REVIEW
The Mass Distribution of Stellar Black Holes
Astrophysics · Submitted 4 Aug 1997 · 23 references
Pith's verdict: The 7 Msun cluster is a real empirical result worth citing; the 'gap' to neutron stars is a posterior on the lower edge of an assumed uniform distribution, not a statement about nature.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
Six of seven measured stellar black holes may sit at nearly the same mass, about seven suns, with V404 Cyg the odd one out.
The reading
What carries the argument
The engine is a Bayesian model-comparison calculation over a grid in the $(m_l, m_u)$ plane. For each candidate uniform parent distribution, the likelihood of each observed mass function is obtained by integrating over the true mass function, the mass ratio $q$ (taken Gaussian around the tabulated value), and the inclination $i$ (taken with $P(∝) sin i$ between the tabulated limits), using $m_1 = f(m)(1+q)^2/ sin^3 i$. Multiplying the per-source likelihoods gives the global likelihood of the model, and the ratio of global likelihoods between models — with and without a given source — is the odds ratio used to argue that V404 Cyg belongs to a different population.
Extended reading notes
Core claim
The authors compile the seven low-mass X-ray transients with measured mass functions and no X-ray bursts, and for each one combine the mass function with the measured mass ratio and the allowed inclination range to get a range of possible primary masses. Because those ranges are strongly non-Gaussian, they do not average them; instead they assume the parent black hole masses are uniform between a lower limit $m_l$ and an upper limit $m_u$, and compute the Bayesian probability of each $(m_l, m_u)$ pair given the data. With all seven sources the 95% contour spans roughly $11$–$17 M_☉$ in $m_u$ and $m_l ≤ 7 M_☉$. Removing V404 Cyg raises the global likelihood of the model by a factor of about 134 and pulls the best-fit limits together to $m_l = 6.91 M_☉$ and $m_u = 6.97 M_☉$, so that a single mass near $7 M_☉$ becomes a plausible description of the remaining six. The same fit gives a 95% probability that $m_l > 3 M_☉$, which the authors read as a real gap between the black hole population and the neutron star population.
Load-bearing premise
The whole result rests on assuming the parent black hole masses are spread uniformly between a lower and an upper cutoff, so that the two fitted endpoints can be read as a cluster near seven solar masses and as a gap above the neutron stars.
Editorial extensions
If this is right
- If six transient black hole binaries share a mass near $7 M_☉$, then the remnant mass is set by something other than a smooth monotonic function of progenitor mass, such as a threshold or step in the amount of fallback material.
- The claimed gap between the black hole lower limit and the $1.7 M_☉$ neutron star ceiling would mean the compact objects of this Galaxy fall into two separated mass groups rather than a continuum.
- V404 Cyg's anomalously high mass, together with its longer orbit and more evolved secondary, would point to post-supernova mass transfer as a way of adding to a black hole's mass.
- Because the authors argue that selection effects do not suppress the detection of low-mass black hole transients, the absence of systems in the gap becomes a statement about astrophysics rather than about survey sensitivity.
Reading between the lines
- The conclusion is stated in terms of the endpoints of a uniform box, so the natural next test is to refit the same seven systems with a Gaussian, a power law, or a two-component parent distribution and compare global likelihoods; a unimodal narrow distribution and a truncated broad one can fit equally well with only seven points.
- The sharpest empirical lever is not a new source but a better inclination for A0620-00, whose tabulated range $31°$–$70.5°$ alone spans a factor of several in inferred mass and dominates the low-mass tail of the fit.
- If the mass gap is real, it should also appear in black holes detected by gravitational-wave mergers, where masses are measured without any of the binary-evolution selection that governs X-ray transients; a merger population filling the $2$–$5 M_☉$ range would argue against a universal gap.
- A step-function fallback threshold would leave a chemical signature, since the material that recollapses is material that never returns to the interstellar medium; comparing the inferred threshold mass against chemical-evolution yields of massive stars is a way to test the proposed mechanism independently.
Original abstract
We examine the distribution of masses of black holes in transient low mass X-ray binary systems. A Bayesian analysis suggests that it is probable that six of the seven systems with measured mass functions have black hole masses clustered near seven solar masses. There appears to be a significant gap between the masses of these systems and those of the observed neutron stars. The remaining source, V404 Cyg, has a mass significantly larger than the others, and our analysis suggests that it is probably drawn from a different distribution. Selection effects do not appear to play a role in producing the observed mass distribution, which may be explained by currently unknown details of the supernova explosions and of binary evolution prior to the supernova.
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.
The abstract, sentence by sentence
We examine the distribution of masses of black holes in transient low mass X-ray binary systems. A Bayesian analysis suggests that it is probable that six of the seven systems with measured mass functions have black hole masses clustered near seven solar masses. There appears to be a significant gap between the masses of these systems and those of the observed neutron stars. The remaining source, V404 Cyg, has a mass significantly larger than the others, and our analysis suggests that it is probably drawn from a different distribution. Selection effects do not appear to play a role in producing the observed mass distribution, which may be explained by currently unknown details of the supernova explosions and of binary evolution prior to the supernova.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We examine the distribution of masses of black holes in transient low mass X-ray binary systems. | contribution 0.96 | 0.87 | 0.03 | asserted 0.78 |
| s1 | A Bayesian analysis suggests that it is probable that six of the seven systems with measured mass functions have black hole masses clustered near seven solar masses. | result 1.00 | 0.90 | 0.59 | hedged possibility 1.00 |
| s2 | There appears to be a significant gap between the masses of these systems and those of the observed neutron stars. | result 0.98 | 0.72 | 0.27 | hedged possibility 0.77 |
| s3 | The remaining source, V404 Cyg, has a mass significantly larger than the others, and our analysis suggests that it is probably drawn from a different distribution. | result 0.96 | 0.90 | 0.13 | hedged possibility 0.90 |
| s4 | Selection effects do not appear to play a role in producing the observed mass distribution, which may be explained by currently unknown details of the supernova explosions and of binary evolution prior to the supernova. | interpretation 0.97 | 0.79 | 0.33 | hedged possibility 0.86 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:astro-ph/9708032 by the authors.
References
How the literature uses it
40 arXiv papers cite this in 47 sentences
Papers citing it · 36 sentences without a confident label
Contests it 1 paper
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[ref] The detection of GW190814 seems to invalidate this hypothesis: with a mass $m_2 = 2.59^+0.08_-0.09 M_⊙$, the secondary object in the GW190814 binary falls right in this lower gap, meaning that this object was either the heaviest neutron star or the lightest black hole ever observed.
Recent LIGO-Virgo discoveries · GW190814 · contest 0.80
Uses its data or values 3 papers
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The ABH mass ranges from $∼5 M_⊙$ to a few tens of solar masses [ref] .
Stochastic Gravitational Wave Background from PBH-ABH Mergers · ABH distribution · 0.88
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For our numerical analysis, we assume that ABH mass have ranges from $5M_⊙$ to a few tens of solar masses [ref] .
Probing the Origin of Primordial Black Holes through Novel Gravitational Wave Spectrum · PBH-ABH Binary Systems · 0.93
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The mass distribution of stellar–mass black holes is not well-determined observationally, but estimates are that it is fairly broad, with a mean of around $∼7M_⊙$ [ref] .
Stellar Black Holes and the Origin of Cosmic Acceleration · Cosmic History of Black Holes and Cosmic Acceleration · 0.85
Compares with it 1 paper
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Our candidate event list includes compact binary mergers that have higher total masses than those in GWTC-1 [ref] as well as mergers with component masses in the purported lower mass gap of $∼2.5$–$5$ [ref] .
GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run · Masses of sources with $m_2>3$ · 0.88
Cites it as background 6 papers
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The existence of a “lower mass gap” in the mass distribution of compact objects, spanning approximately $3$ to $5$, has been proposed since the late 1990s [ref] .
GW230529_181500: A Potential Primordial Binary Black Hole Merger in the Mass Gap · Introduction · 0.99
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The existence or absence of compact objects with masses between $3 M_⊙$ and $5 M_⊙$ (“lower mass gap”) separating BHs and NSs has been long investigated using X-ray binary data [ref] and is now under active scrutiny after some of the most recent LIGO/Virgo events, notably GW190814 [ref] .
Modeling the outcome of supernova explosions in binary population synthesis using the stellar compactness · Introduction · 0.86
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As a consequence, one falsifiable prediction that follows from the interpretation of GW190814 as a PBH binary is the generation of events filling the lower mass gap potentially existing in the ABH sector between the heaviest allowed NS mass (see e.g. Ref. [ref] for a review) and the lightest BH observed [ref] (see also [ref] ).
From inflation to black hole mergers and back again: Gravitational-wave data-driven constraints on inflationary scenarios with a first-principle model of primordial black holes across the QCD epoch · Single-population inference · 0.82
Discussion
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