A reanalysis of the megamaser Hubble constant: from spot catalogues to peculiar velocities

Harry Desmond; Richard Stiskalek

REVIEW

A reanalysis of the megamaser Hubble constant: from spot catalogues to peculiar velocities

Richard Stiskalek, Harry Desmond

Cosmology and Nongalactic Astrophysics · Submitted 15 Sep 2026 · 6 references

Pith's verdict: A careful, transparent reanalysis of the megamaser H0 that advances the methodology but does not resolve the tension; deserves referee time.

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CitationHarry Desmond, Richard Stiskalek. "A reanalysis of the megamaser Hubble constant: from spot catalogues to peculiar velocities." arXiv:2609.17684 (2026). https://pith.science/paper/742577BO

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Editor's note

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This is a careful, transparent reanalysis of the megamaser Hubble constant that does what you'd want from a methodological improvement: it reproduces previous results when inputs are matched, then shows where the added value is. The new Bayesian forward model with a proper selection term, physical distance priors, and marginalisation over peculiar-velocity reconstructions is a clear step forward. The central result – H0 = 71.6 ± 3.6 km/s/Mpc – is intermediate between Planck and SH0ES and does not resolve the tension, but that's not the paper's fault; it's the data.

What the paper does well: it verifies the disc likelihood to machine precision against the MCP code, tests multiple spot tables, warp orders, and selection models, and quantifies the impact of the MCP reanalysis. The per-galaxy distances are stable across outlier treatments. The paper is honest about its caveats – the coarse selection model, missing per-spot detection model, reliance on external velocity reconstructions.

Where it's soft: the stress-test note about the residual bulk-flow prior (V_ext) is fair but minor. The difference between ignoring peculiar velocities and using Manticore-Local is 1.6–2.1 km/s/Mpc, about half the total uncertainty. Some of that comes from V_ext, whose prior is calibrated from Cosmicflows-4 but not tested for sensitivity. A 50 km/s shift in V_ext projection would change H0 by ~0.3–0.5 km/s/Mpc, which is only ~0.1σ, so it's not a load-bearing flaw, but the paper should report a sensitivity test to the V_ext prior parameters, as the stress-test suggests.

Another soft spot: the selection model is acknowledged as rough, but the paper could be clearer that the two selection variants (redshift vs distance) bracket only a part of the possible selection bias, not the full systematic.

Overall, the paper is thorough, the methodology is solid, and the conclusions are appropriately cautious. It deserves serious peer review. I recommend acceptance after minor revisions that address the V_ext prior sensitivity and clarify the selection model limitations. I would bring it to a reading group and cite it.

Referee report

Significance

If correct, the central claim is a clean, ladder-independent geometric H0 at 5% precision that currently cannot adjudicate the Hubble tension, and the paper is a reusable analysis template for the larger ngVLA-era samples. Its strengths are substantial: the machine-precision verification of the disc likelihood against the MCP code (§3.5), the exact reproduction of P20's population-level result from identical inputs (§4.3), the end-to-end propagation of four spot tables, and the unusually complete robustness grid of Table 5. The critique of Watkins and Feldman (2026) in §5.1 is specific and backed by a reimplementation that recovers their table 2 to 0.07 km/s/Mpc, which makes the claim falsifiable rather than rhetorical. The authors are also commendably honest about the weakest points: caveats 1 and 5 of §5.2 explicitly state that the coarse single-variable selection model cannot bound the true flux/inclination/mass-dependent selection, and that the missing per-spot detection probability may bias the inferred disc geometry and distance.

Major objections (2)

[Section 3.4, Eq. (23), Table 6] The residual bulk-flow component V_ext is the most prior-dominated ingredient of the headline H0, and its sensitivity is never tested. With only five galaxies the posterior replicates the informative Gaussian prior calibrated from Cosmicflows-4 (stated in §4.3 and visible in Figs. 8–9). For UGC 3789 and NGC 6323 the V_ext projection is the dominant term of the assigned line-of-sight peculiar velocity (Table 6: −97 ± 15 and −57 ± 15 km/s out of total V_pec = −45 ± 42 and +495 ± 83 km/s), and the text itself notes that the C15-vs-Manticore difference 'arises mostly from the V_ext projection'. Because the peculiar-velocity correction shifts H0 by 1.6–2.1 km/s/Mpc — roughly half the statistical uncertainty — but the two reconstruction runs differ simultaneously in the field and in the V_ext prior (111 ± 15 vs 201 ± 16 km/s), the 0.7 km/s/Mpc spread between them (Table 5) does not isolate the prior effect. I request a dedicated sensitivity test: re-run the fiducial configuration with the V_ext prior mean shifted by, e.g., the difference between the two calibrations, or with the prior width doubled, and report the H0 response. From the inverse-variance weights of the five galaxies I estimate that a 50 km/s prior-mean shift moves H0 by roughly 0.3–0.5 km/s/Mpc (about 0.1σ), so I do not expect the headline value to change; but without this test, the quoted 'statistical' uncertainty omits an unquantified systematic of that size, and the claim that the peculiar-velocity treatment is one of the paper's key advances is only as strong as this prior.
[Section 5.2, caveat 5] The unmodelled per-spot detection probability is, in my reading, the deepest unquantified systematic in the distance chain, and I would weigh it slightly more heavily than the authors do. Maser amplification favours long velocity-coherent paths, so the systemic/midline spots — the population that anchors the disc geometry — are preferentially detected, yet the likelihood conditions on the reported spots. The authors state that this 'may thus lead to a bias in the inferred disc geometry and distance' and leave its quantification to future work. Because this selection flaw is shared with the P20 baseline, the 0.3σ agreement with P20 and even the 0.13σ NGC 4258 agreement do not bound the absolute bias; they bound only the difference between two analyses with the same selection treatment. I agree that a full per-spot detection model is out of scope, but I ask for two modest additions: (i) a statement of the expected sign and rough size of the geometric/distance bias from the known amplification path-length physics, and (ii) a crude robustness test, such as refitting the distances with the systemic and high-velocity spot populations treated separately (accepting that the systemic-only fit will be weaker), to see whether DA shifts by more than the statistical error; if such a test is not feasible, one explicit sentence to that effect in §5.2 would suffice.

Minor objections (6)

[Abstract, Section 4.3, Section 6] The headline uncertainty is quoted three ways: '71.6 ± 3.7' in the abstract, '71.6 +3.8/−3.5' in Table 5 and §4.3, and '±3.6' in the conclusion. Please adopt one convention, since the symmetric conclusion value is not directly derivable from the asymmetric intervals.
[Section 3.4] The priors on the selection nuisance parameters (cz_lim, cz_width, D_lim, D_width) are never stated in the text; they matter because the five galaxies constrain these parameters only weakly, so the posteriors in Figs. 8–9 are prior-dominated. Please add these priors to Table 2 or to the text.
[Table 4] With seven numeric columns under headers that visually span only the six this-work columns plus the P20 column, the plain-text layout makes the P20 column easy to misread as part of the quadratic-warp block; please make the column spans explicit.
[Figure 3] The caption phrase 'a 250 km s−1 redshift uncertainty, representing the host peculiar velocity' is misleading because σ_pec is a sampled parameter with a Maxwell prior of mean 250 km/s rather than a fixed input; reword to describe the plotted scale as the adopted peculiar-velocity scatter.
[Section 4.4] The 2.1σ discrepancy between the inferred eccentricity (0.0041 ± 0.0009) and the Reid et al. (2019) value (0.007 ± 0.001) is reported in a single clause; a sentence discussing whether the difference reflects the eccentric-warp parametrisation or the data would help readers place the excellent 0.13σ distance agreement in context.
[Section 3.4, Table 2] The stage-2 priors (H0 ∼ U(10,200), the Maxwell prior on σ_pec with mean 250 km/s, and the Gaussian prior on V_ext) are given in prose only; since the population-level model is a central contribution, a compact summary of these priors in or beside Table 2 would aid reproducibility.

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The paper

The paper claims

A Bayesian reanalysis of five megamaser galaxies, incorporating warped disc models, sample selection, and peculiar-velocity corrections, yields a geometric Hubble constant of 71.6 ± 3.7 km/s/Mpc (statistical), intermediate between the CMB…

The reading

This paper reanalyzes the five megamaser galaxies of the Megamaser Cosmology Project using a Bayesian forward model that jointly infers each galaxy's angular-diameter distance and warped Keplerian disc parameters directly from VLBI observables. It then combines these distances with host redshifts, including a physical volume prior, a sample selection correction, and a non-linear peculiar-velocity reconstruction (Manticore-Local), to obtain H0 = 71.6 ± 3.7 km/s/Mpc (statistical). This value sits between the Planck CMB measurement (67.4) and the SH0ES distance-ladder measurement (73.2), and its uncertainty does not yet distinguish between the two. The analysis shows that both the peculiar-velocity treatment and the choice of distance prior appreciably shift the result, while the updated maser spot tables from the MCP move it by about 2 km/s/Mpc relative to the original published catalogues.

What carries the argument

The central machinery is a warped Keplerian accretion disc model that maps each maser spot's orbital coordinates (radius and azimuth) to its observed sky position, LOS velocity, and LOS acceleration, with the angular-diameter distance D_A and black hole mass M_BH entering through the Keplerian velocity and centripetal acceleration equations. The authors break the mass–distance degeneracy by sampling the combination η = log[(M_BH/M_⊙)/(D_A/Mpc)] and then infer D_A jointly with disc geometry parameters using a two-step procedure: a differential-evolution global search locates the posterior maximum, after which a Metropolis-within-Gibbs sampler (NUTS for global parameters, adaptive random-walk for per-spot coordinates) explores the full posterior, including a dedicated reflection move to handle the bimodal azimuthal angles.

Extended reading notes

Core claim

From five megamaser-hosting galaxies, the authors obtain a purely geometric, ladder-independent constraint on the Hubble constant of H0 = 71.6 ± 3.7 km/s/Mpc (statistical) using a fiducial configuration that includes a redshift-based selection threshold, the non-linear Manticore-Local peculiar-velocity reconstruction, and a uniform-in-volume distance prior. This result resolves none of the Hubble tension but places the megamaser measurement in the intermediate regime, inconsistent with neither Planck nor SH0ES at the current 5% precision. The paper further demonstrates that the MCP's internal reanalysis of maser spot measurements (affecting mainly NGC 6264 and NGC 6323) raises H0 by 1.8–2.1 km/s/Mpc relative to the published catalogues, and that the non-linear peculiar-velocity correction lowers it by 1.6–2.1 km/s/Mpc relative to ignoring peculiar motions.

Load-bearing premise

The non-linear peculiar-velocity reconstruction (Manticore-Local) and its residual bulk-flow prior, calibrated from Cosmicflows-4, provide unbiased predictions for the line-of-sight velocities of the five maser hosts when evaluated at the sampled comoving distances.

Editorial extensions

If this is right

If this result is correct, the megamaser H0 no longer favours the local distance ladder over the CMB, as previous MCP analyses suggested; it is consistent with both at the ~1σ level.
The sample selection correction, though crude, matters: omitting it shifts H0 downward by ~2 km/s/Mpc, so future larger maser samples will require well-characterized selection functions.
The non-linear peculiar-velocity reconstruction from Manticore-Local gives a larger H0 reduction than the linear Carrick+15 field, and the difference is driven by the residual bulk-flow prior; proper marginalization over the local velocity field is essential.
The MCP's updated spot tables change the inferred distances significantly for two galaxies (NGC 6264 and NGC 6323), indicating that re-reduction of the raw VLBI data can shift H0 by ~2 km/s/Mpc, comparable to the current statistical uncertainty.
The separate analysis of NGC 4258 with an eccentric quadratic warp yields D_A = 7.558 ± 0.073 Mpc, consistent with the published trigonometric distance to <0.2σ, validating the disc model for the nearest maser galaxy.

Reading between the lines

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

If future megamaser samples reach 1% precision, the intermediate H0 value found here could either narrow the Hubble tension if it stays near 71–72 or sharpen it if it moves closer to SH0ES or Planck. The present uncertainty is too large to discriminate.
The paper's sensitivity to the choice of distance prior (flat vs. log-flat vs. volume-squared) suggests that any two-stage analysis that first derives distances under a non-physical prior and then reweights may be suboptimal; a full joint inference of all distances and H0 within a single hierarchical model would eliminate this reweighting ambiguity.
The reliance on a single, pre-computed peculiar-velocity reconstruction (Manticore-Local) calibrated with a Cosmicflows-4 prior means the H0 error bar does not include uncertainty from the reconstruction method itself. Comparing multiple independent reconstructions would provide a more robust estimate.
Because the MCP spot catalogue updates were only revealed through an erratum, this analysis highlights the importance of transparent data releases in high-stakes cosmology: the H0 shift from updated measurements exceeds the formal uncertainty of some earlier analyses.

Original abstract

The Hubble tension motivates careful scrutiny of the redshift-independent distances underpinning the local distance ladder. Water megamasers afford a purely geometric distance from orbital dynamics in an accretion disc. For five of the six Megamaser Cosmology Project (MCP) galaxies, we present a Bayesian forward model that infers the angular-diameter distance and warped Keplerian disc parameters jointly from the very long baseline interferometry quasi-observables: maser spot positions, velocities, and accelerations. We then constrain $H_0$ from these distances and the host redshifts, including a physical distance prior, modelling the galaxy sample selection and testing a linear and a non-linear peculiar-velocity reconstruction. Accounting for peculiar velocities with the non-linear Manticore reconstruction, we infer $H_0 = 71.6 \pm 3.7$ km/s/Mpc, where the uncertainty is statistical. Relative to ignoring peculiar velocities, the linear and non-linear reconstructions lower $H_0$ by $0.8$--$1.4$ and $1.6$--$2.1$ km/s/Mpc, respectively, whereas changing the selection variable alters it by less than $1$ km/s/Mpc. We analyse the sixth galaxy, NGC 4258, separately. Modelling its disc as eccentric and quadratically warped, we infer an angular-diameter distance of $7.558 \pm 0.073$ (stat.) Mpc, within $0.13\sigma$ of the published maser distance.

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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.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.49 · human participants 0.02 · controlled comparison 0.70 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.95 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

The Hubble tension motivates careful scrutiny of the redshift-independent distances underpinning the local distance ladder. Water megamasers afford a purely geometric distance from orbital dynamics in an accretion disc. For five of the six Megamaser Cosmology Project (MCP) galaxies, we present a Bayesian forward model that infers the angular-diameter distance and warped Keplerian disc parameters jointly from the very long baseline interferometry quasi-observables: maser spot positions, velocities, and accelerations. We then constrain $H_0$ from these distances and the host redshifts, including a physical distance prior, modelling the galaxy sample selection and testing a linear and a non-linear peculiar-velocity reconstruction. Accounting for peculiar velocities with the non-linear Manticore reconstruction, we infer $H_0 = 71.6 \pm 3.7$ km/s/Mpc, where the uncertainty is statistical. Relative to ignoring peculiar velocities, the linear and non-linear reconstructions lower $H_0$ by $0.8$--$1.4$ and $1.6$--$2.1$ km/s/Mpc, respectively, whereas changing the selection variable alters it by less than $1$ km/s/Mpc. We analyse the sixth galaxy, NGC 4258, separately. Modelling its disc as eccentric and quadratically warped, we infer an angular-diameter distance of $7.558 \pm 0.073$ (stat.) Mpc, within $0.13\sigma$ of the published maser distance.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
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s0	The Hubble tension motivates careful scrutiny of the redshift-independent distances underpinning the local distance ladder.	background 1.00	0.06	0.03	asserted 0.92
s1	Water megamasers afford a purely geometric distance from orbital dynamics in an accretion disc.	background 0.89	0.06	0.02	asserted 0.98
s2	For five of the six Megamaser Cosmology Project (MCP) galaxies, we present a Bayesian forward model that infers the angular-diameter distance and warped Keplerian disc parameters jointly from the very long baseline interferometry quasi-observables: maser spot positions, velocities, and accelerations.	method 0.83	0.96	0.04	asserted 1.00
s3	We then constrain $H_0$ from these distances and the host redshifts, including a physical distance prior, modelling the galaxy sample selection and testing a linear and a non-linear peculiar-velocity reconstruction.	method 0.96	0.95	0.05	asserted 0.98
s4	Accounting for peculiar velocities with the non-linear Manticore reconstruction, we infer $H_0 = 71.6 \pm 3.7$ km/s/Mpc, where the uncertainty is statistical.	result 1.00	0.97	0.79	asserted 1.00
s5	Relative to ignoring peculiar velocities, the linear and non-linear reconstructions lower $H_0$ by $0.8$--$1.4$ and $1.6$--$2.1$ km/s/Mpc, respectively, whereas changing the selection variable alters it by less than $1$ km/s/Mpc.	result 0.96	0.95	0.13	asserted 1.00
s6	We analyse the sixth galaxy, NGC 4258, separately.	contribution 0.82	0.88	0.02	asserted 0.81
s7	Modelling its disc as eccentric and quadratically warped, we infer an angular-diameter distance of $7.558 \pm 0.073$ (stat.) Mpc, within $0.13\sigma$ of the published maser distance.	result 0.99	0.96	0.05	asserted 1.00

What kind of paper the classifier reports this is: empirical study 0.78 · evidence from analysis of existing data 0.99.

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

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P abstract

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C citations
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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.** — Position–velocity diagrams of the maser spots in NGC 5765b, CGCG 074-064, and NGC 6264, coloured by spectral class, for the updated-MCP tables (Section 2.1). The vertical axis is the LOS velocity offset from the systemic velocity. For illustration, the horizontal axis is the maser sky position projected onto the disc major axis, which we take empirically as the direction of maximum variance of the spot positions. The systemic spots cluster near the origin, in front of the black hole, while the approaching and receding high-velocity spots populate the disc tangents at opposite ends…

**Figure 2.** — Illustration of the per-spot azimuthal bimodality in ϕ for NGC 5765b. Each panel shows the data likelihood L(di | r, ϕ, θ) of a single maser spot as a function of its orbital angular radius r and azimuthal angle ϕ, with the disc parameters θ fixed at the baseline linear-warp posterior median and the colour scale normalised to each spot’s peak. The likelihood splits into the two solutions ϕ and π − ϕ, symmetric about the tangent point ϕ = π/2 for receding spots (panels a and b) and ϕ = 3π/2 for approaching spots (panel c). In every panel the two solutions lie on the near and far…

**Figure 3.** — Observed CMB-frame redshift zobs for each galaxy against its inferred comoving distance DC on the updated-ours spot table (Section 2.1), with the horizontal error bars giving the central 68% interval about the posterior median. The vertical error bars show a 250 km s−1 redshift uncertainty, representing the host peculiar velocity. The dashed and dotted lines are the flat-ΛCDM distance–redshift relations for the SH0ES distance-ladder (H0 = 73.2 km s−1 Mpc−1 ) and CMB (H0 = 67.4 km s−1 Mpc−1 ) values. since omitting them biases the result (Desmond et al. 2026). The per-galaxy…

**Figure 4.** — Angular-diameter distance posterior of each galaxy under the four spot tables of Section 2.1—original-all (blue), updated-MCP (red), updated-all (brown), and updated-ours (yellow)—together with the P20 posterior (black, dashed). The priors, sampler, and disc model are held fixed across the four inferences, except that the updated-MCP model has no NGC 5765b clump 2 floors (Section 3.1). The updated-MCP and updated-ours tables are based on the current MCP measurements and differ in the outlier treatment. criterion is applied, or, for the NGC 5765b clump 2 spots, on whether they are…

**Figure 5.** — Inferred H0 (median and central 68% interval) over the reconstruction × selection grid, for the linear warp and the volume prior. Markers denote the baseline input spot table: filled circles the updated-MCP table, filled squares the updated-ours table (Section 2.1). Bands give the CMB (Planck Collaboration and others 2020a) and SH0ES (Breuval et al. 2024) values for reference. values reproduce their published results. Passing the same distance posteriors through our own population model instead (the uniform-in-volume prior, sampled σv, the selection term, and the five-galaxy…

**Figure 6.** — Posterior on the global disc parameters of NGC 5765b for the baseline linear-warp model on the updated-ours table, typical of the five galaxies. Contours are the 68% and 95% credible regions. The four σ (2) parameters are the clump 2 error floors, which the model contains only on the tables the MCP cut is not applied to. All global disc parameters have R <ˆ 1.01, with ≈6.2 × 103 effective samples on DA

**Figure 7.** — Posterior on the global disc parameters of NGC 4258 under the eccentric quadratic-warp model, inferred from the full 358-spot table with no outlier rejection. Contours are the 68% and 95% credible regions. The eccentricity enters through the Cartesian components ex and ey, with e = (e 2 x + e 2 y ) 1/2 = 0.0041 ± 0.0009, and dω/dr is the periapsis warp rate

**Figure 8.** — Joint posterior over the shared population parameters for the redshift-selection runs on the updated-ours baseline spot table (Section 2.1), overlaying the Manticore-Local (blue) and linear (red) reconstructions, both with a linear warp. Contours are the 68% and 95% credible regions. The two reconstructions give consistent H0, while σpec and Vext recover their priors

Showing 8 of the paper's 9 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2609.17684 by the authors.

References

Works cited (6)

[1]

Planck Collaboration and others, A&A641, A6 (2020a), arXiv:1807.06209 [astro-ph.CO]. L. Breuval, A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, M. Romaniello, Y. S. Murakami, D. Scolnic, G. S. Anand, and I. Soszy´ nski, ApJ973, 30 (2024), arXiv:2404.08038 [astro-ph.CO]. A. G. Riess, W. Yuan, L. M. Macri, D. Scolnic, D. Brout, S. Casertano, D. O. Jones, ...

View on Pith Pith review arXiv 2020
[3]

On theupdated-ourstable, the NGC 5765b inclination curvature is−6.5 +0.9 −0.9 deg mas−2, offset from zero by 7σ, a stronger detection of cur- vature than any coefficient on theupdated-MCPtable (Section 4.1). The two tables differ in which spots are retained and in the clump 2 floors (Section 3.1), so the preference for curvature in that disc cannot be at-...

View on Pith 2019
[45]

R. Stiskalek, A. G. Riess, H. Desmond, G. Lavaux, and D. Scolnic, MNRAS550, stag1272 (2026c), arXiv:2603.09880 [astro-ph.GA]. S. D. Landy and A. S. Szalay, ApJ391, 494 (1992). M. J. Hudson, MNRAS266, 468 (1994). M. A. Strauss and J. A. Willick, Phys. Rep.261, 271 (1995), arXiv:astro-ph/9502079 [astro-ph]. S. Barua, V. Ramakrishnan, and S. Desai, Ap&SS370,...

View on Pith Pith review arXiv 2026
[1973]

APPENDIX A.DATA-DRIVEN ESTIMATES OF DISTANCE, MASS, AND ORBITAL RADIUS We derive inexpensive, approximate estimates of the comoving distance, black hole mass, and per-spot or- bital radii directly from the spot data, without sampling the full disc model. They seed the differential-evolution search of Section 3.2.1: the distance and mass estimates set theD...

View on Pith 1973
[2004]

pp. 195–206, arXiv:astro-ph/0409387 [astro-ph]. B. C. Kelly, ApJ665, 1489 (2007), arXiv:0705.2774 [astro-ph]. B. C. Kelly, X. Fan, and M. Vestergaard, ApJ682, 874 (2008), arXiv:0805.2946 [astro-ph]. D. W. Hogg, A. D. Myers, and J. Bovy, ApJ725, 2166 (2010), arXiv:1008.4146 [astro-ph.SR]. D. Foreman-Mackey, D. W. Hogg, and T. D. Morton, ApJ795, 64 (2014), ...

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[2018]

p. 821, arXiv:1810.06686 [astro-ph.CO]. R. P. Brent,Algorithms for Minimization without Derivatives, Prentice-Hall Series in Automatic Computation (Prentice-Hall, Englewood Cliffs, NJ,

View on Pith Pith review arXiv

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.

[1] [1]

Planck Collaboration and others, A&A641, A6 (2020a), arXiv:1807.06209 [astro-ph.CO]. L. Breuval, A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, M. Romaniello, Y. S. Murakami, D. Scolnic, G. S. Anand, and I. Soszy´ nski, ApJ973, 30 (2024), arXiv:2404.08038 [astro-ph.CO]. A. G. Riess, W. Yuan, L. M. Macri, D. Scolnic, D. Brout, S. Casertano, D. O. Jones, ...

View on Pith Pith review arXiv 2020

[2] [3]

On theupdated-ourstable, the NGC 5765b inclination curvature is−6.5 +0.9 −0.9 deg mas−2, offset from zero by 7σ, a stronger detection of cur- vature than any coefficient on theupdated-MCPtable (Section 4.1). The two tables differ in which spots are retained and in the clump 2 floors (Section 3.1), so the preference for curvature in that disc cannot be at-...

View on Pith 2019

[3] [45]

R. Stiskalek, A. G. Riess, H. Desmond, G. Lavaux, and D. Scolnic, MNRAS550, stag1272 (2026c), arXiv:2603.09880 [astro-ph.GA]. S. D. Landy and A. S. Szalay, ApJ391, 494 (1992). M. J. Hudson, MNRAS266, 468 (1994). M. A. Strauss and J. A. Willick, Phys. Rep.261, 271 (1995), arXiv:astro-ph/9502079 [astro-ph]. S. Barua, V. Ramakrishnan, and S. Desai, Ap&SS370,...

View on Pith Pith review arXiv 2026

[4] [1973]

APPENDIX A.DATA-DRIVEN ESTIMATES OF DISTANCE, MASS, AND ORBITAL RADIUS We derive inexpensive, approximate estimates of the comoving distance, black hole mass, and per-spot or- bital radii directly from the spot data, without sampling the full disc model. They seed the differential-evolution search of Section 3.2.1: the distance and mass estimates set theD...

View on Pith 1973

[5] [2004]

pp. 195–206, arXiv:astro-ph/0409387 [astro-ph]. B. C. Kelly, ApJ665, 1489 (2007), arXiv:0705.2774 [astro-ph]. B. C. Kelly, X. Fan, and M. Vestergaard, ApJ682, 874 (2008), arXiv:0805.2946 [astro-ph]. D. W. Hogg, A. D. Myers, and J. Bovy, ApJ725, 2166 (2010), arXiv:1008.4146 [astro-ph.SR]. D. Foreman-Mackey, D. W. Hogg, and T. D. Morton, ApJ795, 64 (2014), ...

View on Pith Pith review arXiv 2007

[6] [2018]

p. 821, arXiv:1810.06686 [astro-ph.CO]. R. P. Brent,Algorithms for Minimization without Derivatives, Prentice-Hall Series in Automatic Computation (Prentice-Hall, Englewood Cliffs, NJ,

View on Pith Pith review arXiv