Synthetic catalog of black holes in the Milky Way

A. Olejak; K. Belczynski; M. Sobolewska; T. Bulik

REVIEW 3 major objections 6 minor 8 cited by

Synthetic catalog of black holes in the Milky Way

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The Milky Way likely hosts about 130 million stellar-origin black holes, mostly single, with the most massive one formed from a low-metallicity binary merger.

desk verdict Open catalog and new three-component SFR model are genuinely useful, but the headline BH census has an internal IMF scaling inconsistency that shifts the numbers by a factor of a few. read the letter →

arxiv 1908.08775 v3 pith:TQJPV42Y submitted 2019-08-23 astro-ph.SR astro-ph.GAastro-ph.HE

A. Olejak , K. Belczynski , T. Bulik , M. Sobolewska This is my paper · ORCID

classification astro-ph.SRastro-ph.GAastro-ph.HE

keywords blackholesMilkyWaypopulationsynthesisstarformationhistorybinarystarsgravitationalwavesmicrolensingdarkmatter

topics Dark Matter

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

This paper tries to establish a census of every stellar-origin black hole in the Milky Way by simulating how single and binary stars evolve in each Galactic component. It reports that the present-day Galaxy contains about 1.2e8 single black holes (average mass ~14 solar masses) and 9.3e6 black holes in binaries (average mass ~19 solar masses), for a total near 130 million. Roughly half of single black holes come from single-star evolution, about 30% from binary mergers, and about 20% from disrupted binaries. The authors also derive current double-compact-object merger rates and bound the halo dark matter that could hide as stellar black holes.

What carries the argument

The central machinery is the StarTrack population-synthesis code, run on 18 discrete stellar populations representing the bulge, thin and thick disk, and halo, each with an assigned star formation rate and metallicity. The new Galactic star formation history and chemical evolution model (Section 2.5) is what makes this census different from older single-component, constant-metallicity estimates. The code combines a Kroupa IMF, binary orbital-parameter draws from observed massive-star binaries, a rapid supernova remnant model, pulsational pair-instability and pair-instability limits, and an explicit merger-product prescription with mass-retention fractions f_MS=0.8, f_He=0.8, and f_G=0.5. Two common-envelope models A and B bracket the uncertain fate of Hertzsprung-gap donors, and all population weights are scaled linearly to the adopted total stellar masses of the Galactic components.

What would settle it

A microlensing survey sensitive to lenses of 10-100 solar masses toward the Galactic bulge could count dark compact objects; if the measured event rate is far below the predicted billion-scale single-BH population, the census overcounts, and if far above, the census undercounts.

Watch

Extended reading notes

Core claim

The paper claims that at the current moment the Milky Way, including disk, bulge, and halo, contains about 1.2e8 single black holes with average mass about 14 solar masses and about 9.3e6 black holes in binary systems with average mass about 19 solar masses. Most binary black holes reside in BH-BH pairs, and the three main single-BH formation channels are single-star evolution (~50%), binary-system mergers (~30%), and disrupted binaries (~20%). The most massive single black hole in the simulation, about 113 solar masses, forms from a BH+helium-star merger in the low-metallicity halo, while the most massive black hole in a binary reaches about 60 solar masses. The paper further limits stellar-origin black holes in the 20-100 solar mass range to at most about 0.006% of the total Galactic halo mass, and estimates present-day Galactic merger rates of roughly 3-81 per Myr for BH-BH, 1-9 per Myr for BH-NS, and 14-59 per Myr for NS-NS systems.

Load-bearing premise

The hand-approximated star formation history and metallicity values for each Galactic component—especially the thin disk's ten discrete episodes and the halo's two low-metallicity bursts—are the load-bearing premise; if the real assembly history differs, every black-hole count scales with it.

Editorial extensions

If this is right

Most Galactic black holes are invisible to current surveys; the census implies that the roughly 20 detected systems form a tiny and likely unrepresentative sample.
If the numbers are right, gravitational-wave detectors should see present-day Milky Way merger rates of about 3-81 BH-BH, 1-9 BH-NS, and 14-59 NS-NS events per Myr.
Stellar-origin black holes cannot make up a significant fraction of the halo's dark matter: at most about 0.006% of total halo mass is hidden in 20-100 solar mass black holes.
About 5% of single black holes and well under 0.001% of binary black holes are moving fast enough to escape the Galaxy, giving an upper bound on ejected black holes.
The most massive local black holes should be found in old, low-metallicity halo environments, with masses above the usual pair-instability gap, up to about 113 solar masses.

Reading between the lines

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

Inference (editorial): The same simulation machinery could be reused to predict the Galactic neutron-star and white-dwarf census, and the catalog's spatial and velocity distributions could be tested against future astrometric surveys of dark companions.
Inference (editorial): A microlensing survey sensitive to 10-100 solar mass lenses would provide a direct counting experiment for the predicted single-BH population, since these objects otherwise emit nothing.
Inference (editorial): The gap between mean binary BH mass (~19 solar masses) and mean single BH mass (~14 solar masses) implies that mass-selected search strategies will over-represent binaries, which matters for interpreting future space-based gravitational-wave detections of Galactic binaries.
Inference (editorial): The claimed 0.006% halo bound is conditional on the modeled halo stellar mass of about 2e9 solar masses; a heavier stellar halo would raise the hidden BH mass fraction proportionally.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Useful paper, with an important flaw.

The genuinely new piece is the three-component SFR and chemical evolution model for disk, bulge, and halo. That is a real improvement over the old single-constant-SFR disk. The open database and the split of results by component and by two CE models give observers something concrete to use, and the paper is transparent about the physical choices. The merger-rate history plots and the BH mass distributions are worth having.

The soft spot is not the SFR model; it is Section 2.1. They state 5e6 single stars with M>5 Msun per population and a total simulated mass of 7.6e8 Msun. With the stated Kroupa IMF, one star above 5 Msun corresponds to roughly 46 Msun of total mass down to 0.08 Msun. That makes 5e6 stars correspond to about 2.3e8 Msun, not 7.6e8. The binary number has the same problem. If the linear scaling uses the quoted simulated masses, every final count is off by roughly a factor of three. This is independent of the SFR choices and it directly controls the headline 1.2e8 single BHs and 9.3e6 binary BHs. The authors need to clarify what the quoted mass means: either it is the mass of the evolved M>5 stars (then 7.6e8 implies 5e7 stars, not 5e6), or it is the full IMF mass (then it should be about 2.3e8). Either way the catalog needs re-scaling.

Other issues are minor by comparison: no error bars on the headline numbers; the merger mass retention fractions fMS=fHe=0.8 and fG=0.5 are ad hoc, though the paper does test alternatives; the BH-BH merger rate spans a factor of about 25 across the two CE models; Table 5's thick disk total looks like a typo. The self-cited LIGO/Virgo agreement is reasonable but should not be treated as independent validation. Their own removal of MS+He merger BHs above 70 Msun is an honest caveat.

The central argument—that the Milky Way holds of order 1e8 stellar-origin BHs, mostly single—is probably right and consistent with older estimates. But the specific catalog numbers should not be used as a quantitative reference until the scaling inconsistency is resolved.

I would send it to review: the SFR model and the catalog are worth publishing, and the flaw is fixable. The referee should insist on the re-scaling and a clear description of the normalization, ideally with the code or a precise enumeration of what was simulated.

Referee Report

3 major / 6 minor

Summary. The paper presents a forward population-synthesis census of stellar-origin black holes in the Milky Way, using the StarTrack code with 18 discrete stellar populations representing the bulge, thin disk, thick disk, and halo under a newly constructed star formation history and metallicity model. It reports about 1.2e8 single BHs with average mass ~14 Msun and 9.3e6 BHs in binaries with average mass ~19 Msun, with component-by-component tables, mass and velocity distributions, orbital parameters, a dark-matter constraint for halo BHs, and current Galactic merger rates for BH-BH, BH-NS, and NS-NS systems. Two common-envelope treatments (A and B) and three merger mass-retention prescriptions are explored.

Significance. If the numerical results are correct, this is a useful reference catalog and a clear step beyond single-component constant-SFR models: the SFR/metallicity model is more realistic, the forward-modeling approach does not fit the headline numbers, the two CE treatments bracket an important uncertainty, and the sensitivity of merger-mass prescriptions is at least partially explored. The public database is a valuable community resource. However, the quantitative census currently rests on a scaling step in Sec. 2.1 that appears internally inconsistent, so the headline numbers cannot be taken at face value until that normalization is corrected and the impact on all tables is assessed.

major comments (3)

[2.1] The total simulated masses quoted in Sec. 2.1 are inconsistent with the stated sample sizes and the adopted Kroupa IMF. For the given slopes (alpha=-1.3, -2.2, -2.3), the mean mass of stars drawn from 5-150 Msun is about 461 Msun; hence 5.0e6 single stars alone have a total initial mass of roughly 2.3e9 Msun, and 2.5e6 binary primaries alone contribute about 1.15e9 Msun before adding secondaries. The text instead gives 7.6e8 Msun and 3.1e8 Msun for the total simulated masses. Because every entry in Tables 2-9 is obtained by scaling simulated BH counts linearly with the ratio of real stellar mass to this simulated mass, the headline numbers (1.2e8 single BHs and 9.3e6 binary BHs) and all component counts are shifted by roughly a factor of three if the quoted simulated masses are used. Please specify how the total simulated masses were computed and re-derive the scale factors and all resulting numbers.
[2.5] The new SFR and metallicity model is a clear improvement over a single-component constant-SFR disk, but the construction relies on hand-drawn discrete episodes with round-number SFRs and metallicities, and the final census scales linearly with the adopted stellar masses. The paper should propagate at least the quoted uncertainties from Licquia & Newman (2015) (disk 5.17 +/- 1.11e10 Msun, bulge 0.91 +/- 0.07e10 Msun) and bracket the effect of the SFR episode decomposition, for example by shifting the 10-12 Gyr bulge formation peak or varying the ten 1 Gyr thin-disk episodes. Without such a bracket, the abstract's 'about 1.2e8' cannot be distinguished from a range that may span 30-50% or more.
[2.4/3.5] The merger mass-retention fractions fMS=fHe=0.8 and fG=0.5 are acknowledged as ad hoc, and Sec. 3.5 shows that the number of BHs in the first and second mass gaps depends strongly on them. The highlighted 113 Msun halo BH is produced in the CO+He merger channel and therefore inherits fHe=0.8. Since the f=0 and f=0.5 tests in Sec. 3.5 do not report the maximum single-BH mass, the paper should state the maximum mass and the number of objects above, say, 70 Msun in the alternative retention models; otherwise the abstract's emphasis on 113 Msun overstates the robustness of that endpoint.

minor comments (6)

[Sec. 3.3 / Conclusions] The formation channel of the 113 Msun BH is described as 'BH + He' in Sec. 3.3 and in the Abstract, but Conclusion item 3 says 'BH-MS system coalescence'; please correct the inconsistent statement.
[Table 5] The model-B total for thick-disk single BHs is printed as 8.5e7, while the row entries sum to about 8.5e6; in the same table, the MS-He row has an empty average mass for model B (19.9/()).
[Sec. 3.5] The text states that the average single BH mass in the halo is ~17 Msun, while Table 8 gives 21.0 Msun (model A) and 19.9 Msun (model B); please align text and table.
[Sec. 2.6] The velocity and coordinate model is very simplified, for example a uniform disk height of 0.3 kpc and a flat rotation curve used for both disk and halo; this is acceptable for a rough catalog, but the paper should state explicitly that the reported velocities are not dynamical predictions and should not be used for kinematic studies without caveats.
[Sec. 3.10] The sentence noting 'full agreement' with LIGO/Virgo estimates via Belczynski et al. (2017) is not a comparison performed in this paper and uses the same StarTrack model family; either remove the claim or show the comparison directly.
[General] There are numerous typographical problems in figure captions and text ('surrvive', 'botton', 'wavelenghts', 'distrupted', 'unenvolved'); a careful proofreading pass is needed.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor self-citation used for LIGO/Virgo agreement; central census is a forward population-synthesis calculation with no circular reduction.

self citation load bearing [Section 3.10 (paragraph before Table 13; also Abstract merger-rate claim)]
"We do not compare our current Galactic results with LIGO/Virgo estimates since to calculate cosmic merger rate of DCO one needs to take into account entire cosmic star formation rates SFR(z) and metallicity distribution Z(z) as a function of redshift. However, such calculation for StarTrack physical models (including presented in this work) were carried out in Belczynski et al. (2017), Sec. 3.2 noting full agreement with BH-BH, BH-NS and NS-NS LIGO/Virgo estimates."

The paper outsources the external validation of its physical model to a prior paper from the same group, stating 'full agreement' with LIGO/Virgo estimates without presenting the comparison. This is a self-citation used to lend credibility to the model, but it is not the derivation of the headline BH census: the 1.2e8 single BHs and 9.3e6 binary BHs are forward products of StarTrack simulation plus the newly adopted SFR/metallicity model, linearly scaled to adopted Milky Way component masses. The cited agreement therefore is not load-bearing for the main census, only for the secondary merger-rate validation, so the circularity is minor.

full rationale

No significant circularity in the central derivation. The census is a forward population-synthesis calculation: initial masses are drawn from a stated IMF, binary parameters from stated distributions, evolution is run with StarTrack, and the resulting BH counts are linearly scaled by adopted Milky Way stellar masses per component (Sec. 2.1 and 2.5). The headline numbers are not fitted to the target results, and the new SFR model is constructed from external observational/theoretical data, not from the BH counts. The merger mass-retention fractions (fMS=0.8, fHe=0.8, fG=0.5) are assumptions, not fitted predictions. The one circularity-adjacent item is the self-citation to Belczynski et al. (2017) for LIGO/Virgo agreement; it is a credibility citation rather than a step that forces the central results. The Section 2.1 simulated-mass normalization inconsistency noted in the skeptic brief would affect the numerical calibration of the scaling factor, but that is an arithmetic/correctness concern, not a definitional reduction of the result to its inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central census rests on the StarTrack population synthesis machinery and on a new, hand-approximated SFR and metallicity model for the three Galactic components. The merger mass retention fractions and binary fraction are explicit ad hoc choices that directly shape the headline numbers. No new physical entities are introduced.

free parameters (4)

Merger mass retention fractions fMS, fHe, fG = 0.8, 0.8, 0.5
Adopted in Section 2.4 to estimate masses of merger products; directly set the mass of the most massive BHs (e.g., 113 Msun) and the filling of the first and second mass gaps. Not derived from data.
Binary fraction = 0.5
Assumed in Section 2.2 from observational estimates; controls the number of binary BHs and merger products.
Natal kick velocity dispersion sigma = 265 km/s
Adopted from Hobbs et al. (2006) in Section 2.2; controls the single/binary BH split and the fraction of BHs that escape the Galaxy.
SFR model parameters for disk/bulge/halo = e.g., thin disk 5 Msun/yr episodes, bulge 2.3/0.5 Msun/yr, halo 0.5 Msun/yr; metallicities 0.01-1.5 Zsun
The new Galactic SFR and chemical evolution model in Section 2.5 is approximated from observational and theoretical figures; these values determine the total stellar mass formed and thus the total BH count.

assumptions (5)

domain assumption Kroupa IMF with alpha3=-2.3 applies to massive stars in all Galactic components
Adopted in Section 2.1; sets the number of BH progenitors.
domain assumption Sana et al. (2012) initial binary orbital parameter distributions, extrapolated to log(P/days)=5.5, apply to all massive binaries
Adopted in Section 2.1; sets the binary population from which binary BHs form.
domain assumption Rapid supernova engine (Fryer et al. 2012) with fallback-dependent natal kicks describes BH formation
Adopted in Section 2.2; sets BH remnant masses and kicks.
ad hoc to paper CE phase with HG donor either follows energy balance (model A) or always merges (model B)
Section 2.3; the two bracketing models produce a factor of about 25 spread in BH-BH merger rates.
domain assumption Stellar masses of Galactic components from Licquia and Newman (2015) and halo stellar mass about 2e9 Msun
Section 2.5; total BH numbers scale linearly with these masses.

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Cite this review

Pith. "Pith review of Synthetic catalog of black holes in the Milky Way." pith.science (2026). https://pith.science/paper/TQJPV42Y

@misc{pith2026190808775,
  author       = {Pith},
  title        = {Pith review of: Synthetic catalog of black holes in the Milky Way},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TQJPV42Y}},
  note         = {Machine review of arXiv:1908.08775}
}

read the original abstract

We present an open-access database which includes a synthetic catalog of black holes in the Milky Way. To calculate evolution of single and binary stars we used updated population synthesis code StarTrack. We applied a new model of star formation history and chemical evolution of Galactic disk, bulge and halo synthesized from observational and theoretical data. We find that at the current moment Milky Way (disk+bulge+halo) contains about 1.2 x 10^8 single black holes with average mass of about 14 Msun and 9.3 x 10^6 BHs in binary systems with average mass of 19 Msun. We present basic statistical properties of BH populations such as distributions of single and binary BH masses, velocities, orbital parameters or numbers of BH binary systems in different evolutionary configurations. We find that the most massive BHs are formed in mergers of binary systems, such as BH-MS, BH+He, BH-BH. The metallicity of stellar population has a significant impact on the final BH mass due to the stellar winds. Therefore the most massive single BH in our simulation, 113 Msun, originates from a merger of a helium star and a black hole in a low metallicity stellar environment in Galactic halo. The most massive BH in binary system is 60 Msun and was also formed in Galactic halo. We constrain that only 0.006% of total Galactic halo mass (including dark matter) could be hidden in the form of stellar origin BHs which are not detectable by current observational surveys. Galactic binary BHs are minority (10% of all Galactic BHs) and most of them are in BH-BH systems. The current Galactic merger rates for two considered common envelope models which are: 3-81 Myr^-1 for BH-BH, 1-9 Myr^-1, for BH-NS and 14-59 Myr^-1 for NS-NS systems. Data files are available at https://bhc.syntheticuniverse.org/.

Figures

Figures reproduced from arXiv: 1908.08775 by the authors.

**Figure 1.** Star formation rate of all Galactic components as a function of lookback time. Current time is 0. The old SFR model (blue dotted line) has been plotted for comparison. We approximate metallicity and age relations in the following way: -half of the stars in bulge formed 10-12 Gyr ago (a formation peak, SFR=∼2.3 M yr−1 ) and another half of stars formed from 10 Gyr ago to the current time with a constant star formatio… view at source ↗

**Figure 2.** Star formation rate and metallicity in Galactic bulge as a function of lookback time. Current time is 0. Vertical dashed lines separate star populations with different metallicities. Article number, page 4 of 21 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Star formation rate and metallicity of Galactic halo as a function of lookback time. Current time is 0. Vertical dashed line separates star populations with different metallicities. 2.6. Velocities and coordinates of Galactic black holes In our online database (https://bhc.syntheticuniverse.org/) we give simple estimations of Galcatic coordinates and velocities of BHs. The coordinates of black holes were randomly se… view at source ↗

Figures from the paper (12 more)

**Figure 3.** Figure 3: Star formation rate and metallicity of Galactic disk as a function of lookback time. Current time is 0. Vertical dashed lines separate star populations with different metallicities. 2.5.3. Galactic halo Galactic halo is the most massive Galactic component. Total mass o…

**Figure 5.** Figure 5: Total number of formed Galactic BHs single and binary as a function of time. Current time is 0. Results for two calculated models A and B (Sec. : 2.3). 3.1. Galactic bulge We find that Galactic bulge hosts about 1.7×107 single BHs and about 1 × 106 BHs in different typ…

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 7.** Figure 7: Merger rates of double compact object binaries (BH-BH, BHNS, NS-NS) as a function of time since Big Bang. Results for old Galactic SFR and chemical evolution model and two evolutionary models A and B, see section 2.3. Current time is 0 [PITH_FULL_IMAGE:figures/full_…

**Figure 8.** Figure 8: Single (top) and binary (bottom) BHs mass distribution in three Galactic components for model A. In model A we allow binary system to survive CE phase with HG donor star. Mass of the objects formed in merger estimated as explained in 2.4 [PITH_FULL_IMAGE:figures/full_…

**Figure 10.** Figure 10: Single BH mass distribution in three Galactic components for model A. In model A we allow binary system to survive CE phase with HG donor star. Mass of the objects formed in merger estimated as a lower limit assuming total mass loss from the second merging object (exc…

**Figure 11.** Figure 11: Single BH mass distribution in three Galactic components for model B. In model B we assume that CE phase with HG star donor always leads to binary system merger. Mass of the objects formed in merger estimated as a lower limit assuming total mass loss from the second m…

**Figure 14.** Figure 14: Distribution of separation in all Galactic BH binary systems in three Galactic components (bulge, disk, halo) and for CE model A (top) and B (bottom) [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]

**Figure 16.** Figure 16: Single (top) and binary (bottom) BHs velocity distribution in three Galactic components for model A. In model A we allow binary system to surrvive CE phase with HG donor star. With the red, dashed line we marked the velocity equal 580 km/s which is an estimated value …

**Figure 18.** Figure 18: Distribution of BH (top) and its companion masses (botton) in Galactic BH binary systems with non evolved companion in three Galactic components, for evolutionary model A [PITH_FULL_IMAGE:figures/full_fig_p017_18.png]

**Figure 20.** Figure 20: Distribution of separation in Galactic BH binary systems with non evolved companion in three Galactic components, for evolutionary model A (top) and B (bottom) [PITH_FULL_IMAGE:figures/full_fig_p018_20.png]

**Figure 22.** Figure 22: Diagram with orbital parameters - separation and eccentricity for BH binary systems with non compact companion. Results for two models A (top) and B (bottom). Article number, page 19 of 21 [PITH_FULL_IMAGE:figures/full_fig_p019_22.png]

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