the argument

The central mechanism is the fallback-scaled natal kick: a black hole's birth velocity is multiplied by the fraction of supernova ejecta that falls back onto the collapsed core, so above roughly 14 solar masses the kick vanishes. This single scaling generates the headline results — the mass–location correlation, the bimodal BH-star binary population, and the 3% escape fraction — and the paper isolates it by showing that the no-fallback variation inverts the correlation and raises the escape fraction to 15.5%. The supporting machinery is a coupled pipeline: binary population synthesis feeding orbit integration through a model Galactic potential, plus a time-evolving potential variation whose

Load-bearing premise

The load-bearing premise is the fallback-scaled natal kick — the assumption that heavier black holes, formed with more ejecta falling back, are born with weaker or no kicks — because the paper's own variation without that scaling inverts the mass–location correlation and raises the escape fraction from 3% to 15.5%.

What would settle it

One decisive check: measure masses of hundreds of isolated black holes found by microlensing at varying heights above the plane. The model predicts median mass falling with distance from the plane, a trend that inverts if kicks do not scale with fallback; a 100-object sample settles the direction. A complementary count: the escape fraction is 3% in the fiducial model versus 15.5% without fallback scaling, so any census of ejected intergalactic black holes discriminates the two worlds.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Microlensing surveys expecting hundreds of isolated black holes can test remnant mass prescriptions directly: the model's 'islands of explodability' variant predicts an almost empty gap between 10 and 18 solar masses, while the fiducial prescription does not.
  • Astrometric surveys hunting black holes in binaries will be biased toward lighter black holes, because selection favors short orbital periods and the model ties short periods to low masses and to orbits that reach far from the plane.
  • Roughly 11,000 black holes in the Milky Way are accreting from a stellar companion today; removing fallback-scaled kicks would cut that X-ray-emitting population to about 1,500, so X-ray binary counts constrain kick physics.
  • The Galaxy's past mass growth doubles the fraction of black holes that escape (2.7% to about 7%), so early-formed black holes are more likely to be free-floating intergalactic wanderers.
  • About 13% of the model's black-hole binaries toward the Galactic center have angular separations near the Einstein radius and could be detected as binary microlenses, making their formation rate — which is highly kick-sensitive — observable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The mass–location correlation could be the cleanest selection-independent probe of core-collapse asymmetry: if confirmed by the first large astrometric and microlensing samples, no individual event reconstruction would be needed to know that heavy black holes form quietly.
  • The same machinery predicts neutron stars are formed 2.9 times more often and escape more readily; a dedicated neutron-star forecast, which the paper explicitly defers, would quantify how much they contaminate black-hole microlensing and X-ray samples.
  • The period–mass boundary that separates common-envelope systems from wide binaries (99.7% accurate in the model) is directly testable with the dozens of astrometric black holes expected in the next data release; the three known systems already sit near the boundary, so the test is close at hand.
  • Because the correlation is inverted at formation and reversed by kicks, measuring it in dwarf galaxies — where weak potentials eject low-mass black holes preferentially — may isolate the kick contribution from the metallicity-driven gradient in where heavy stars are born.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper presents cogsworth simulations of the Milky Way's intrinsic black hole (BH) population, self-consistently combining binary population synthesis, a distribution-function-based star formation history, and Galactic orbit integration. The fiducial model predicts ~1.7e8 BHs formed over the Galaxy's history, with ~91% currently isolated, ~3% escaped, and an effective scale height of ~786 pc versus ~306 pc for visible stars. The central new diagnostic is a mass–location correlation: BHs close to the plane are more massive on average, and BH–star binaries split into tight low-mass post-common-envelope systems and wide high-mass non-interacting systems. A suite of 32 variations explores natal kicks, remnant mass prescriptions, binary mass-transfer physics, initial distributions, and a time-evolving potential.

Significance. If correct, this paper provides the reference intrinsic population against which Roman microlensing, Gaia DR4 astrometry, and X-ray observations will be interpreted. The mass–location correlation and its binary counterpart are proposed as direct diagnostics of BH natal kick physics and remnant mass prescriptions. The work is especially valuable because the central predictions are forward-model outputs rather than fits to the quantities they predict; the code and data are publicly released; and the sensitivity suite is unusually broad and honestly reports order-of-magnitude variations in the BH census. The Appendix C re-analysis of S22 is transparent and useful. The main weakness is that the headline correlation is contingent on a single, deterministic kick–fallback prescription, and the paper's bounding variations do not fully bracket the physically motivated stochastic/mixed kick scenario.

major comments (2)
  1. [§4.1, Fig. 7, Table 3] The headline mass–location correlation is not bracketed by the two bounding kick variations. The fiducial correlation is produced by the deterministic Fryer+12 fallback scaling (Fig. 2). The 'No BH kicks' and 'No fallback rescaling' extremes bracket the overall kinematic heating, but not the shape of the mass dependence: in the latter model f_esc changes from 2.7% to 15.5% and f_bound from 9% to 0%, so a stochastic mixture of weak and strong kicks could flatten or invert the mass–height slope while keeping the aggregate escape and bound fractions near the fiducial values. This is not merely academic, because §4.1 itself cites observational evidence for a mixture (VFTS 473, Swift J1727.8-162, Nagarajan & El-Badry 2025). I request an additional variation with a mixed kick prescription, reporting the Table 3 columns and the Fig. 7 slope. If this cannot be added, the abstract and §3.3 should
  2. [§3.3 and abstract] The present-day negative mass–height slope is an inversion of the positive slope imprinted at birth (grey line in Fig. 7), produced by the competition between metallicity-dependent formation sites and fallback-scaled kicks. The paper explains this correctly in §4.1, but the abstract and Figure 5 present the correlation without that context. For a paper whose main diagnostic is this correlation, the abstract should state that the correlation is a prediction of the fiducial fallback-scaled kick prescription, not an assumption-free result. This is closely tied to the previous comment but deserves explicit editorial attention.
minor comments (4)
  1. [Fig. 1] The pie chart percentages in the text sum to 101% (59% disruption + 33% merger + 9% bound). This is presumably rounding, but the numbers should be adjusted for internal consistency.
  2. [§3.2] The estimate of the nearest BH distance, 'on average, 19 pc away,' should clarify the estimator. With a number density of 1.6e-4 pc^-3, the mean interparticle spacing is n^{-1/3} ~ 18 pc, while the mean nearest-neighbor distance in a Poisson process would be ~10 pc. Please state which definition is used.
  3. [Eq. (1)] The classification boundary in Eq. (1) is quoted with 99.7% accuracy. Please state the mass and period range over which this accuracy is evaluated, and ideally give the accuracy under the mass-transfer physics variations in Appendix E, since the boundary is derived from the fiducial model.
  4. [Appendix C] The reanalysis of S22 is valuable and well explained. To avoid confusion, the re-derived values of 590 pc and 850 pc should be explicitly labeled as using the authors' CDF-based definition of h_z,eff, since S22's published 900±40 pc used an exponential fit in the solar neighborhood.

Circularity Check

0 steps flagged

No significant circularity: the census and kinematic claims are emergent outputs of a version-pinned forward simulation; none is defined in terms of a fitted target.

full rationale

The paper's derivation chain is a forward population-synthesis model: initial distributions (Kroupa IMF, Sana et al. period/eccentricity), a Sanders & Binney quasi-isothermal star-formation history with Frankel et al. metallicities, COSMIC binary evolution with Fryer et al. (2012) delayed remnant masses and fallback-scaled natal kicks, and Gala orbit integration through MilkyWayPotential. Every headline quantity — N_BH = 1.7e8, 91% isolated, f_esc ~ 3%, h_z,eff = 786 pc, the mass–|z| anticorrelation, and the BH-star binary bimodality — is computed from these inputs, not fitted to them. The mass-location correlation follows from the input mass-kick mapping (Figure 2) combined with orbit integration, but its quantitative form is emergent; the paper demonstrates it is non-tautological by erasing the correlation in the 'No BH kicks' run and inverting it in the 'No fallback rescaling' run (Figure 7, Table 3), and by showing the correlation at formation is reversed (grey line, Figure 7). Thus this is a falsifiable model outcome, not X defined in terms of Y. Self-citations (cogsworth, COSMIC, Gala) are to version-pinned (v4.0.2, v4.1.1, v1.11.1), open-source, code-reproduced tools, with reproduction code provided, and results are checked against external benchmarks (O20, S22) rather than presupposed. The one fitted-to-output element, the P_orb-m_BH mass-transfer separator (Eq. 1, '99.7% of the time'), is a descriptive summary of the simulation's own data, explicitly cautioned as model-dependent, and is not load-bearing for the census claims. No uniqueness theorem is imported from the authors and no parameter fitted to target data is relabeled as a prediction. Score 1 reflects minor toolchain self-citation, which is not circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The paper introduces no new physical entities; its parameters are either imported from the cited literature (IMF, kick distributions, remnant prescriptions), fitted to external simulations (m12i mass growth in Appendix A), or fit to the paper's own simulation output (Eq. 1 classifier). The heaviest model-dependence sits in the fallback-scaled kick prescription and the steady-state SFH sampling assumption, which jointly generate the headline spatial correlations.

free parameters (3)
  • Eq. 1 mass-transfer boundary: 7000-day normalization and 2.2 exponent = P_orb/7000 days < (m_BH/3 M⊙)^2.2
    Fitted to the fiducial simulation's own output to separate common-envelope from non-interacting BH-star binaries; claimed 99.7% accurate within that model (§5.3).
  • Time-evolving potential mass-growth coefficients = DM: M_f(2.32−0.16τ/Gyr) for τ>9 Gyr, M_f(1−0.12τ/9 Gyr) otherwise; baryons: M_f(1−0.8τ/12 Gyr)
    Fit to the enclosed mass within 50 kpc of the FIRE m12i halo (Appendix A, Eqs. A1-A2). The reported 2.5× escape-fraction increase and +20% scale-height correction depend directly on these coefficients.
  • Minimum BH mass / NS-BH boundary = 3 M⊙
    The fiducial Fryer-delayed prescription differentiates NSs from BHs only via this mass cut (noted in §3.1 footnote). The BH mass distribution peaks at this chosen boundary, so it shapes the low-mass end of the claimed distribution.
axioms (6)
  • domain assumption The sampled initial positions/velocities from the quasi-isothermal distribution function are in steady state, so integrating orbits forward preserves the stellar distribution absent kicks, and every deviation is attributable to SN kicks (§2.3).
    The paper states 'any changes in the distribution of positions of BHs in this model are fully a result of supernova kicks.' If the SFH sampling is not actually in equilibrium (e.g., due to disc growth or radial migration not captured by the steady-state DF), the kick attribution for the scale-height excess would be contaminated.
  • domain assumption BSE/COSMIC fitting formulae (Tout et al. 1997; Hurley et al. 2000, 2002; Breivik et al. 2020) adequately represent stellar and binary evolution from ZAMS through core collapse.
    All binary outcomes — mergers, common-envelope phases, mass transfer, and which stars become BHs — rest on these fast fitting formulae rather than resolved stellar models.
  • domain assumption The Gala MilkyWayPotential v2 static model adequately describes the present-day Galactic potential (§2.5).
    All orbital integrations, scale heights, and the 3% fiducial escape fraction are computed in this fitted potential.
  • domain assumption BH natal kicks scale with the Fryer et al. (2012) fallback mass fraction (§2.4, Figure 2).
    The mass-dependence of kicks produced by this scaling is the mechanism behind the mass-location correlation, the bimodal BH-star binaries, and the escape fraction; Figure 7 shows that removing it inverts the correlation.
  • domain assumption The FIRE m12i halo mass-growth tracks, with the analytic fits of Eqs. A1-A2, represent the Milky Way's potential evolution (Appendix A).
    The time-evolving potential results (2.5× escape fraction, +20% scale height) rest on a single simulated dwarf-analog halo being representative of the Milky Way's growth history.
  • domain assumption All massive stars are born in binaries (100% binary fraction), with 85% effectively single (§2.2).
    The initial population contains no truly single stars, only binaries; the 85% effectively-single fraction is asserted to match Offner et al. (2023).

pith-pipeline@v1.3.0-alltime-deepseek · 42163 in / 18616 out tokens · 183064 ms · 2026-08-01T04:23:18.337314+00:00 · methodology

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read the original abstract

With upcoming data from Roman, Gaia DR4, and spectroscopic surveys, we will soon have an unprecedented dataset of Milky Way black holes (BHs) to constrain their formation and evolution. To prepare, we simulate the intrinsic population of Milky Way BHs with cogsworth, self-consistently accounting for their binary evolution and trajectories through the Galactic potential. We report the rate, demographics, and kinematics of these BHs, and their sensitivity to 32 variations in binary evolution, supernova physics, and Galactic potentials. In the fiducial model, ~$1.7 \times 10^8$ BHs have formed in the Milky Way (though this total spans an order of magnitude across our variations), where the vast majority (~91%) are currently isolated and ~3% have escaped the Galaxy. Most of the ~$10^7$ BHs in binaries have another BH or a white dwarf companion, but ~$10^5$ retain a luminous stellar companion. BHs are distributed more diffusely than visible stars, with a scale height around ~$2.5\times$ larger. BH masses correlate with present-day location: the most massive BHs are preferentially close to the Galactic plane. This correlation is especially strong for BH-star binaries, which separate into tight, low-mass post-common-envelope systems and wide, high-mass non-interacting ones. The BH mass distribution and kinematics are highly sensitive to the remnant mass prescription and natal kick model, so observations could constrain explodability criteria and BH kicks. Accounting for the time-evolution of the Galactic potential more than doubles the escape fraction and increases the bound population's scale height by ~20%, whilst neglecting binary interactions overestimates it by 30%.

Figures

Figures reproduced from arXiv: 2607.22814 by Adrian M. Price-Whelan, Julianne J. Dalcanton, Katelyn Breivik, Mathieu Renzo, Natasha S. Abrams, Tom Wagg.

Figure 1
Figure 1. Figure 1: The mass distribution of Milky Way BHs in the fiducial model is shown in black (c.f., Figure 8a). Coloured histograms separate this distribution based on whether the BH is isolated due to a binary disruption (purple), isolated after a stellar merger (orange), or in a bound binary at present day (red). The inset panel focuses on the high-mass tail, which is dominated by BHs in binaries and those formed from… view at source ↗
Figure 2
Figure 2. Figure 2: BH natal kicks decrease with increasing mass in the fiducial model (applying C. L. Fryer et al. 2012). This trend is driven by the increasing fallback mass fraction at higher masses, which negates the asymmetry in core-collapse events that produces kicks. The relation is shown with a 2D density distribution in BH mass and natal kick velocity. The white contour lines show the 50th, 75th, and 95th percentile… view at source ↗
Figure 3
Figure 3. Figure 3: BHs are more diffusely distributed in the Galaxy than visible stars as a result of natal kicks. The left side shows the 2D density distribution of simulated BHs. The right side shows the distribution of an equal number of stars following the assumed star formation history model. is more comparable with that of the thick, high [α/Fe], disk (500–1000 pc, e.g., J. Bovy et al. 2012, [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 4
Figure 4. Figure 4: The scale height of Galactic BHs is increased relative to the visible galaxy due to supernova natal kicks. The cumulative distribution functions of absolute Galactic heights are shown in solid lines (stars in gold and BHs in black). Dashed lines are shown at the height that contains 1−1/e of the distribution (equivalent to the scale height of an exponential distribution). The stellar distribution is drawn … view at source ↗
Figure 5
Figure 5. Figure 5: BHs that are further from the Galactic plane are less massive on average at present day, due to low-mass BHs receiving large natal kicks on average. Normalised his￾tograms of BH mass, separated into bins of distance from the Galactic plane at present day, |z|. The black histogram shows the total distribution as a guide. Dotted lines indicate the median value of each histogram. 3.3. BHs further from the Gal… view at source ↗
Figure 6
Figure 6. Figure 6: Left: The scale height of BHs in our model vari￾ations. The dashed line and shaded area indicates the scale height for the fiducial model. Right: The number of BHs in the Milky Way at present day. The dashed line indicates the total for the fiducial model. Variations of natal kicks and remnant mass prescriptions are shown as circles, while varia￾tions of initial distributions are triangles. See Figures 6 &… view at source ↗
Figure 7
Figure 7. Figure 7: Correlations between BH mass and location are sensitive to choices regarding BH natal kicks. Lines show a running median of BH mass (averaged over a window of 0.25 dex) as a function of distance from the Galactic plane. The black line shows the running average when using the present-day location of BHs in the fiducial model (this is an alternate visualisation of the same trend as [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 8
Figure 8. Figure 8: The distribution, and number, of BHs is very sen￾sitive to variations in the remnant mass prescription. Each panel shows the distribution of BH masses for a range of variations. Panel (a) changes the remnant mass prescrip￾tion, where K. Maltsev et al. (2025) has the default values of ffb = 0.5 and P(pf) = 0.1. Panel (b) varies the fallback mass fraction in the case of partial fallback for the K. Maltsev et… view at source ↗
Figure 9
Figure 9. Figure 9: The number of Milky Way BH binaries for our suite of simulations, described in Section 4. Each panels show the total number of BH-star, BH-white dwarf, BH-NS, and BH-BH binaries respectively. Variations of natal kicks and remnant mass prescriptions are shown as circles, variations of initial distributions are triangles, and variations of mass transfer physics are circles. natal kicks are drawn from a distr… view at source ↗
Figure 11
Figure 11. Figure 11: BHs with luminous companions have a bimodal distribution in mass and orbital period. Low-mass BHs are found in close binaries (after a common-envelope event) and receive strong natal kicks, while high-mass BHs receive lit￾tle to no kick and remain in wide, non-interacting binaries. Black points are BHs that achieved full fallback and therefore received no natal kick. The diagonal dashed line separates sys… view at source ↗
Figure 12
Figure 12. Figure 12: The spatial distribution of BH-star binaries is strongly influenced by the mass of the BH. Points show the distribution of BH mass and the maximum distance from the Galactic plane achieved on the binary’s orbit around the Galaxy, coloured by binary orbital period. We also add points for the 3 Gaia BH detections. in the Milky Way. From [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: A fraction of BH-BH binaries may be detectable as binary lenses with microlensing. The blue histogram shows the distribution of the ratio between the angular sepa￾ration, θsep, and approximate Einstein radius, ˜θE, (see Eq. 2) for simulated BH-BHs. We overlay the normalised cumula￾tive distribution function of this population as a black line (using the right y-axis). The annotations indicate the re￾gions … view at source ↗

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