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The Galactic Black Hole mass distribution

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L S. Rocha, N. Pires, L. M. de Sá, B. B. Martins, L. G. Barão, G. R. C. Sampaio, D. V. Rodrigues, R. M. G. Takahashi
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M. G. B. de Avellar, J.E. Horvath, A. Bernardo

High Energy Astrophysical Phenomena · Submitted 12 Sep 2026 · 181 references

Pith's verdict: A careful, well-documented update to the Galactic BH mass distribution, but the load-bearing limitation is the unmodeled selection bias that the authors themselves flag.

T0 · AI review

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arXiv ID2609.14154 (version 1)
Pith IDGYI3O6T3, Pith's permanent record of this paper and its review
CitationA. Bernardo, B. B. Martins, D. V. Rodrigues, G. R. C. Sampaio, J.E. Horvath, L. G. Bar\~ao, L. M. de S\'a, L S. Rocha, M. G. B. de Avellar, N. Pires, R. M. G. Takahashi. "The Galactic Black Hole mass distribution." arXiv:2609.14154 (2026). https://pith.science/paper/GYI3O6T3
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The paper

The paper claims

Power law best describes Galactic black hole masses; lower mass gap may be partially filled.

The reading

This paper analyzes the mass distribution of 42 Galactic black holes using a hierarchical Bayesian framework with five parametric models. The authors find that for the full sample, a power law with slope \$\alpha$ = -2.47 and mass range 4.68 to 34.25 solar masses is overwhelmingly preferred. For the 28 low-mass X-ray binary systems alone, a Gaussian with mean 7.74 solar masses fits best. The 1% quantile computed from each preferred model shows that the lower mass gap (2–5 solar masses) is not necessarily empty: the LMXB sample allows masses as low as 2.56 solar masses at 90% confidence. This challenges the traditional assumption of a completely empty gap and suggests a sparsely populated region instead.

What carries the argument

A hierarchical Bayesian framework that combines individual mass likelihoods (categorized by how well orbital parameters i and q are constrained) with five parametric population models: Gaussian, two-Gaussian, log-normal, power-law, and decaying exponential. The posterior is sampled via Hamiltonian Monte Carlo with NUTS, and model selection uses WAIC, LOO, AIC, and BIC with Akaike-style normalized weights. The central object is the mass distribution itself, inferred from the catalog CatNoir, which collates updated orbital parameters for all 42 systems.

Extended reading notes

Core claim

Using an updated sample of 42 Galactic black holes (28 LMXBs, 6 HMXBs, 7 detached binaries, 1 isolated) and a Bayesian model comparison, the authors establish that the power law is the best description of the full mass distribution, with parameters $m_{\min}=4.68^{+0.58}_{-0.65}\,M_\odot$, $m_{\max}=34.25^{+5.25}_{-2.26}\,M_\odot$, and $\alpha=-2.47^{+0.68}_{-0.82}$ (90% intervals). For the LMXB-only subset, a Gaussian with $\mu=7.74^{+0.71}_{-0.65}\,M_\odot$ and $\sigma=1.56^{+0.70}_{-0.49}\,M_\odot$ is preferred. The 1% quantile of the posterior predictive distribution is $M_{1\%}>2.56\,M_\odot$ (90% C.I.) for the LMXB sample, indicating that the lower mass gap is at most partially depleted rather than entirely empty.

Load-bearing premise

The observed sample of 42 Galactic black holes is assumed to be representative of the underlying population, even though strong selection effects favor X-ray binaries and microlensing events and almost entirely exclude isolated or dormant BHs; the Bayesian analysis does not include a selection function.

Editorial extensions

If this is right

  • If the power law is correct for the full Galactic BH population, the majority of stellar-mass BHs in the Galaxy have masses concentrated near the lower cutoff (~4.7 M_sun), with a steep decline toward higher masses.
  • The preferred Gaussian for LMXBs implies that the formation channel for these systems (likely via common-envelope evolution) produces a relatively narrow range of remnant masses around 7.7 M_sun.
  • The M_{1%} lower bound of 2.56 M_sun for LMXBs suggests that the traditional lower mass gap (2–5 M_sun) is not an absolute desert; future surveys may discover more objects in this region.
  • Comparison with GW-detected BH masses (which show a peak near ~35 M_sun) requires caution because Galactic selection effects are poorly modeled, but the two populations may originate from distinct formation channels.

Reading between the lines

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

  • The strong preference for a power law over an exponential decay in the full sample is driven by the inclusion of massive objects (Gaia BH3 at ~33 M_sun and IC 10 X-1 at ~29 M_sun), which an exponential tail cannot accommodate. This shift from the earlier exponential-based result (Farr et al. 2011) illustrates how adding a few high-mass outliers can change the inferred function form.
  • If the Bayesian analysis were extended to explicitly model selection effects (e.g., via a detection probability that depends on mass), the derived distribution parameters could shift significantly, especially the lower cutoff m_min, which currently is driven by the lightest observed objects.
  • The paper provides strong Bayesian evidence that the lower mass gap is not empty, but it does not identify the physical origin of the sparsely populated region. Combining these results with core-collapse simulations that predict low-mass BH formation (e.g., direct collapse of low-mass progenitors) could test whether the observed sample is consistent with stochastic supernova outcomes.
Original abstract

The population of extragalactic black holes has been significantly expanded and better understood since the first detection of gravitational waves. Over the past decade, approximately 290 events have been confirmed to involve at least one black hole. In contrast, the galactic black hole population has grown at a much slower pace, with only 42 systems possessing mass estimates, while the vast majority remain as candidates. In this work, we present the first update of a Bayesian analysis of the mass distribution of galactic black holes since 2011, previously based on a sample of 15 low-mass X-ray binaries and 5 high-mass X-ray binaries. Our update includes 28 low-mass X-ray binaries, 6 high-mass X-ray binaries, 7 detached binaries and 1 isolated black hole, also present in the living catalog \textit{CatNoir} which we introduce. We apply a Bayesian framework using five parametric models -- Gaussian, two-Gaussian, log-normal, power-law, and decaying exponential -- and compare their performance in fitting the observed data. Furthermore, we inspect the effect of removing model-dependent systems from the sample. Our results suggest that the power law better describes the Combined sample, while the Gaussian is preferred for the LMXB-only sample, closely followed by the two-Gaussian and log-normal. We derive the $1\%$-quantile of the preferred model's posterior predictive distribution to access information about the lower mass gap. For the Combined and LMXB Samples, we find $M_{1\%} > 4.06\,M_\odot$ and $M_{1\%} > 2.56\,M_\odot$ (at $90\%$ C.I.), respectively. The LMXB result allows for the existence of a sparsely populated Gap, instead of a completely empty one.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 8,426 input tokens.

What the abstract itself states, as probabilities: claims first 0.65 · states limitation 0.55 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.75 · mentions code or data availability 0.35.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The population of extragalactic black holes has been significantly expanded and better understood since the first detection of gravitational waves. Over the past decade, approximately 290 events have been confirmed to involve at least one black hole. In contrast, the galactic black hole population has grown at a much slower pace, with only 42 systems possessing mass estimates, while the vast majority remain as candidates. In this work, we present the first update of a Bayesian analysis of the mass distribution of galactic black holes since 2011, previously based on a sample of 15 low-mass X-ray binaries and 5 high-mass X-ray binaries. Our update includes 28 low-mass X-ray binaries, 6 high-mass X-ray binaries, 7 detached binaries and 1 isolated black hole, also present in the living catalog \textit{CatNoir} which we introduce. We apply a Bayesian framework using five parametric models -- Gaussian, two-Gaussian, log-normal, power-law, and decaying exponential -- and compare their performance in fitting the observed data. Furthermore, we inspect the effect of removing model-dependent systems from the sample. Our results suggest that the power law better describes the Combined sample, while the Gaussian is preferred for the LMXB-only sample, closely followed by the two-Gaussian and log-normal. We derive the $1\%$-quantile of the preferred model's posterior predictive distribution to access information about the lower mass gap. For the Combined and LMXB Samples, we find $M_{1\%} > 4.06\,M_\odot$ and $M_{1\%} > 2.56\,M_\odot$ (at $90\%$ C.I.), respectively. The LMXB result allows for the existence of a sparsely populated Gap, instead of a completely empty one.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The population of extragalactic black holes has been significantly expanded and better understood since the first detection of gravitational waves. background 1.00 0.04 0.02 asserted 1.00
s1 Over the past decade, approximately 290 events have been confirmed to involve at least one black hole. background 1.00 0.07 0.02 asserted 1.00
s2 In contrast, the galactic black hole population has grown at a much slower pace, with only 42 systems possessing mass estimates, while the vast majority remain as candidates. background 0.56 0.07 0.03 asserted 1.00
s3 In this work, we present the first update of a Bayesian analysis of the mass distribution of galactic black holes since 2011, previously based on a sample of 15 low-mass X-ray binaries and 5 high-mass X-ray binaries. contribution 0.99 0.78 0.04 asserted 1.00
s4 Our update includes 28 low-mass X-ray binaries, 6 high-mass X-ray binaries, 7 detached binaries and 1 isolated black hole, also present in the living catalog \textit{CatNoir} which we introduce. contribution 0.61 0.78 0.03 asserted 1.00
s5 We apply a Bayesian framework using five parametric models -- Gaussian, two-Gaussian, log-normal, power-law, and decaying exponential -- and compare their performance in fitting the observed data. method 0.99 0.95 0.03 asserted 0.97
s6 Furthermore, we inspect the effect of removing model-dependent systems from the sample. method 0.90 0.92 0.02 asserted 0.56
s7 Our results suggest that the power law better describes the Combined sample, while the Gaussian is preferred for the LMXB-only sample, closely followed by the two-Gaussian and log-normal. result 0.99 0.96 0.61 hedged possibility 0.98
s8 We derive the $1\%$-quantile of the preferred model's posterior predictive distribution to access information about the lower mass gap. method 0.95 0.96 0.06 asserted 0.89
s9 For the Combined and LMXB Samples, we find $M_{1\%} > 4.06\,M_\odot$ and $M_{1\%} > 2.56\,M_\odot$ (at $90\%$ C.I.), respectively. result 1.00 0.98 0.30 asserted 1.00
s10 The LMXB result allows for the existence of a sparsely populated Gap, instead of a completely empty one. interpretation 0.99 0.92 0.21 hedged possibility 0.70

What kind of paper the classifier reports this is: empirical study 0.72 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. 1000 posterior samples (grey lines) drawn from the best-model posterior for the Combined sample (power law, left) and the LMXB-only sample (Gaussian, right). The red curve shows the MAP distribution in each case. sample we generate 1000 draws from the posterior of the preferred model, compute the 1% quantile of each draw, and build the resulting M1% distribution. For the Com￾bined sample we use the power-law posterior, which is the overwhelmingly preferred model (Section 4.3). For the LMXB sample, we use the Gaussian posterior, since the power law is excluded from that comparison on…
Figure 2. Distribution of the 1% quantile (M1%) built from 1000 posterior draws of the preferred model for each sample, shown in
Figure 5. Left: For each individual BH, 50000 masses are sampled from the skewed-Gaussian (given at Eq. (B1)), and combined into the histogram plotted above, so uncertainties are taken into account. The parameters values of each skewed-Gaussian are informed at
Figure 6. Resulting fits using a Skewed Gaussian as described in eq. (B1). The histogram bins are represented by the black bars. A total of 1000 bins were considered, indicating the probable BH mass, while its height shows its Probability Density Function (PDF). The red line shows the resulting fit
Figure 7. Marginalized distributions of µ (left graph) and σ (right graph) for the Gaussian distribution for the Combined Sample
Figure 8. Marginalized distributions of r (left graph), µ1,2 (middle graph, in which the lighter graph indicated the µ1 distribution while the darker one, µ2) and σ1,2 (right graph, in which the lighter graph indicated the σ1 distribution while the darker one, σ2) for the Two Gaussian distribution for the Combined Sample
Figure 9. Marginalized distributions of the average BH mass ⟨MBH⟩ (left graph) and the uncertainty of the BH mass σMBH (right graph) for the Log Normal distribution for the Combined Sample
Figure 10. Marginalized distributions of α (left graph), mmin (middle graph) and mmax (right graph) for the Power Law distribution for the Combined Sample
Figure 11. Marginalized distributions of mmin (left graph) and m0 (right graph) for the Decaying Exponential distribution for the Combined Sample
Figure 12. Marginalized distributions of µ (left graph) and σ (right graph) for the Gaussian distribution for the LMXB Sample
Figure 13. Marginalized distributions of r (left graph), µ1,2 (middle graph, in which the lighter graph indicated the µ1 distribution while the darker one, µ2) and σ1,2 (right graph, in which the lighter graph indicated the σ1 distribution while the darker one, σ2) for the Two Gaussian distribution for the LMXB Sample
Figure 14. Marginalized distributions of the average BH mass ⟨MBH⟩ (left graph) and the uncertainty of the BH mass σMBH (right graph) for the Log Normal distribution for the LMXB Sample
Figure 15. Marginalized distributions of α (left graph), mmin (middle graph) and mmax (right graph) for the Power Law distribution for the LMXB Sample
Figure 16. Marginalized distributions of mmin (left graph) and m0 (right graph) for the Decaying Exponential distribution for the LMXB Sample
Figure 17. Left: Predictive posterior distribution obtained from the power-law model in the Refined sample case. Grey lines represent 1000 posterior samples. The red curve shows the MAP distribution. Right: Distribution of the 1% quantile built from the predictive posterior distribution

Showing 15 of the paper's 17 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2609.14154 by the authors.

References

Discussion

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