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The frozen outskirts: a cold Hubble flow and the mass of the Local Group

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The Local Group's outer Hubble flow is so cold—only 15 km/s of velocity scatter—that its total mass can be measured as 2.47 trillion solar masses, fully contained within the virial zones of the Milky Way and Andromeda.

desk verdict Plausible Local Group mass, but the 15 vs 70 km/s discrepancy likely rests on an apples-to-oranges selection; send to review with a request for a matched simulation test. read the letter →

arxiv 2505.06642 v1 pith:Q5OJ5QT3 submitted 2025-05-10 astro-ph.GA

Danila Makarov , Dmitry Makarov , Lidia Makarova , Noam Libeskind This is my paper · ORCID
classification astro-ph.GA
keywords LocalGroupHubbleflowdarkmatterdwarfgalaxiesvirialmassbarycenterzero-velocityspherecosmologicalsimulations
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

The paper sets out to show that the outer Local Group is expanding so calmly that its total mass can be read off from the Hubble flow itself. For 7 of the 11 dwarf galaxies lying between 400 and 1400 kpc from the Local Group barycenter, the line-of-sight velocity scatter is only 15 km/s, compared with the roughly 70 km/s that constrained cosmological simulations produce. Applying an analytical spherical Hubble-flow model for a flat $\Lambda$CDM universe to these velocities gives a total mass of $(2.47 \pm 0.15)\times 10^{12}\,M_\odot$. Since this equals the sum of the Milky Way's and Andromeda's satellite-derived masses and does not grow with radius, the paper concludes that essentially all of the Local Group's mass sits inside the virial zones of its two giant galaxies.

What carries the argument

The load-bearing mechanism is a published analytical solution for the Hubble flow around a spherical mass concentration in a flat $\Lambda$CDM universe: it relates a particle's recession velocity at radius $R$ to the enclosed mass $M(<R)$, so the inverse problem — given an observed velocity and distance, recover the mass — becomes well posed. The paper couples this solution to a deprojection chain. Heliocentric velocities are converted to Galactocentric ones, the Milky Way's own motion toward the Local Group barycenter (set by the mass ratio $x$) is subtracted, and each galaxy's barycentric speed is recovered by dividing the line-of-sight velocity by $\cos\Theta$, assuming purely radial infall. The central result is the flat profile of $M(<R)$ from 400 to 1400 kpc, which is what supports the claim that the whole mass lies within the virial zones.

What would settle it

Measure proper motions for the seven flow dwarfs, in particular WLM and NGC 6822, to a transverse-velocity accuracy near 10 km/s: if their three-dimensional motions do not point back at the derived barycenter, the radial-infall deprojection $V = v_{LG}/\cos\Theta$ fails and the mass estimate collapses. A cheaper check is to obtain radial velocities for the three peripheral dwarfs that lack them (Leo K, Leo M, Pegasus W); if they scatter by tens of km/s instead of joining the 15 km/s flow, the cold flow is a small-sample selection effect.

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Extended reading notes

Core claim

Within 400–1400 kpc of the Local Group barycenter, seven dwarf galaxies outside the virial zones of the Milky Way and Andromeda trace a nearly perfect radial infall: their line-of-sight velocities scatter by only 15 km/s around the spherical Hubble-flow model. Inverting that model yields $M_{LG} = (2.47 \pm 0.15)\times 10^{12}\,M_\odot$, and the constancy of the mass estimate with radius shows the mass is enclosed within roughly 400 kpc, inside the two galaxies' virial radii. Minimizing the scatter in the per-galaxy mass estimates fixes the barycenter at a Milky Way-to-Andromeda mass ratio of $0.74 \pm 0.10$, corresponding to individual masses $(1.06 \pm 0.11)\times 10^{12}\,M_\odot$ and $(1.42 \pm 0.12)\times 10^{12}\,M_\odot$. The Milky Way therefore moves at $62.6 \pm 2.6$ km/s toward the barycenter, and the Sun's apex relative to that barycenter is $(l,b,V) = (+94.0^\circ \pm 0.7^\circ,\,-2.7^\circ \pm 0.3^\circ,\,301 \pm 3 \;\mathrm{km\,s^{-1}})$.

Load-bearing premise

The load-bearing premise is that the dwarf galaxies beyond the virial zones fall purely radially toward a single spherical barycenter located on the Milky Way–Andromeda line, so that line-of-sight velocities can be deprojected with $\cos\Theta$ and inverted into a mass.

Editorial extensions

If this is right

  • The Local Group's total mass is $(2.47 \pm 0.15)\times 10^{12}\,M_\odot$, with no additional mass detected between 400 and 1400 kpc; the entire mass is inside the virial zones of the Milky Way and Andromeda.
  • The Milky Way-to-Andromeda mass ratio is $0.74 \pm 0.10$, implying $M_{MW} = (1.06 \pm 0.11)\times 10^{12}\,M_\odot$ and $M_{M31} = (1.42 \pm 0.12)\times 10^{12}\,M_\odot$.
  • The Milky Way approaches the Local Group barycenter at $62.6 \pm 2.6$ km/s, placing the solar apex at Galactic coordinates $(l,b,V) = (+94.0^\circ, -2.7^\circ, 301 \pm 3 \;\mathrm{km\,s^{-1}})$.
  • Constrained cosmological simulations predict a velocity scatter near 70 km/s for the same region, roughly five times the observed 15 km/s, so the cold flow is a genuine challenge to simulated Local Group dynamics.
  • The earlier paradox where the zero-velocity-sphere mass came out below the sum of the two virial masses disappears once dark energy is properly included in the flow model.

Reading between the lines

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

  • If the 15 km/s scatter is not a small-sample fluke, the Local Group's outskirts are far smoother than typical $\Lambda$CDM groups, which may mean that the local void environment suppresses tidal stirring or that simulations overproduce substructure in group outskirts; measuring velocities for the remaining peripheral dwarfs without radial velocities would test this directly.
  • The barycenter-minimization step could be exported to other nearby groups with two dominant galaxies: minimizing the scatter of per-galaxy flow masses may be a generic way to measure mass ratios without satellite kinematics.
  • The four outliers (Cetus, Tucana, Pegasus, NGC 6822) may be backsplash objects rather than first-infall dwarfs; if deeper proper-motion measurements confirm this, their status as 'outliers' would itself become a probe of orbital histories in the Local Group.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper analyzes the radial-velocity field of peripheral Local Group galaxies at distances 400–1400 kpc from the barycenter, using the spherical Hubble-flow model of Baushev (2020). After excluding six objects in the 300–450 kpc virial-zone layer and four outliers (Cetus, Tucana, Pegasus, NGC 6822), seven of eleven remaining galaxies are found to follow a very cold line-of-sight Hubble flow with a quoted dispersion of 15 km/s. Inverting the model gives a total Local Group mass M_LG = (2.47 ± 0.15) × 10^12 M_sun, with no significant mass trend over the fitted distance range. Minimizing the scatter of the mass estimates fixes the barycenter and yields a Milky Way-to-Andromeda mass ratio M_MW/M_M31 = 0.74 ± 0.10, individual masses (1.06 ± 0.11) × 10^12 M_sun and (1.42 ± 0.12) × 10^12 M_sun, and a solar apex relative to the Local Group barycenter. A comparison with HESTIA constrained simulations reports a much larger simulated velocity scatter, about 70 km/s, which the paper interprets as a challenge to ΛCDM predictions.

Significance. If the cold-flow claim is robust, this is a significant result: a 15 km/s line-of-sight dispersion over 400–1400 kpc is a sharp, falsifiable constraint on galaxy formation and infall dynamics in the Local Group, and the inferred total mass agrees well with independent estimates from satellite kinematics and with the zero-acceleration-surface analysis of Benisty et al. (2024). The paper is transparent in its data assembly, uses high-precision distances, and makes a concrete, reproducible model comparison to a constrained cosmological simulation suite. The mass estimate itself is plausible and independently cross-checked; the main risk is that the headline cold-flow discrepancy may depend on a post hoc selection and on a simulation comparison that is not selection-matched. The analysis would benefit from explicit uncertainty propagation through the barycenter fit and from a clearly defined dispersion statistic.

major comments (3)
  1. [§4, Fig. 5] The headline comparison between a 15 km/s observed dispersion and a ~70 km/s simulated dispersion is not made on the same statistic. The observational value is measured on 7 of 11 galaxies after excluding four outliers (Cetus, Tucana, Pegasus, NGC 6822), whereas the HESTIA value appears to include all halos with M* >= 1.5 × 10^5 M_sun outside 300 kpc, including backsplash and other non-first-infall objects that the paper itself invokes to explain the observed outliers. Please define the 15 km/s and 70 km/s statistics precisely, apply the identical selection and outlier-rejection procedure to the simulated analogs, and report the scatter of the coherent subset in HESTIA. If a selection-matched scatter remains about 70 km/s, the cold-flow claim is supported; if it drops to ~15 km/s, the discrepancy is an artifact of the selection procedure.
  2. [§3, Fig. 4] The barycenter position is obtained by minimizing the scatter of the mass estimates derived from the same seven galaxies, so the quoted individual masses M_MW = 1.06 ± 0.11 and M_M31 = 1.42 ± 0.12, the mass ratio 0.74 ± 0.10, and the solar apex are fitted parameters rather than independent predictions. In addition, the reported uncertainty σ_M = 0.39 and the quoted M_LG error of 0.15 do not propagate the covariance with the barycenter fit, with the choice of which seven galaxies survive the outlier cut, or with the deprojection assumptions. Please provide a bootstrap, leave-one-out, or profile-likelihood treatment that includes selection and fitting degrees of freedom; the total mass may remain stable, but its quoted precision needs to be verified.
  3. [§2, Eqs. (2)–(5)] The deprojection V = v_LG / cos Θ assumes purely radial infall toward a barycenter that lies on the MW–M31 line, and the construction assumes zero tangential motion of M31. This is a strong assumption for a dumbbell-shaped system whose outer members are concentrated in planes roughly perpendicular to the MW–M31 line (Fig. 1). The paper should quantify how a nonzero M31 tangential velocity or a non-radial component of infall changes V for the seven selected galaxies, and test in HESTIA whether applying the same deprojection recipe to simulated line-of-sight velocities recovers the true mass and reduces the scatter as much as it does for the real data. Without this, the cold-flow dispersion and the mass estimate could be an artifact of the projection model.
minor comments (4)
  1. [Abstract and §4] The 70 km/s simulated scatter is quoted without a formal definition or error; specify whether it is the rms line-of-sight residual about the model, the rms of deprojected velocities, or a different quantity.
  2. [§5] There is a typo in the paragraph on NGC 6822: 'NCG 6822' should read 'NGC 6822'.
  3. [§3] The sentence listing six excluded galaxies mixes the 300–450 kpc layer objects with the four outliers; itemizing the final 11 galaxies and the selected 7 explicitly (e.g., in a table or in the text) would make the selection transparent.
  4. [Table 1] Leo K, Leo M, and Pegasus W have no velocity entries; state explicitly that they are excluded for lack of radial velocities rather than by the quality cut.

Circularity Check

1 steps flagged · score 4.0 of 10

Partial circularity: the MW/M31 mass ratio, individual masses, and solar apex are algebraic transforms of the barycenter parameter fitted to minimize the scatter of the same mass estimates, while the total Local Group mass retains independent support.

  1. fitted input called prediction [Section 3, 'Mass estimation from the Hubble flow model' (barycenter fit), and Abstract]
    "The minimum scatter is achieved for the MW-to-M31 mass ratio of MMW/MM31 = 0.74 ± 0.10, placing the barycenter 447 ± 26 kpc from the MW center and implying the MW velocity of 62.6 ± 2.6 km/s... This allows us to estimate individual masses MMW = (1.06 ± 0.11) × 10^12 M⊙ and MM31 = (1.42 ± 0.12) × 10^12 M⊙."

    The ratio x = MMW/MM31 is the free parameter varied to minimize the scatter of the mass estimates M_flow,i(x). The individual masses, the MW barycentric velocity, and the solar apex are then computed algebraically from that same x via Eqs. (2)-(3) and the adopted M31 radial velocity. No independent observable constrains these quantities after the fit, so they are re-expressions of the fitted input rather than independent predictions. The quoted uncertainties also omit the covariance with the fitting and with the selection of the 7-of-11 galaxy subset.

full rationale

The paper's central mass result, MLG = (2.47 ± 0.15) × 10^12 M⊙, is not the target of the barycenter minimization and is cross-checked against satellite-kinematics masses from an independent method, so that claim has independent grounding. The barycenter-derived mass ratio and solar apex are, however, transformations of the fitted ratio rather than standalone predictions, which is a partial circularity. A separate methodological concern—the 15 km/s cold-flow dispersion is measured on the 7 of 11 galaxies selected for consistency with the model, while the ~70 km/s simulation scatter is quoted for all halos—is a potential selection mismatch rather than a by-construction circularity; it should be tested by applying the same selection to HESTIA analogs. No load-bearing self-citation chain or imported uniqueness theorem was found.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The method rests on one fitted parameter (the mass ratio x), several idealizations about spherical symmetry and radial infall, and a post hoc partition of the sample. No new physical entities are introduced.

free parameters (1)
  • MW-to-M31 mass ratio x = 0.74 +/- 0.10
    Varied in Eq. (2) to place the barycenter and minimize the scatter of the Hubble-flow mass estimates (Section 3). Used to derive individual masses and solar apex.
assumptions (5)
  • domain assumption The Local Group potential is approximately spherically symmetric at radii beyond 400 kpc.
    Invoked in the Introduction to justify applying a spherical overdensity model to the dumbbell-shaped Local Group.
  • domain assumption The selected dwarf galaxies are on radial infall toward the Local Group barycenter, with no significant tangential component.
    Assumed when using Eq. (5), V = vLG/cos(Theta), to deproject line-of-sight velocities.
  • domain assumption The barycenter lies on the straight line connecting the Milky Way and M31 centers.
    Used in Eq. (2) to define the barycenter from the mass ratio; motivated by the dominance of the two giant galaxies.
  • standard math The Baushev (2020) analytical solution for the Hubble flow around a spherical overdensity in flat Lambda CDM is valid here.
    The model is cited and not re-derived; it provides the mass-velocity-distance mapping used throughout.
  • ad hoc to paper The seven galaxies used in the analysis are representative free-falling particles, while the four excluded outliers are not.
    The division into flowing and non-flowing galaxies is made after inspecting the kinematics (Section 3, Fig. 3), which is a post hoc classification.

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Cite this review

Pith. "Pith review of The frozen outskirts: a cold Hubble flow and the mass of the Local Group." pith.science (2026). https://pith.science/paper/Q5OJ5QT3

@misc{pith2026250506642,
  author       = {Pith},
  title        = {Pith review of: The frozen outskirts: a cold Hubble flow and the mass of the Local Group},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q5OJ5QT3}},
  note         = {Machine review of arXiv:2505.06642}
}
abstract

We analyze the velocity field of peripheral members of the Local Group. The Hubble flow at distances from 400 to 1400~kpc, formed by 7 of 11 nearby galaxies, is characterized by an extremely small line-of-sight velocity dispersion of 15 km/s, which differs significantly from the predictions of cosmological simulations of about 70 km/s. This fact allows us to determine the total mass of the Local Group as $M_{LG} = (2.47 \pm 0.15) \times 10^{12}$ $M_\odot$ using an analytical model of the Hubble flow around a spherical overdensity in the standard flat \LCDM{} universe. The practical equality of this mass to the sum of the masses of our Galaxy and the Andromeda Galaxy, as well as the absence of mass growth in the range of distances under consideration, gives grounds to conclude that the entire mass of the Local Group is confined within the virial radii around its two main galaxies. The barycenter, found from the minimal scatter of mass estimates, corresponds to the mass ratio of the Milky Way and the Andromeda Galaxy equal to $M_{MW}/M_{M31} = 0.74\pm0.10$. The velocity of our Galaxy to the barycenter turns out to be $62.6\pm2.6$ km/s. This allows us to determine the apex of the Sun relative to the barycenter of the Local Group to be $(l,b,V) = ( +94.0^\circ \pm 0.7^\circ, -2.7^\circ \pm 0.3^\circ, 301 \pm 3$ km/s in the Galactic coordinates.

Figures

Figures reproduced from arXiv: 2505.06642 by the authors.

Figure 1
Figure 1. Distribution of Local Group galaxies in a cylindrical projection, where the X axis is directed from the center of the Milky Way to the center of the Andromeda Galaxy, and the Y axis corresponds to the dis￾tance from the X axis. The dashed semicircles with a radius of 300 kpc roughly correspond to the size of the virial zones around the two main galaxies. A solid semicircle with a radius of 1 Mpc shows the approx￾ima… view at source ↗
Figure 2
Figure 2. presents a schematic diagram of the corrections de￾scribed below. The barycenter of the Local Group is designated as BC. Small letters refer to observed values, and uppercase let￾ters denote values relative to the barycenter. The blue dots indi￾cate real objects: MW, M 31, and a galaxy under consideration. The position of the observer is marked by the Sun symbol. As part of our Galaxy, the observer does not particip… view at source ↗
Figure 3
Figure 3. There is a noticeable gap between UGC 4879 at 1.35 Mpc and the next “cloud” of objects beyond 1.6 Mpc, which includes Antlia B, Sextants B, NGC 3109, Antlia, Sextans A and so on. This provides us a natural upper limit for the use of the model, as the analysis of the motion of more distant galaxies may need to consider the influence of neighboring giant galaxies—M 81, M 94, Cen A, NGC 253, and IC 342—located at dista… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The total mass of the Local Group from the Hubble flow model versus the distance to the center of mass of the Local Group, which minimizes the spread of the mass estimates. total mass estimates. Given the previous result that the sum of the individual masses of the MW …
Figure 5
Figure 5. Figure 5: The Hubble flow in the neighborhood of the Local Group ana￾log in the high-resolution HESTIA simulations 09_18. Colored circles indicate halos with stellar particles, M∗ ≥ 1.5×105 M⊙, but only outside the virial zones of 300 kpc around of two most massive halos. The la…
Figure 6
Figure 6. Figure 6: Estimation of the mass of the system from the Hubble flow, as in [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

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Reference graph

Works this paper leans on

60 extracted references · 50 canonical work pages · cited by 1 Pith paper

  1. [1]

    S., Bucciarelli, B., Crosta, M., et al

    Akhmetov, V . S., Bucciarelli, B., Crosta, M., et al. 2024, MN RAS, 530, 710

    work page 2024

  2. [2]

    D., Allende Prieto, C., et al

    Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, Ap JS, 219, 12

    2015

  3. [3]

    S., Rizzi, L., Tully, R

    Anand, G. S., Rizzi, L., Tully, R. B., et al. 2021, AJ, 162, 80

    work page 2021

  4. [4]

    Bahcall, J. N. & Tremaine, S. 1981, ApJ, 244, 805

    work page 1981

  5. [5]

    V ., Chernin, A

    Baryshev, Y . V ., Chernin, A. D., & Teerikorpi, P . 2001, A&A, 378, 729

    work page 2001

  6. [6]

    F., & Fritz, T

    Battaglia, G., Taibi, S., Thomas, G. F., & Fritz, T. K. 2022, A &A, 657, A54

    work page 2022

  7. [7]

    Baushev, A. N. 2020, Phys. Rev. D, 102, 083529

    work page 2020

  8. [8]

    N., Karachentsev, I

    Begum, A., Chengalur, J. N., Karachentsev, I. D., Kaisin, S. S., & Sharina, M. E. 2006, MNRAS, 365, 1220

    work page 2006

Show all 60 references
  1. [9]

    2024, A&A, 689, L1

    Benisty, D. 2024, A&A, 689, L1

    2024

  2. [10]

    M., & Tureanu, A

    Benisty, D., Chaichian, M. M., & Tureanu, A. 2024, Physics Le tters B, 858, 139033

    2024

  3. [11]

    W., et al

    Benisty, D., V asiliev, E., Evans, N. W., et al. 2022, ApJ, 928, L5

    2022

  4. [12]

    J., Monelli, M., Gallart, C., et al

    Bernard, E. J., Monelli, M., Gallart, C., et al. 2013, MNRAS, 432, 3047

    2013

  5. [13]

    2023, arXiv e-prints, arXiv:2305.03293

    Bhattacharya, S. 2023, arXiv e-prints, arXiv:2305.03293

    2023

  6. [14]

    Bobylev, V . V . & Baykova, A. T. 2023, Astronomy Reports, 67, 812

    2023

  7. [15]

    Collins, M. L. M., Karim, N., Martinez-Delgado, D., et al. 20 24, MNRAS, 528, 2614 Crnojevi´c, D., Sand, D. J., Zaritsky, D., et al. 2016, ApJ, 824, L14

    2016

  8. [16]

    2013, MNRAS, 430, 888

    Doumler, T., Ho ffman, Y ., Courtois, H., & Gottlöber, S. 2013, MNRAS, 430, 888

    2013

  9. [17]

    O., & Pa turel, G

    Ekholm, T., Baryshev, Y ., Teerikorpi, P ., Hanski, M. O., & Pa turel, G. 2001, A&A, 368, L17

    2001

  10. [18]

    J., & Cole, A

    Fraternali, F., Tolstoy, E., Irwin, M. J., & Cole, A. A. 2009, A&A, 499, 121 Gaia Collaboration, Brown, A. G. A., V allenari, A., et al. 20 18, A&A, 616, A1

    2009

  11. [19]

    2015, ApJ, 811, L1 8

    Gallart, C., Monelli, M., Mayer, L., et al. 2015, ApJ, 811, L1 8

    2015

  12. [20]

    Grand, R. J. J., Gómez, F. A., Marinacci, F., et al. 2017, MNRA S, 467, 179 GRA VITY Collaboration, Abuter, R., Amorim, A., et al. 2021, A&A, 647, A59

    2017

  13. [21]

    P ., Giovanelli, R., Kent, B

    Haynes, M. P ., Giovanelli, R., Kent, B. R., et al. 2018, ApJ, 8 61, 49

    2018

  14. [22]

    Heisler, J., Tremaine, S., & Bahcall, J. N. 1985, ApJ, 298, 8 Hoffman, Y ., Martinez-V aquero, L. A., Y epes, G., & Gottlöber, S. 2008, MN- RAS, 386, 390

    1985

  15. [23]

    2017, MNRAS , 466, 2006

    Kacharov, N., Battaglia, G., Rejkuba, M., et al. 2017, MNRAS , 466, 2006

    2017

  16. [24]

    Kahn, F. D. & Woltjer, L. 1959, ApJ, 130, 705

    1959

  17. [25]

    & Makarov, D

    Karachentsev, I. & Makarov, D. 2001, Astrofizika, 44, 1

    2001

  18. [26]

    Karachentsev, I. D. 2005, AJ, 129, 178

    2005

  19. [27]

    D., Kashibadze, O

    Karachentsev, I. D., Kashibadze, O. G., Makarov, D. I., & Tul ly, R. B. 2009, MNRAS, 393, 1265

    2009

  20. [28]

    Karachentsev, I. D. & Makarov, D. A. 1996, AJ, 111, 794

    1996

  21. [29]

    Karachentsev, I. D. & Nasonova, O. G. 2010, MNRAS, 405, 1075

    2010

  22. [30]

    Kashibadze, O. G. & Karachentsev, I. D. 2018, A&A, 609, A11

    2018

  23. [31]

    N., Bullock, J

    Kirby, E. N., Bullock, J. S., Boylan-Kolchin, M., Kaplinghat, M., & Cohen, J. G. 2014, MNRAS, 439, 1015

    2014

  24. [32]

    Y ., Brosch, N., Hoffman, G

    Kniazev, A. Y ., Brosch, N., Hoffman, G. L., et al. 2009, MNRAS, 400, 2054

    2009

  25. [33]

    2003, ApJ, 590, L17 Article number, page 7 of 8 A&A proofs: manuscript no

    Komiyama, Y ., Okamura, S., Y agi, M., et al. 2003, ApJ, 590, L17 Article number, page 7 of 8 A&A proofs: manuscript no. main

    2003

  26. [34]

    S., Staveley-Smith, L., Kilborn, V

    Koribalski, B. S., Staveley-Smith, L., Kilborn, V . A., et al. 2004, AJ, 128, 16

    2004

  27. [35]

    A., Kirby, E

    Kvasova, K. A., Kirby, E. N., & Beaton, R. L. 2024, ApJ, 972, 18 0

    2024

  28. [36]

    & Liddle, A

    Lahav, O. & Liddle, A. R. 2022, arXiv e-prints, arXiv:2201.0 8666

    2022

  29. [37]

    B., Primack, J

    Lahav, O., Lilje, P . B., Primack, J. R., & Rees, M. J. 1991, MNR AS, 251, 128

    1991

  30. [38]

    F., Ibata, R

    Lewis, G. F., Ibata, R. A., Chapman, S. C., et al. 2007, MNRAS, 375, 1364

    2007

  31. [39]

    I., Carlesi, E., Grand, R

    Libeskind, N. I., Carlesi, E., Grand, R. J. J., et al. 2020, MN RAS, 498, 2968

    2020

  32. [40]

    1981, The Observatory, 101, 111

    Lynden-Bell, D. 1981, The Observatory, 101, 111

    1981

  33. [41]

    2025, arXiv e-prints, arXiv:2503.12612

    Makarov, D., Makarov, D., Kozyrev, K., & Libeskind, N. 2025, arXiv e-prints, arXiv:2503.12612

    2025 arXiv

  34. [42]

    Makarova, L. N. & Makarov, D. I. 2021, MNRAS, 502, 1623

    2021

  35. [43]

    F., Chambers, K

    Martin, N. F., Chambers, K. C., Collins, M. L. M., et al. 2014, ApJ, 793, L14

    2014

  36. [44]

    W., Higgs, C

    McConnachie, A. W., Higgs, C. R., Thomas, G. F., et al. 2021, M NRAS, 501, 2363

    2021

  37. [45]

    McConnachie, A. W. & V enn, K. A. 2020, AJ, 160, 124

    2020

  38. [46]

    McQuinn, K. B. W., Mao, Y .-Y ., Buckley, M. R., et al. 2023, ApJ, 944, 14

    2023

  39. [47]

    McQuinn, K. B. W., Mao, Y .-Y ., Tollerud, E. J., et al. 2024, ApJ, 967, 161

    2024

  40. [48]

    B., Erkal, D., & Li, T

    Pace, A. B., Erkal, D., & Li, T. S. 2022, ApJ, 940, 136

    2022

  41. [49]

    Reid, M. J. & Brunthaler, A. 2020, ApJ, 892, 39

    2020

  42. [50]

    B., Ibata, R., Reylé, C., et al

    Salomon, J. B., Ibata, R., Reylé, C., et al. 2021, MNRAS, 507, 2592

    2021

  43. [51]

    A., & Hardy, E

    Sandage, A., Tammann, G. A., & Hardy, E. 1972, ApJ, 172, 253

    1972

  44. [52]

    R., Skillman, E

    Savino, A., Weisz, D. R., Skillman, E. D., et al. 2022, ApJ, 93 8, 101

    2022

  45. [53]

    Sawala, T., Teeriaho, M., & Johansson, P . H. 2023, MNRAS, 521, 4863

    2023

  46. [54]

    2018, A&A, 618 , A122

    Taibi, S., Battaglia, G., Kacharov, N., et al. 2018, A&A, 618 , A122

    2018

  47. [55]

    V ., & Kuhlen, M

    Teyssier, M., Johnston, K. V ., & Kuhlen, M. 2012, MNRAS, 426, 1808

    2012

  48. [56]

    B., Courtois, H., Ho ffman, Y ., & Pomarède, D

    Tully, R. B., Courtois, H., Ho ffman, Y ., & Pomarède, D. 2014, Nature, 513, 71

    2014

  49. [57]

    B., Courtois, H

    Tully, R. B., Courtois, H. M., Dolphin, A. E., et al. 2013, AJ, 146, 86

    2013

  50. [58]

    Wang, W., Han, J., Cautun, M., Li, Z., & Ishigaki, M. N. 2020, S cience China

    2020

  51. [59]

    L., Evans, N

    Watkins, L. L., Evans, N. W., & van de V en, G. 2013, MNRAS, 430, 971

    2013

  52. [60]

    R., Dolphin, A

    Weisz, D. R., Dolphin, A. E., Martin, N. F., et al. 2019, MNRAS , 489, 763 Article number, page 8 of 8

    2019

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.