A Fundamental Relation Between Supermassive Black Holes and Their Host Galaxies

Laura Ferrarese (UCLA) & David Merritt (Rutgers University)

REVIEW

A Fundamental Relation Between Supermassive Black Holes and Their Host Galaxies

Laura Ferrarese (UCLA) & David Merritt (Rutgers University)

Astrophysics · Submitted 4 Jun 2000 · 2 references

Pith's verdict: The M–σ paper: the slope of 4.8 is the durable part, and the 'negligible intrinsic scatter' claim is the part that does not survive scrutiny.

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arXiv IDastro-ph/0006053 (version 2)

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CitationLaura Ferrarese (UCLA) & David Merritt (Rutgers University). "A Fundamental Relation Between Supermassive Black Holes and Their Host Galaxies." arXiv:astro-ph/0006053 (2000). https://pith.science/paper/6M3PP4YV

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Editor's note

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You already know how this one turned out — it is the origin of M–σ, and the slope has held up in every larger sample since. What is genuinely new relative to Magorrian et al. is threefold: a homogeneous SBF distance scale, dispersions put on a common aperture system (r_e/8, Jorgensen et al.), and a bivariate regression that carries errors in both variables. That is careful work. The best thing in the paper is the v_rms cross-check in §3: substituting the rms velocity at r_e/4 for σ_c and recovering the same slope is a real argument that the correlation is not just the black hole's own gravity contaminating the central dispersion. The Magorrian offset argument is also solid — five of 36 best-fit masses negative, a quarter consistent with M < 0, discrepancy growing with distance. Checkable, and it was right. The authors' own caution against extrapolating below ~10^5 M_sun is well placed and worth keeping in mind when people quote Eq. (1) for dwarfs and clusters. Where I would push back is the tightness claim, not the slope. [abstract:s1] says the scatter is no larger than measurement error alone, and §3 backs that with χ²_r = 0.8. That number is doing more work than it can bear. The authors state outright that they made no attempt to homogenize the mass errors; Sample A mixes maser kinematics, stellar proper motions, HST gas-disk rotation and HST absorption-line kinematics, each with different systematics. A χ² assembled from non-comparable error bars is not a calibrated goodness-of-fit, and with 10 degrees of freedom χ² = 8 bounds intrinsic scatter from above without making it small. On selection, the reader is right that Sample A is cut on resolved r_inf ∝ M•/σ², but the stress-test has the direction right: that cut removes points below the line at low σ, which flattens the recovered slope. So 4.8 is if anything conservative, and the selection damages the tightness claim rather than the slope. One correction to the reader: the sentence in §3 that the real uncertainties are often much larger is scoped to the Magorrian-type ground-based masses, not to Sample A, so it cannot be used to discount the Sample A χ². Minor point: the 30% prediction-accuracy line leans on Fig. 1b harder than 12 points justify. Read it if you work on black hole demographics or AGN feedback — it is the empirical target those models are built to hit. Send it to referees.

Referee report

Significance

If it holds, this is a landmark empirical result: a one-parameter relation connecting black hole mass to a global property of the host bulge, with immediate consequences for black hole demographics, for the interpretation of quasar evolution, and for models in which feedback regulates both bulge and black hole growth. The analysis has real methodological strengths that should be named: the use of a bivariate regression (Akritas & Bershady 1996) that accommodates errors in both variables and intrinsic scatter, an explicit and quantified aperture correction to r_e/8, a robustness check on the low-σ end, and a physically motivated cross-check using v_rms at r_e/4 that addresses whether the correlation is driven by the black hole's own gravitational influence on the nucleus. The paper also makes a falsifiable prediction, that M• can be recovered from a single dispersion measurement, which is exactly the kind of claim that can be tested by later data. The authors are candid about several limitations (non-homogenized mass errors, the resolution-based sample definition, the poorly constrained inclinations entering v_rms), and my comments below build on those acknowledged points ratherthan

Major objections (3)

[§3 and abstract [abstract:s1]] The headline claim that the scatter is 'no larger than expected on the basis of measurement error alone' rests on χ²_r = 0.8, but §3 states plainly that the mass errors were not homogenized and are 'those quoted by the respective authors.' Sample A mixes water-maser kinematics, stellar proper motions, HST gas/dust-disk rotation, and HST stellar absorption-line kinematics, each with different systematics and different error conventions. A χ² assembled from non-comparable error bars is not a calibrated goodness-of-fit: χ²_r = 0.8 can reflect over-conservative errors in a few entries as easily as small intrinsic scatter, and with roughly 10 degrees of freedom χ² = 8 bounds intrinsic scatter from above without establishing that it is small. The word 'negligible' is therefore not supported by the quoted statistic. I recommend estimating the intrinsic scatter directly within the Akritas–Bershady framework (or an equivalent maximum-likelihood/Bayesian treatment) and reporting it with a confidence interval, and softening 'almost perfectly' and 'no larger than expected' in the abstract to match whatever that estimate yields.
[§1–§2, Sample A definition] Sample A is defined in §1 as galaxies 'in which the observations have resolved the sphere of gravitational influence of the BH,' i.e. r_inf = GM•/σ² above the resolution limit. That selection is correlated with the ordinate M• at fixed σ and truncates the (σ, M•) plane along a line of slope 2, which is shallower than the fitted slope of 4.8; it can therefore bias both the recovered slope and, more importantly for the paper's distinguishing claim, the inferred scatter. The existing robustness check (excluding the Milky Way and M32) tests only the low-σ end and does not address a selection boundary that depends jointly on M• and σ. I recommend a direct test: show that the residuals of the fit do not correlate with r_inf or with the resolution limit, or restrict the fit to a σ range in which the selection is inoperative, and report whether the slope and scatter survive. This is a correctness-risk concern about the tightness claim, not about the existence of the relation.
[§3, 'M• can be predicted with an accuracy of ~30% or better'] This sentence conflates the internal rms scatter of a 12-point fit with a predictive accuracy for arbitrary galaxies. The slope uncertainty (±0.54) and intercept uncertainty (±1.3) alone propagate to a systematic error that grows toward the ends of the σ range, and the selection effect discussed above is unquantified. The statement should be recast as the internal scatter of Sample A about Eq. (1), with the systematic caveats stated, rather than as a general predictive accuracy. As written it invites over-interpretation by readers who will apply Eq. (1) outside the fitted range, which the paper itself warns against in §4 for dwarf ellipticals and globular clusters.

Minor objections (8)

[Abstract] 'Almost perfectly' is stronger than a 12-point fit with heterogeneous errors can support; 'tightly' would be more defensible and would survive whatever intrinsic-scatter estimate the revision produces.
[Table 1] Table 1 carries the entire evidential weight of the paper, but in the version supplied it is not legible, so I could not verify the individual M•, σ, distance, and magnitude entries. The published version should render the table legibly and, ideally, make it machine-readable, since the fit cannot be independently checked without it.
[§2, aperture corrections] The text states that the r_e/8 corrections rarely exceed 5% and are accurate to 1%, and that correcting does not bias slope or intercept. Please state how many galaxies actually required a correction larger than 1% and show the fit parameters with and without the correction, so the claim can be checked rather than asserted.
[§3 and Figure 2, v_rms] The v_rms comparison requires the inclination angle, which the text says is available for only NGC 3115 and NGC 4342. The claim that the σ_c and v_rms slopes coincide should be qualified accordingly, since unknown sin i for the remaining galaxies will both scatter and bias the v_rms fit low, as the authors themselves note.
[Eq. (1)] Please state the units and the precise definition of σ_c (aperture-corrected central dispersion) in the equation or its caption, and give the rms scatter about the fit explicitly alongside the slope and intercept.
[§4, M ∝ σ^5 argument] The chain L ∝ σ^4 (Faber–Jackson) and M ∝ L^{5/4} giving M ∝ σ^5 uses scaling relations that carry their own scatter; the text should say explicitly that this is an order-of-magnitude consistency argument, not a derivation, so that the agreement with the Silk–Rees σ^5 scaling is not over-read.
[§3, Magorrian comparison] The argument that the Magorrian et al. masses are systematically high is supported by the negative best-fit masses in 5 of 36 galaxies and the 8 of 36 consistent with M• < 0, which is persuasive. The additional point that the discrepancy grows with distance is consistent with a resolution/systematics explanation and supports the authors' case, but the text should state that this is an inference from the pattern rather than a direct measurement.
[References] Merritt & Ferrarese (2000) is cited as 'in press' and is said to contain the Sample B data; the editor may wish to confirm that it is available to readers, since the Sample B comparison in §3 depends on it.

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The paper

The paper claims

Black hole mass tracks the random motions of bulge stars, not the bulge's brightness, and the fit is tight enough that one low-resolution spectrum predicts the mass.

The reading

The paper asks what property of a galaxy actually sets the mass of its central black hole. Using twelve galaxies whose black hole masses are measured directly — the Milky Way's own centre, the water-maser disk in NGC 4258, and ten galaxies resolved with the Hubble Space Telescope — the authors fit black hole mass against the central velocity dispersion $sigma_c$ of the host bulge and find $M_*{BH} propto sigma_c^{4.8 pm 0.5}$, a relation far tighter than the older correlation with bulge blue luminosity. The scatter about that line is no larger than the quoted measurement errors allow, which is the part that carries weight: it says there is little room left for any second variable hiding in the data. If the relation is real, a single modest-resolution measurement of a galaxy's stellar velocity dispersion gives its black hole mass to roughly thirty percent, and the growth of the black hole is tied to the depth of the potential well it sits in rather than to how many stars the bulge contains.

What carries the argument

The machinery is a bivariate linear regression that allows for intrinsic scatter as well as errors in both variables (Akritas & Bershady 1996), applied with black hole mass as the dependent variable and either bulge absolute magnitude $B^0_T$ or aperture-corrected central velocity dispersion $sigma_c$ as the independent one. The aperture correction, which brings every dispersion to the equivalent of a radius $r_e/8$ following Jorgensen, Franx & Kjaergaard (1995), is small, rarely above five percent, and the authors check that it changes neither slope nor intercept. The comparison between the two independent variables is what makes the argument: the same sample, the same fitting method, two different galaxy properties, and only one of them produces a residual scatter that the error bars can account for.

Extended reading notes

Core claim

The central claim is Eq. (1): $log M_*{BH} = 4.80(pm 0.54),log sigma_c - 2.9(pm 1.3)$, with $M_*{BH}$ in solar masses and $sigma_c$ in km/s, fitted to the twelve galaxies of Sample A. The reduced chi-squared of that fit is 0.8, i.e. the spread about the line is consistent with the stated measurement errors alone, whereas the same galaxies scatter far more widely about the $M_*{BH}$–luminosity plane. The authors argue the correlation is not an artifact of the black hole perturbing the stars whose motions are being measured: substituting the rms velocity $v_*{rms}$ at a quarter of the effective radius, well outside the black hole's gravitational reach, leaves the slope unchanged. They also report that the Magorrian et al. (1998) masses, derived from ground-based stellar kinematics, sit systematically above the Sample A line, some by two orders of magnitude, and they read that offset as evidence that those mass estimates are upper limits rather than detections.

Load-bearing premise

The twelve galaxies were chosen because the observations resolved the black hole's sphere of influence, and that radius grows with black hole mass, so the sample is not independent of the quantity being predicted.

Editorial extensions

If this is right

Black hole masses can be estimated for large galaxy samples from existing stellar velocity dispersion measurements, without spatially resolved kinematics, opening population studies that were previously limited to a dozen objects.
If the slope is near five, then combining the Faber–Jackson relation $L propto sigma^4$ with the early-type mass-to-light scaling $M propto L^{5/4}$ gives $M_*{BH}$ roughly proportional to bulge mass, i.e. a roughly universal baryon-to-black-hole conversion fraction.
The same $sigma^5$ scaling follows from models in which quasar outflows halt accretion once the outflow energy matches the bulge binding energy, so the observed slope is a natural test of that feedback picture.
Correlation studies built on the Magorrian et al. (1998) masses, such as Merriefield, Forbes & Terlevich (2000), should be re-examined, since those masses appear to be biased high for distant galaxies.
The relation should not be extrapolated to black holes below roughly $10^5$ solar masses, where the formation channel may differ.

Reading between the lines

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

The sample was assembled from galaxies in which the black hole's sphere of influence was spatially resolved, and that radius scales as $G M_*{BH}/sigma^2$; a sample selected that way preferentially keeps large black holes at a given dispersion, so an independent test using galaxies selected purely by distance or by observability, with no reference to black hole mass, would be the cleanest check on
Because the relation predicts mass from a quantity measurable in a single low-resolution spectrum, it converts every nearby early-type galaxy with a published dispersion into a black hole mass estimate, which is the practical reason the result propagated so widely.
The systematic upward offset of the ground-based stellar-kinematic masses is itself a claim about measurement, not about black holes: if it is right, the same bias should appear in any other mass estimator whose resolution element is larger than the sphere of influence, and that is checkable galaxy by galaxy.

Original abstract

The masses of supermassive black holes correlate almost perfectly with the velocity dispersions of their host bulges, M(BH) ~ sigma^alpha, where alpha =4.8 +/- 0.5$. The relation is much tighter than the relation between M(BH) and bulge luminosity, with a scatter no larger than expected on the basis of measurement error alone. Black hole masses estimated by Magorrian et al. (1998) lie systematically above the M(BH)-sigma relation defined by more accurate mass estimates, some by as much as two orders of magnitude. The tightness of the M(BH)-sigma relation implies a strong link between black hole formation and the properties of the stellar bulge.

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, 3,695 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The masses of supermassive black holes correlate almost perfectly with the velocity dispersions of their host bulges, M(BH) ~ sigma^alpha, where alpha =4.8 +/- 0.5$. The relation is much tighter than the relation between M(BH) and bulge luminosity, with a scatter no larger than expected on the basis of measurement error alone. Black hole masses estimated by Magorrian et al. (1998) lie systematically above the M(BH)-sigma relation defined by more accurate mass estimates, some by as much as two orders of magnitude. The tightness of the M(BH)-sigma relation implies a strong link between black hole formation and the properties of the stellar bulge.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The masses of supermassive black holes correlate almost perfectly with the velocity dispersions of their host bulges, M(BH) ~ sigma^alpha, where alpha =4.8 +/- 0.5$.	result 1.00	0.67	0.68	asserted 1.00
s1	The relation is much tighter than the relation between M(BH) and bulge luminosity, with a scatter no larger than expected on the basis of measurement error alone.	result 1.00	0.75	0.16	asserted 1.00
s2	Black hole masses estimated by Magorrian et al. (1998) lie systematically above the M(BH)-sigma relation defined by more accurate mass estimates, some by as much as two orders of magnitude.	result 0.91	0.39	0.07	asserted 1.00
s3	The tightness of the M(BH)-sigma relation implies a strong link between black hole formation and the properties of the stellar bulge.	interpretation 1.00	0.54	0.59	asserted 0.76

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from analysis of existing data 0.75.

What was examined, and what was not

sources read

arXiv listing abstract v2

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

References

Works cited (2)

[1]

Akritas, M. G. & Bershady, M. A. 1996, ApJ, 470, 706 Bower, G.A., et al. 1998, ApJL, 492, L111 (B98) Cardelli, J. A., Clayton, G. C. & Mathis, J. S. 1989, ApJ, 345, 245 Cretton, N., & van den Bosch, F.C. 1999, ApJ, 514, 704 (CB99) Davies, M. et al. 1987, ApJ, 64, 581 de Vaucouleurs, G. & Pence, W. D. 1978, AJ, 83, 1163 de Vaucouleurs, G., de Vaucouleurs, ...

View on Pith 1996
[221]

Merritt, D., & Ferrarese, L. 2000, ApJL, in press Miyoshi, M. et al. 1995, Nature, 373, 127 (M95) Mould, J. R. et al. 2000, ApJ, 529, 786 Newman, J.A., et al. 1997, ApJ, 485, 570 (N97) Schlegel, D. J., Finkbeiner, D. P. & Davis, M. 1998, ApJ, 500,525 Scorza, C., & van den Bosch, F. C. 1998, MNRAS, 300, 469 Silk, J. & Rees, M. J. 1998, A& A, 331, L4 Simien...

View on Pith 2000

Forward citations

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AT2021yky: A Fast-Rising Optical Transient with Evolving Broad Hydrogen Emission Consistent with an Ambiguous Nuclear Transient
astro-ph.HE 2026-08 accept novelty 5.0 of 10

AT2021yky is a fast-rising, cool nuclear flare with only broad H-alpha emission, best classified as an ambiguous nuclear transient rather than a typical TDE, AGN flare, supernova, or LFBOT.
XMM-Newton and Swift Unveil Another X-Ray Transient in NGC 4945, XMM J130514.64-493311.27
astro-ph.HE 2026-07 accept novelty 5.0 of 10

A previously undetected X-ray transient, XMM J130514.64-493311.27, was discovered in NGC 4945 with properties consistent with an X-ray binary caught in outburst.
Bolometric correction factor and radiative efficiency for the super-Eddington accretion flow in tidal disruption events
astro-ph.HE 2026-07 unverdicted novelty 5.0 of 10

Radiation hydro simulations produce black hole mass and viewing angle dependent bolometric correction factors (tens to thousands) and radiative efficiencies (0.001-0.1) for super-Eddington TDE flows that alleviate the...
The Impact of Non-Gaussian Line Spread Functions on Stellar Kinematic Recovery: Consequences for Dynamical Models
astro-ph.GA 2026-06 unverdicted novelty 5.0 of 10

Non-Gaussian LSF shapes bias kinematic extraction from spectra; matching the LSF of templates to the target reduces dispersion bias below 1%.
When Jets Don't Quench: Near-Infrared H$_{2}$ in Star Forming Low-Excitation Radio Galaxies
astro-ph.GA 2026-06 unverdicted novelty 5.0 of 10

New Gemini/GNIRS observations of star-forming radio galaxies show warm H2 emission driven primarily by mergers rather than jets.
Dust destruction signals shock-accelerated outflows in the nearby active galaxy NGC 1068
astro-ph.GA 2026-06 unverdicted novelty 5.0 of 10

Line ratio diagnostics in NGC 1068 indicate that AGN outflows are accelerated by shocks that destroy dust and compress gas.
Insights from Analytical Theory of Eccentric Circumbinary Disks II. Forced Modes and Resonance for Precessing Binaries
astro-ph.GA 2026-05 unverdicted novelty 5.0 of 10

Semi-analytical theory derives radial scalings for forced disk eccentricity (E ~ r^{-1} or r^{-2}) and resonance criteria for precessing binaries, plus a conjecture that cavity size tunes the ground eccentric mode to ...
Co-evolution of Supermassive Black Holes and their Host L* galaxies: implications for Milky Way and M31
astro-ph.GA 2026-05 unverdicted novelty 5.0 of 10

ARTEMIS and EAGLE simulations classify L* galaxies by central BH-to-stellar-mass ratio and trace how merger history drives divergence in BH growth, star formation, and morphology, offering an explanation for the obser...
Constraints on the extreme mass-ratio inspiral population from LISA data
gr-qc 2025-08 unverdicted novelty 5.0 of 10

A neural-network-accelerated hierarchical Bayesian pipeline is developed and validated on a phenomenological model to constrain EMRI population parameters from LISA data.
Confirming HSC strong lens candidates with DESI Spectroscopy. I. Project overview and first results
astro-ph.GA 2025-05 conditional novelty 5.0 of 10

Serendipitous DESI DR1 spectra confirm 27 HSC strong-lens systems and add 76 candidates with lensing galaxies at z>0.8.
Science with the space-based interferometer eLISA. I: Supermassive black hole binaries
gr-qc 2015-11 conditional novelty 5.0 of 10

Across 24 eLISA design variants and three black hole population models, only six-link configurations with the better low-frequency noise retain the high-redshift detections and sky localizations needed for multi-messe...
Direct measures of black hole masses through cosmic time
astro-ph.IM 2026-10 conditional novelty 4.0 of 10

Simulations show that a future ALMA2040 facility could measure black hole masses via cold gas kinematics from the local universe to redshift 7.
Investigating the Spectral Properties of Dual Nuclei in Galaxy Mergers from the GOTHIC survey: Supermassive Black Hole Growth, metal enrichment and Dual AGN
astro-ph.GA 2026-06 unverdicted novelty 4.0 of 10

Spectroscopic analysis of dual nuclei shows SMBH masses higher in galaxy mergers than single nuclei at fixed stellar mass.
Ultralight Bosonic Field Mass Bounds from Astrophysical Black Hole Spin
hep-ph 2020-09 conditional novelty 4.0 of 10

Applying published superradiance rates to an ensemble of black hole mass and spin measurements excludes ultralight bosons of spin 0, 1, and 2 over several mass windows between roughly 10^-22 and 10^-11 eV.
The Next Generation Global Gravitational Wave Observatory: The Science Book
gr-qc 2021-11 accept novelty 3.0 of 10

A community roadmap arguing that a network of 3G gravitational-wave detectors would detect hundreds of thousands of compact-binary mergers per year and enable decisive measurements of dense matter, black-hole populati...
The origins of massive black holes
astro-ph.GA 2021-10 accept novelty 3.0 of 10

No new result: the authors synthesize the proposed formation channels for massive black hole seeds and the electromagnetic and gravitational wave observations that could discriminate among them.
Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures
astro-ph.HE 2021-05 accept novelty 3.0 of 10

Hierarchical black hole mergers should leave a distinctive high-mass, high-spin signature, and GW190521 is the best current candidate, though population-level evidence remains inconclusive.
Toward the Italian Astronomical Community's Contribution to HWO: Science, Technology, and Instrument Concepts
astro-ph.IM 2026-09 unverdicted novelty 2.0 of 10

The Italian astronomical community has compiled its science cases, technology expertise, and five instrument concepts into a mission-planning manifesto for the Habitable Worlds Observatory.
Exploring the physics of ram pressure stripping with radio continuum observations in the SKA era
astro-ph.GA 2026-06 unverdicted novelty 2.0 of 10

Perspective on using SKA-Low and SKA-Mid radio continuum to extend ram pressure stripping studies to southern clusters and z~0.5.
Unification models of Active Galactic Nuclei
astro-ph.GA 2026-06 unverdicted novelty 2.0 of 10

Overview chapter summarizing traditional orientation-based and radiation-regulated unification models for AGN, including evolutionary aspects and changing-look AGN.
Waveform Modelling for the Laser Interferometer Space Antenna
gr-qc 2023-11 unverdicted novelty 2.0 of 10

A review of existing waveform models for LISA sources and the challenges that must still be overcome.
The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy
astro-ph.HE 2019-03 conditional novelty 2.0 of 10

Extreme mass-ratio inspirals will let LISA measure black hole masses, spins, distances and spacetime multipoles with percent-to-parts-per-million precision, provided waveform models reach second-order self-force accuracy.
A brief overview of the baryon cycle in galaxies
astro-ph.GA 2026-11 unverdicted

A concise review of the baryon cycle in galaxies, summarizing gas accretion, star formation, stellar feedback, AGN feeding and feedback, and outstanding open questions.

How later papers used it

681 later papers cite it

Evidence: substantial. 677 of the citing papers share no author with it, and 38 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 767 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

4 later papers by other authors are listed below: 3 used its method or tool and 1 used its data or values.

Uses its method or tool 3 of 15 papers with this label

Estimated the black hole mass using this paper's scaling law with the observed stellar velocity dispersion of 70±10 km/s.

A (likely) X-ray jet from NGC6217 observed by XMM-Newton (2017) · 0.98 · paraphrased: the licence does not allow quoting
Used the empirical correlation between black hole mass and host galaxy stellar velocity dispersion from this paper to estimate the black hole mass for the AGN in 3C 223.

The Complex X-ray Obscuration Environment in the Radio Loud Type 2 Quasar 3C 223 (2023) · 0.88 · paraphrased: the licence does not allow quoting
The SMBH mass is $3.3×10^7 M_⊙$, $2.3×10^7 M_⊙$ and $3.9×10^7 M_⊙$ based on the empirical relations $M_BH-σ_*$ in [ref] , [ref] and [ref] respectively.

A Composite Broad-Line Region in SDSS J1609+4902: a Double-Peaked Disk component and a Gaussian Component (2025) · Spectrum Decomposition · 0.87

Uses its data or values 1 of 9 papers with this label

Fit the normalization A to the observational data of this paper for each alpha varied between 3.5 and 5.

AGN feedback in dwarf galaxies? (2017) · 0.81 · paraphrased: the licence does not allow quoting

How the literature uses it

107 arXiv papers cite this in 119 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 80 sentences without a confident label

Uses its method or tool 3 papers

For many of these, masses were derived from the relation between $M_BH$ and the bulge stellar velocity dispersion $σ_⋆$ [ref] .

Mapping the nuclear environments of extreme coronal line emitting galaxies · Black hole masses · 0.87
For the remaining quasars, the tight correlation between the mass $M$ and the stellar velocity dispersion $σ$ is exploited to estimate their masses [ref] .

Excavating black hole continuum spectrum: Possible signatures of scalar hairs and of higher dimensions · Numerical analysis: What does observations tell us? · 0.82
For thirteen quasars the $M-σ$ relation is also used to constrain their masses [ref] .

In quest of axionic hairs in quasars · Results Based on Numerical Analysis · 0.99

Uses its data or values 1 paper

For a sub-sample of thirteen quasars [ref] , the masses are also reported by $M-σ$ method [ref] .

Imprints of the Janis-Newman-Winicour spacetime on observations related to shadow and accretion · Observational sample · 0.88

Compares with it 1 paper

Interestingly, all our sources except NGC 4945 lie on the M-$σ$ relation predicted by different models [ref] .

Unveiling the Fast Acceleration of AGN-Driven Winds at Kiloparsec Scales · Theoretical predictions on AGN outflow acceleration · 0.84

Cites it as support 1 paper

Furthermore, the [ref] models also provides a deep solution for the existence of the black hole mass – galaxy scaling relationships (e.g., [ref] ).

A Review of Galaxy Quenching -- Part II: Theoretical Solutions and Direct Observational Tests · II) The quasar-mode AGN feedback paradigm · 0.96

Cites it as background 32 papers

The correlation between a supermassive black hole's mass, $M_bh$, and the stellar velocity dispersion, $σ$, of its host spheroid [ref] is often regarded as the most fundamental of the black hole scaling relations.

Galaxy morphology dependent (black hole mass)-(velocity dispersion) relations: implications for gravitational wave forecasts and cosmological simulations · Introduction · 1.00
While the direct black hole masses can only be derived in a small portion of nearby galaxies, some empirical relations are proposed, e.g. the relation between the supermassive black hole mass and stellar velocity dispersion ($M_BH - σ_⋆$) [ref] .

Even central galaxies feel their environment: cosmic siphoning of cool gas accretion · The black hole masses · 0.84
Empirically, this co-evolutionary nature is manifested in well-established local scaling relations between BH masses and key host galaxy properties, including stellar bulge mass ($M_∙- M_⋆$), stellar velocity dispersion ($M_∙- σ_⋆$), dynamical mass ($M_∙- M_dyn$) and luminosity ($M_∙- L$) [ref] .

Small hosts, big appetites: unveiling rapid and early low-mass black hole growth in cosmological zoom-in simulations of dwarf galaxies · Introduction · 0.94

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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