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REVIEW 4 major objections 4 minor 47 references

Local Hole revisited: evidence for bulk motions and self-consistent outflow

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper argues that the Local Hole's outflow is self-consistent with observed galaxy motions and can raise the local Hubble constant by about 2–3%.

desk verdict A self-consistency claim between the Local Hole density field and z(m) 'peculiar velocities' that are themselves density-weighted—but the authors are candid about the caveats, and the paper is worth a serious referee. read the letter →

arxiv 1909.01878 v3 pith:7QUJOV7O submitted 2019-09-04 astro-ph.CO

T. Shanks (1) , L.M. Hogarth (2) , N. Metcalfe (1) , J. Whitbourn (1) , ((1) CEA , Durham University , UK , (2) UCL
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UK)
This is my paper · ORCID
classification astro-ph.CO
keywords LocalHoleHubbleconstanttensionpeculiarvelocitiesbulkflowredshift-magnitudediagramgalaxyunderdensityK-bandluminosityfunctionoutflowmodel
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 argues that the Local Hole, a galaxy underdensity extending to $z\approx0.05$ ($\approx150\,h^{-1}\,\mathrm{Mpc}$), is also a dynamical feature, not merely a static one. It compares the outflow predicted by a simple linear-theory model built on the measured underdensity with peculiar velocities derived from the galaxy redshift–magnitude diagram $z(m)$, and reports good agreement. Adding this outflow to a bulk flow in the Local Group frame improves the fit in the southern-sky field where the hole is deepest, without worsening the other two directions. The paper concludes that the same underlying flow raises the locally measured Hubble constant by $\approx2$–$3\%$, enough to ease the tension between CMB and local expansion-rate estimates. Supernova peculiar velocities from the Pantheon sample fit the outflow less well, but the paper argues that the larger published SN sample rules it out only at the $1$–$2\sigma$ level.

What carries the argument

The load-bearing object is the linear-theory outflow model of Shanks et al. (2019), which turns a measured cumulative galaxy density contrast into a peculiar velocity through $\Delta v/v_H = -(1/3)(\delta\rho_g(<r)/\bar\rho_g)\Omega_m^{0.6}/b$. The density input comes from the WS14 galaxy $n(z)$ counts in three sky fields, combined by area weighting and assumed to be roughly isotropic around our position; the output is an outflow velocity to compare with data. The confirming observable is the $z(m)$ statistic originally proposed by Soneira (1979): the mean galaxy redshift in $K$-magnitude bins, compared with a homogeneous model built on a $K$-band luminosity function, with residuals interpreted as peculiar velocities. The same $K<12.5$ sample supplies both the density and the velocity estimates, which is what makes the cross-check meaningful.

What would settle it

A decisive test is to re-derive the $z(m)$ residuals with a $K$-band luminosity function calibrated independently of the Local Hole volume, for example from galaxies at $z>0.1$, or split by galaxy colour and morphology to check the standard-candle assumption; if the roughly $500\,\mathrm{km\,s^{-1}}$ outflow signature at $60$–$150\,h^{-1}\,\mathrm{Mpc}$ vanishes, the agreement is an artifact. A complementary test is a future southern-sky SNIa survey with even 100 supernovae at $0.02<z<0.05$: the outflow model predicts a mean peculiar velocity of about $400$–$500\,\mathrm{km\,s^{-1}}$ in that shell, so a measurement consistent with zero at an uncertainty well below $100\,\mathrm{km\,s^{-1}}$ would falsify the model.

Watch

Extended reading notes

Core claim

On the paper's terms, the discovery is that the Local Hole's underdensity and the peculiar velocities inferred from the $z(m)$ Hubble diagram are two sides of one flow: an outflow driven by the hole. The claimed self-consistency is new: the density contrast measured in galaxy counts, when fed through the dynamical outflow model, predicts peculiar velocities that match the $z(m)$ residuals. The model's prediction is $$\frac{\$\Delta$ v}{v_H} = -\frac{1}{3}\,\frac{\delta\rho_g(<r)}{\bar\rho_g}\,\frac{\$Omega_m^{{0.6}}$}{b},$$ with the cumulative density contrast taken from the combined WS14 fields (median underdensity $\approx-23\%$ within $150\,h^{-1}\,\mathrm{Mpc}$). With this, the predicted outflow reaches roughly $500\,\mathrm{km\,s^{-1}}$ at $z\approx0.1$, and the observed $z(m)$ residuals follow it out to the final $K=12.5$ bin at $\approx150\,h^{-1}\,\mathrm{Mpc}$. The paper reads the agreement as evidence that outflow plus bulk motion, not bulk motion alone, describes the local velocity field, and that the corresponding local $H_0$ is $2$–$3\%$ higher than the global value.

Load-bearing premise

The load-bearing premise is that the $z(m)$ residuals are genuine peculiar velocities: the $K$-band galaxy luminosity function must be a standard candle with no evolutionary or environmental shift, and the correction for the very local inhomogeneities under study must not itself create the apparent outflow signal.

Editorial extensions

If this is right

  • If the outflow model is right, distance-ladder measurements of $H_0$ made inside $\approx150\,h^{-1}\,\mathrm{Mpc}$ sit in a volume that is expanding $\approx2$–$3\%$ faster than the cosmic mean, so applying a local-density correction would bring them closer to CMB-based values.
  • The model predicts a coherent outflow plus bulk flow pattern out to $\approx150\,h^{-1}\,\mathrm{Mpc}$; independent peculiar-velocity surveys with dense southern coverage should see the same flow, including the enhanced outflow in the southern Galactic cap direction.
  • The Pantheon supernova data are the main point of tension in the paper; the paper's own reading is that larger, more isotropic SN samples are needed, and that the current disagreement is only at the $1$–$2\sigma$ level once volume weighting is applied.
  • The consistency between galaxy number counts and $z(m)$ velocities, if it survives, would let the same $K$-band standard candle constrain both the density and velocity fields, tightening joint estimates of the galaxy bias $b$ and $\Omega_m$.

Reading between the lines

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

  • A testable extension would be to apply the same $z(m)$ machinery at fainter $K$ limits ($K<14$) to see whether the outflow signal continues to $z\approx0.1$ or turns over; the current result leans heavily on the highest-magnitude bin at $K=12.5$.
  • The same logic could be inverted: use the $z(m)$ residuals as an independent probe of the local density field, rather than predicting velocities from counts, which would give a cross-check on galaxy bias and luminosity-function assumptions that does not require a complete redshift survey.
  • If future SNIa data with better southern coverage still prefer zero outflow, the fork in the road is clear: either the $K$-band standard-candle assumption or the assumed isotropy of the Local Hole would be the part to give way.
  • The 2–3% local expansion excess is close to the level needed to reconcile Planck CMB values with the TRGB distance scale; if confirmed, it would mean most of the 'tension' in that particular comparison is a local calibration effect rather than new physics.
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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

4 major / 4 minor

Summary. The paper revisits the Local Hole, a roughly 150 h^-1 Mpc underdensity, and compares peculiar velocities inferred by Whitbourn & Shanks (2014) from the K-band \bar{z}(m) Hubble diagram with a linear outflow model based on the WS14 density profile. It claims that the outflow model agrees with the \bar{z}(m) velocities, that adding the outflow improves the bulk-flow interpretation in the 6dF-SGC direction, and that the outflow could raise the local Hubble constant by 2-3%. It also compares with Pantheon SNIa and argues, using the larger D'Arcy Kenworthy et al. sample, that the SNIa rejection of the model is only at the 1-2 sigma level.

Significance. If the outflow interpretation is correct, it would provide a local-structure explanation for part of the H0 tension and would strengthen the evidence for the Local Hole. The linear-theory calculation is transparent, and the connection between the density field and the velocity field is a useful consistency check. However, the central comparison is not an independent confirmation, because the \bar{z}(m) residuals are not corrected for the same density field used to build the model, and the most direct SNIa test in Table 1 rejects the model at 3-4 sigma in two fields. The result is interesting but not yet established; the paper's own caveats in Section 4 identify the load-bearing weakness.

major comments (4)
  1. [Section 3.2, Eq. (2), and Section 4] The comparison in Figs. 2-3 is not an independent test of the outflow model. The WS14 \bar{z}(m) residuals are derived from a magnitude-limited sample, and the paper itself states in Section 4 that they 'need substantial correction for the same local inhomogeneities that are the subject of the n(m) and n(z) studies.' Without that correction, a density-weighted average redshift in a magnitude bin can produce an apparent peculiar velocity even for galaxies at rest, and the outflow model is computed from the same density contrast (Eq. 2). The agreement may therefore be partly built into the construction. The authors should either apply the density correction to the \bar{z}(m) residuals or compare the model against independent peculiar-velocity data before claiming confirmation.
  2. [Table 1 and Section 3.3] The Pantheon SNIa comparisons in Table 1 reject the outflow model at 3.0 sigma in 6dF-SGC (p=2.8e-3), 4.2 sigma in SDSS-NGC (p=2.5e-5), and 3.1 sigma all-sky (p=2.1e-3). This is difficult to reconcile with the abstract's statement that the model is 'not significantly inconsistent' with SNIa peculiar velocities. The later reduction to 1-2 sigma relies on summary statistics from D'Arcy Kenworthy et al. rather than on a reanalysis of the 397 SNIa sample presented here; until that reanalysis is shown, the per-field Pantheon results remain the strongest direct test and disfavor the model.
  3. [Section 3.3] The chi-square values in Table 1 are described as 'illustrative' because SNIa systematics, inter-bin covariances, and covariances with the model prediction are ignored. Since these same chi-squares are used both to claim consistency for the \bar{z}(m) data (p=0.79 all-sky) and to quantify the SNIa discrepancy, the assumed independence of bins and the neglected systematics are not innocuous. The authors should propagate the model uncertainty, including the galaxy bias b, and test whether the conclusions survive marginalization over b or inclusion of off-diagonal covariances.
  4. [Section 3.2] The paper acknowledges that 'much depends on the final K=12.5, r~150h^-1 Mpc vpec point that WS14 regarded as uncertain, partly due to its amplitude.' Because this outermost point carries much of the apparent agreement, the comparison should be repeated with and without it. If the agreement disappears when that point is removed, the claimed self-consistency is not robust.
minor comments (4)
  1. [Abstract] The phrase 'not significantly inconsistent with SNIa peculiar velocity measurements from at least the largest previous survey' is misleading when Table 1 shows 3-4 sigma rejections in the Pantheon sub-samples; the abstract should qualify this statement to refer only to the D'Arcy Kenworthy et al. sample.
  2. [Figures 2 and 3] The model lines are plotted without uncertainty bands. Since the model depends on the galaxy bias b and on the density profile, adding a band would make the agreement in Figs. 2-3 easier to assess, especially at the uncertain K=12.5 point.
  3. [Eq. (1)] The adopted value of the galaxy bias b is not stated in the text. The authors should give the value and source of b and, ideally, its uncertainty, since Eq. (1) scales the predicted outflow inversely with b.
  4. [Section 4] The statement that the paper recognises 'for the first time the self-consistency' of the WS14 density and velocity measurements is accurate, but the word 'self-consistency' should be used throughout the abstract and conclusions; the current wording at times implies independent confirmation, which the method does not provide.

Circularity Check

1 steps flagged · score 6.0 of 10

The claimed z(m) confirmation of the Local Hole outflow is partly circular: the outflow model and the uncorrected z(m) 'peculiar velocities' both inherit the same WS14 density field, so Figs 2–3 compare the Local Hole with itself.

  1. self definitional [Section 3.1 Eq. (2), Section 3.2 and Section 4 (Figs 2–3 and caveat)]
    "Since WS14 only showed the individual n(z)’s for their three areas, for completeness we first show in Fig. 1 the overall average density contrast ( dn n ) i found by combining the three areas of WS14 that leads to the Δv/vH(z) result shown in Fig. 1 of Shanks et al. (2019). ... there are still possible issues with the z(m) results: they need substantial correction for the same local inhomogeneities that are the subject of the n(m) and n(z) studies"

    The outflow model plotted in Figs 2–3 is obtained from Eq. (1) using Eq. (2), where (dn/n)_i are the WS14 Local Hole density contrasts. The plotted 'peculiar velocities' are the WS14 z(m) residuals, i.e. observed \bar z(m) minus a homogeneous-model \bar z(m); the paper concedes these residuals still need 'substantial correction for the same local inhomogeneities that are the subject of the n(m) and n(z) studies'. In a magnitude-limited sample, an uncorrected density contrast shifts \bar z(m) by a density-weighted selection term, so the residual is a functional of the same (dn/n)_i that generates the predicted outflow. The agreement in Fig.

full rationale

The paper's main new comparison is between a linear-theory outflow computed from WS14's n(z) underdensity and WS14's z(m) residuals interpreted as peculiar velocities. This would be a legitimate test if the z(m) residuals were clean line-of-sight velocities after subtracting all density effects. But the paper itself says they are not: they 'need substantial correction for the same local inhomogeneities that are the subject of the n(m) and n(z) studies.' Since the same inhomogeneities are the input to Eq. (2), the 'excellent agreement' in Fig. 3 is at least partly built in, so the paper's 'self-consistent' description is accurate but the stronger implicit claim—that this confirms the outflow and hence a 2–3% local H0 correction—is not independently supported by this comparison. The external SNIa check is present in Table 1 and actually disfavors the model (χ2 rejections at 3σ and 4.2σ in 6dF-SGC and SDSS-NGC), although the authors argue the larger D'Arcy Kenworthy et al. sample reduces this to 1–2σ; that argument is not circular but is a debate over sample weighting. The Shanks et al. (2019) self-citation is not itself load-bearing in a problematic way because the model is a standard linear-theory expression; the circularity is the shared WS14 density field. Overall, score 6: partial circularity of the central comparison, with an external SNIa check preventing a higher score.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The core derivation uses a linear bias parameter b and the assumption that the three WS14 fields can be averaged into an isotropic underdensity. The z(m) peculiar velocities assume the K-band LF is a standard candle. The SNIa comparison fits Omega_m and H0. No invented entities are introduced beyond previously claimed structures (Local Hole, Shapley Supercluster).

free parameters (3)
  • galaxy bias b
    Scales the predicted outflow in Eq. (1); value is not stated in this paper and is inherited from Shanks et al. (2019), so the comparison assumes a particular bias without a sensitivity test.
  • Omega_m (full-sample SNIa fit) = 0.28 +/- 0.015 (no outflow), 0.32 +/- 0.015 (with outflow)
    Reported best fits to 1048 Pantheon SNIa; the outflow model requires a higher Omega_m to fit, a change of about 1 sigma. Used to argue the outflow model is an acceptable fit.
  • H0 (full-sample SNIa fit) = 73.7 +/- 0.2 km/s/Mpc (no outflow), 72.7 +/- 0.2 km/s/Mpc (with outflow)
    Fitted along with Omega_m; the roughly 1 km/s/Mpc shift is the claimed local effect of the outflow, though the chi-squared difference is only 3.66 for two fitted parameters.
assumptions (5)
  • domain assumption Linear theory gravitational growth applies to the Local Hole outflow, giving Eq. (1) with growth suppressed by Omega_m^0.6
    The paper uses this standard model to predict the peculiar velocity from the density contrast, assuming the underdensity is in the linear regime on scales up to 150 h^-1 Mpc. Cited in Section 3.1, Eq. (1).
  • domain assumption Galaxy density contrast traces matter density contrast with a constant bias b that is the same on all scales
    Eq. (1) divides by b, implying an assumed linear relation between galaxy and matter overdensities. The value of b is not specified in this paper.
  • domain assumption The Local Hole is approximately isotropic around our position
    Eq. (2) uses a 4 pi factor to extrapolate the average density contrast from the three WS14 fields to the full sky. The paper argues this is supported by the combined density contrast in Fig. 1 and by REFLEX II/CLASSIX cluster samples, but it remains an assumption.
  • domain assumption The K-band galaxy luminosity function is a standard candle with no evolution or environmental dependence when interpreting z(m) residuals as peculiar velocities
    The z(m) peculiar velocities are residuals from a homogeneous model assuming a fixed LF; the paper admits this could be vulnerable to LF evolution (Sections 3.2 and 4).
  • ad hoc to paper The chi-squared comparisons are valid despite ignored SNIa systematics and inter-bin covariances
    The paper calls the chi-squared results 'illustrative' and says they are sensitive to the handling of model errors; this weakens the formal statistical interpretation of Table 1.

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Cite this review

Pith. "Pith review of Local Hole revisited: evidence for bulk motions and self-consistent outflow." pith.science (2026). https://pith.science/paper/7QUJOV7O

@misc{pith2026190901878,
  author       = {Pith},
  title        = {Pith review of: Local Hole revisited: evidence for bulk motions and self-consistent outflow},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7QUJOV7O}},
  note         = {Machine review of arXiv:1909.01878}
}
abstract

We revisit our mapping of the `Local Hole', a large underdensity in the local galaxy redshift distribution that extends out to redshift, $z\approx0.05$ and a potential source of outflows that may perturb the global expansion rate and thus help mitigate the present `$H_0$ tension'. First, we compare local peculiar velocities measured via the galaxy average redshift-magnitude Hubble diagram, $\bar{z}(m)$, with a simple dynamical outflow model based on the average underdensity in the Local Hole. We find that this outflow model is in good agreement with our peculiar velocity measurements from $\bar{z}(m)$ and not significantly inconsistent with SNIa peculiar velocity measurements from at least the largest previous survey. This outflow could cause an $\approx2-3$\% increase in the local value of Hubble's constant. Second, considering anisotropic motions, we find that the addition of the outflow model may improve the $\bar{z}(m)$ fit of a bulk flow where galaxies are otherwise at rest in the Local Group frame. We conclude that the Local Hole plus neighbouring overdensities such as the Shapley Supercluster may cause outflow and bulk motions out to $\approx150$h$^{-1}$Mpc that are cosmologically significant and that need to be taken into account in estimating Hubble's constant.

Figures

Figures reproduced from arXiv: 1909.01878 by the authors.

Figure 1
Figure 1. Density contrast-redshift relations for all three WS14 fields and for 6dF-NGC+SDSS-NGC, each combined by area weighting. These both show an underdensity out to z ≈ 0.05 im￾plying that the underdensity is not just restricted to the 6dF-SGC area and that our assumption of an approximately isotropic ‘Lo￾cal Hole’ around our position is not unreasonable. 2 PREVIOUS DATASETS AND RESULTS WS14 used 2MASS K band photometry … view at source ↗
Figure 2
Figure 2. The WS14 peculiar velocities (filled circles) estimated from the residuals between the observed z(m) Hubble diagram and a homogeneous model in their three individual fields. The range 10.0 < K < 12.5 translates to 60 < ∼ d < ∼ 150h −1Mpc via this model. WS14 found that bulk motion in the Local Group frame (solid horizontal line) was preferred by these data except in 6dF￾SGC where galaxies appeared more at rest in th… view at source ↗
Figure 3
Figure 3. then shows the area weighted average of the ob￾served peculiar velocities over all three directions. There is clearly now no sensitivity to bulk motion but these data can still be used to look for an outflow due to a global under￾density in this volume. We again see excellent agreement between the outflow model and the z(m) peculiar velocity estimates. We have used χ 2 to compare the z(m) peculiar velocities with th… view at source ↗

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.