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REVIEW 3 major objections 4 minor 1 cited by

The total stellar halo mass of the Milky Way

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper measures the Milky Way's stellar halo at about 1.4 billion solar masses, roughly twice earlier estimates.

desk verdict A credible, genuinely new all-sky measurement that likely places the Milky Way stellar halo near 1e9 solar masses, but with headline uncertainties too small once density-profile and metallicity systematics are folded in. read the letter →

arxiv 1908.02763 v2 pith:UPBDIMP4 submitted 2019-08-07 astro-ph.GA

Alis J. Deason (Durham) , Vasily Belokurov (Cambridge) , Jason L. Sanders (Cambridge) This is my paper · ORCID
classification astro-ph.GA
keywords stellarhaloMilkyWaymassredgiantbranchGaiaDR2propermotiondecompositionluminositygalaxyformationdwarfmerger
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

Using red giant branch stars from Gaia DR2, this paper measures the total luminosity of the Milky Way's stellar halo out to 100 kpc. After separating disc and halo stars by fitting Gaussian mixtures to the proper-motion distributions in many small bins, it converts the halo star counts into luminosity with stellar isochrones and a volume correction based on an assumed halo density profile. It finds $L_{\rm halo}=7.9\pm2.0\times10^8\,L_\odot$ without the Sagittarius stream and $9.4\pm2.4\times10^8\,L_\odot$ including it, implying a stellar halo mass of $1.4\pm0.4\times10^9\,M_\odot$ for a Kroupa IMF. That is two to three times larger than the most commonly cited earlier estimates, and it matches the picture of a single massive ancient merger assembling the inner halo. A sympathetic reader would care because the stellar halo mass ties the Milky Way's assembly history to the properties of its most massive destroyed dwarf.

What carries the argument

The load-bearing object is the conversion from counts of red giant branch stars to total luminosity. Each spatial, magnitude, and colour bin yields a number $N_{\rm halo}$ of halo RGB stars; this is multiplied by two factors. The first, $L_\odot/N_{\rm RGB}$, comes from a stellar population model (PARSEC isochrones) weighted by an assumed age range of 10--14 Gyr and a metallicity distribution with mean $[\mathrm{Fe/H}]\sim-1.5$; it converts star counts into light. The second is a volume correction, the ratio of the total halo volume (out to 100 kpc) to the volume probed by the bin, computed with an Einasto density profile of index $n=1.7$, scale radius $R_e=20$ kpc, and axis ratio $q=0.6$. The disc/halo separation itself is done by extreme deconvolution, fitting a two-component Gaussian mixture to the proper motions; the whole pipeline is calibrated on synthetic Galaxy catalogues and N-body halo models, which fix the claimed 25% systematic uncertainty.

What would settle it

Take a complete sample of RR Lyrae or blue horizontal branch stars with distances from period-luminosity relations out to 100 kpc, integrate their light, and compare to $L_{\rm halo} \approx 8\times10^8\,L_\odot$; a well-calibrated sum outside the range $6$--$12\times10^8\,L_\odot$ would rule out the central claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that the total stellar halo luminosity of the Milky Way within 100 kpc is $L_{\rm halo}=7.9\pm2.0\times10^8\,L_\odot$ (excluding Sagittarius) or $9.4\pm2.4\times10^8\,L_\odot$ (including it), and that with a Kroupa IMF the corresponding stellar mass is $M_{\star,\rm halo}=1.4\pm0.4\times10^9\,M_\odot$. These values are derived by counting red giant branch stars selected from Gaia DR2 at high Galactic latitude with small parallax, decomposing the disc and halo contributions through two-dimensional Gaussian fits to the proper-motion distributions in bins of colour, magnitude, and sky area, then multiplying each bin's halo counts by a volume correction built from an adopted Einasto halo profile, with the counts-to-light conversion made by an age- and metallicity-weighted suite of isochrones. The paper argues that this mass, together with an average halo metallicity of about $[\mathrm{Fe/H}] \sim -1.5$, implies that the bulk of the halo was built by a single massive dwarf galaxy accreted roughly 10 Gyr ago, rather than by many small mergers.

Load-bearing premise

The luminosity estimate assumes the adopted Einasto stellar halo density profile is the true one; every bin's count is multiplied by the ratio of total halo volume to the volume the bin probes, so a wrong profile scales the final luminosity directly, and the paper finds alternative published profiles change the answer by about 30 percent.

Editorial extensions

If this is right

  • The Milky Way's stellar halo mass is $M_{\star,\rm halo}\sim 1.4\times10^9\,M_\odot$, two to three times larger than the canonical values from main-sequence turn-off and blue horizontal branch counts.
  • A halo of this mass supports the Gaia-Sausage/Enceladus interpretation: the inner halo is dominated by debris from one massive dwarf accreted about 10 Gyr ago.
  • The low stellar halo mass fraction ($M_{\star,\rm halo}/M_{\star,\rm gal}\sim0.02$) matches cosmological simulations that form their haloes through an early major merger with little subsequent accretion.
  • The extra light behind the Sagittarius stream corresponds to $L_{\rm Sgr}\sim1.5\times10^8\,L_\odot$, consistent with independent estimates of the stream's luminosity.
  • If the average halo metallicity is actually higher, near $[\mathrm{Fe/H}]\sim-1.2$, the same data imply about $1.05\times10^9\,M_\odot$, still well above earlier estimates.

Reading between the lines

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

  • The 30% systematic variation from the assumed halo density profile is not folded into the quoted $1.4\pm0.4\times10^9\,M_\odot$; combining it in quadrature would widen the error to roughly $\pm0.7\times10^9\,M_\odot$, so the factor-of-two discrepancy with older estimates is the robust part, not the exact value.
  • The same RGB proper-motion decomposition could be applied to external galaxies with future astrometric surveys, turning this into a direct method for measuring stellar halo masses in the Local Group rather than relying on photometric tracers.
  • If an in-situ 'Splash' component contributes at large radii, part of the claimed accreted mass would be misattributed; the paper does not quantify this beyond a 5% estimate at $|z|\sim10$ kpc.
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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 measures the total stellar luminosity of the Milky Way's stellar halo using Gaia DR2 red giant branch stars. RGB stars are selected in bins of magnitude, colour and sky position, and the disc and halo components are decomposed by fitting two-dimensional Gaussian mixtures to the proper motion distributions. The resulting halo star counts are converted to luminosity with PARSEC isochrones weighted by an assumed age and metallicity distribution, and are volume-corrected using an adopted Einasto stellar halo density profile. The method is calibrated on Galaxia models with eleven Bullock & Johnston N-body stellar haloes, giving a claimed recovery of the true luminosity to within 25 percent in robust bins. Applied to Gaia DR2, the paper reports L_halo = 7.9 +/- 2.0 x 10^8 L_sun excluding Sagittarius and L_halo = 9.4 +/- 2.4 x 10^8 L_sun including Sagittarius, within 100 kpc. Assuming a Kroupa IMF mass-to-light ratio of 1.5, the paper derives M*_halo = 1.4 +/- 0.4 x 10^9 M_sun and interprets this as evidence for a dominant ancient (~10 Gyr) massive merger progenitor. The paper also discusses systematic effects from the adopted density profile, metallicity distribution function, and stellar isochrone set, and places the Milky Way in the context of Auriga simulations and external galaxy halo measurements.

Significance. If the central result holds, the paper provides a full-sky, Gaia-based measurement of the Milky Way stellar halo mass that is roughly two to three times larger than the commonly cited Bell et al. (2008) and Deason et al. (2011) estimates, and it helps reconcile the total halo mass with the massive Gaia-Sausage/Enceladus accretion scenario. The methodological strengths are substantial: the proper-motion decomposition is tested on Galaxia models, the calibration uses eleven N-body stellar haloes with known truth, the disc initialization is checked against an independent dynamical model, and the authors explicitly identify and quantify several important systematics rather than hiding them. The principal weakness is that the headline uncertainty budget does not propagate the full systematic error from the adopted density profile, MDF, and isochrone library, so the reported central values are conditional on a set of prior assumptions that shift the result by roughly 30 percent or more.

major comments (3)
  1. [Section 4 and Section 5.2, Eq. (2), Fig. 12] The headline uncertainty of 25 percent is calibrated on Galaxia+BJ05 models in which the Einasto density profile is fitted directly to the true model halo, so it does not cover the uncertainty in the adopted Milky Way density profile used in Eq. (2). Section 5.2 and Fig. 12 show that literature density profiles change the derived luminosity by roughly 30 percent, and the MDF comparison in the same figure changes it by a comparable amount if the mean halo metallicity is -1.2 rather than -1.5. These systematics are larger than the quoted 25 percent model-recovery error, and adding them in quadrature gives a total systematic of roughly 40-50 percent. The abstract and conclusions therefore present L_halo = 7.9 +/- 2.0 x 10^8 L_sun and M*_halo = 1.4 +/- 0.4 x 10^9 M_sun with an error bar that understates the total uncertainty. Since the paper itself recommends including an additional 30 percent systematic for the density profile, the main results should be restated with a broader error budget, or clearly labelled as conditional on the adopted profile and MDF.
  2. [Section 5.2, Fig. 12, Eqs. (3)-(4)] The adopted metallicity distribution function is load-bearing for the central value. The paper's own conversion formulas show that adopting the Conroy et al. (2019) mean metallicity of <[Fe/H]> = -1.2 lowers the derived stellar mass to about 1.05 x 10^9 M_sun, which is 25 percent below the fiducial value. Because the comparison with Bell et al. (2008) and Deason et al. (2011) is one of the paper's main conclusions, the analysis should quantify how the factor-of-two-to-three contrast with earlier estimates changes under the combined density-profile and MDF systematics. A concise error-budget table that lists the density profile, MDF, isochrone, and model-recovery contributions separately would make the conditional nature of the result transparent.
  3. [Section 5.2, isochrone comparison] The stellar population model is an additional systematic that is discussed but not propagated into the headline uncertainty. Repeating the analysis with MIST and BaSTI models yields stellar masses of 0.85 x 10^9 M_sun and 1.1 x 10^9 M_sun, respectively, compared with the fiducial PARSEC-based value of about 1.4 x 10^9 M_sun. The MIST value lies outside the quoted 1.4 +/- 0.4 x 10^9 M_sun error bar, so the statement that these models are 'consistent within the uncertainties' is not fully supported. The isochrone systematic should be included in the final error budget or at least acknowledged as a separate caveat in the abstract and conclusions.
minor comments (4)
  1. [Section 4 and Fig. 11] The paper should state explicitly whether the same mask of excluded bins identified from the Galaxia models is applied to the Gaia data, or whether the robust-bin selection is re-derived from the data; currently this is not fully clear.
  2. [Section 4, quality cuts] The 8 percent correction for the quality cuts that remove stars with unreliable astrometry and photometry is applied to the luminosity estimate, but it is not stated whether this correction is included in the quoted 25 percent systematic; a brief sentence clarifying this would help.
  3. [Section 5.2, Eq. (3)-(4)] The conversion formulas for changing the average halo metallicity are useful, but they are fits to a single isochrone setup and should warn the reader that they are approximate and should not replace a full recomputation with a different stellar population library.
  4. [Section 5.3 and throughout] There are several presentation issues: the introduction contains 'it’s' instead of 'its', Section 5.3 has the garbled LaTeX sequence '\greaterorsimilar10 Gyr', and the text sometimes uses 'these values' or 'this figure' without a clear antecedent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the luminosity estimate is derived from Gaia star counts with external density-profile and metallicity inputs, and the method is calibrated against independent N-body models.

full rationale

The paper's central claim is the total stellar halo luminosity, computed from Gaia DR2 red-giant-branch star counts decomposed into disc and halo populations via proper-motion fits, then converted to luminosity using PARSEC isochrones and a volume correction. The volume correction in Eq. (2) adopts an Einasto density profile with parameters n=1.7, Re=20 kpc, q=0.6 from Deason et al. (2011). That paper is by the same authors, and the adopted profile is load-bearing for the normalization, but it is an externally measured input derived from independent SDSS blue-horizontal-branch data, not a quantity that this paper fits or predicts. The paper explicitly states the result is 'appropriate for our adopted stellar halo density profile and metallicity distribution,' and Section 5.2 quantifies how alternative literature profiles change L_halo by about 30%, so the authors do not treat the profile as a derived consequence of their method. The metallicty distribution is similarly adopted from the literature (An et al. 2013; Zuo et al. 2017). The calibration on the Galaxia and Bullock-Johnston N-body models uses known true halo luminosities to assess recovery accuracy; this is an external test of the estimator, not a renaming of the target quantity. Self-citations to the Gaia-Sausage interpretation and to earlier density-profile work provide context and priors, but the total luminosity is not defined in terms of the final mass, nor is any fitted parameter relabeled as a prediction. The skeptical concern about the 30% density-profile systematic is an uncertainty assessment, not a circularity; it does not make the derivation equivalent to its inputs. Therefore no circular step is exhibited, and the derivation is self-contained apart from standard astrophysical assumptions that are clearly stated and externally sourced.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

Free parameters are the adopted density profile, metallicity and age distribution, the IMF mass-to-light ratio, and the bin-exclusion threshold; they are not measured in this paper but determine the final number. Axioms include the Gaussian decomposition, the adequacy of the model calibrations, the fiducial density profile and MDF, the isochrone set, and the equality of quality cuts between disc and halo. No invented physical entities are introduced.

free parameters (5)
  • Stellar halo Einasto density profile parameters = n=1.7, Re=20 kpc, q=0.6
    Adopted from Deason et al. (2011) and used in Eq. (2) to volume-correct each colour, magnitude, and sky bin. Fig. 12 shows a roughly 30 percent luminosity spread across literature density profiles, so this choice directly sets the central value.
  • Halo metallicity distribution function = <[Fe/H]> = -1.5, sigma = 0.5
    Used to weight PARSEC isochrones and to compute distances and volume corrections. The right panel of Fig. 12 shows the luminosity falls by about 25 percent if the mean metallicity is -1.2 as suggested by Conroy et al. (2019).
  • Halo age distribution = uniform 10-14 Gyr
    Isochrone weighting assumes all halo stars are old. The assumed age range affects the RGB to total luminosity conversion and the volume correction.
  • Stellar mass-to-light ratio for Kroupa IMF = M*/L = 1.5
    Converts L_halo to M*_halo. Chabrier gives 1.3 and Salpeter gives 2.8, so the reported mass scales linearly with this choice.
  • Robust-bin exclusion threshold = 30 percent recovery error in calibration
    Bins where the Galaxia/BJ05 calibration recovers the true halo RGB count with more than 30 percent error are excluded from the final estimate (Section 3 and Fig. 5). Using all bins lowers L_halo by about 10 percent (Section 4).
assumptions (7)
  • domain assumption The halo and disc proper motion distributions are each approximately 2D Gaussian in every magnitude, colour, and sky bin, so a two-component mixture can separate them.
    Section 3 states the Gaussian approximation is reasonable because the fits are done in small bins. The calibration shows about 30 percent of bins fail the 30 percent recovery criterion, so the approximation is not universally valid.
  • domain assumption The Galaxia and Besancon disc model plus the eleven Bullock and Johnston N-body haloes adequately represent the Milky Way for initializing and calibrating the decomposition.
    Sections 2.1 and 3 use these models to set the XD initialization and to define which bins are reliable. If the real Milky Way disc or halo kinematics differ, the bin exclusion and initialization could bias the result.
  • domain assumption The adopted Einasto density profile from Deason et al. (2011), with n=1.7, Re=20 kpc and q=0.6, represents the true stellar halo density out to 100 kpc.
    Section 4 Eq. (2) uses this profile to compute the total volume. Section 5.2 and Fig. 12 show literature profiles give a roughly 30 percent dispersion around the fiducial luminosity.
  • domain assumption The halo metallicity distribution has <[Fe/H]> = -1.5 with sigma = 0.5, and halo stars have ages uniformly distributed between 10 and 14 Gyr.
    Section 4 uses this MDF and age range to weight PARSEC isochrones. Fig. 12 and the text show the luminosity depends strongly on the adopted <[Fe/H]>.
  • domain assumption PARSEC isochrones with [alpha/Fe] = 0.3, converted via [M/H] = [Fe/H] + 0.2, correctly predict the number of RGB stars per unit luminosity.
    Section 4 uses these isochrones to compute N_RGB/L_sun. MIST and BaSTI models give total stellar masses of 0.85 x 10^9 and 1.1 x 10^9 solar masses, respectively, slightly lower than the fiducial 1.4 x 10^9.
  • domain assumption The data quality cuts (RUWE < 1.4 and BP/RP flux-excess cuts) remove stars from disc and halo equally.
    Section 2.2 states that the authors assume equal effects and compensate by increasing the estimated luminosity by 8 percent. If the cuts remove a larger fraction of halo stars, the correction is wrong.
  • domain assumption The Sagittarius stream mask of 12 degrees and the LMC/SMC exclusion regions remove only the intended contaminants.
    Section 3 uses these masks to exclude Sgr and Magellanic Cloud stars. Including Sgr raises L_halo by about 15 percent, so the mask choice affects the quoted range.

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Cite this review

Pith. "Pith review of The total stellar halo mass of the Milky Way." pith.science (2026). https://pith.science/paper/UPBDIMP4

@misc{pith2026190802763,
  author       = {Pith},
  title        = {Pith review of: The total stellar halo mass of the Milky Way},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UPBDIMP4}},
  note         = {Machine review of arXiv:1908.02763}
}
read the original abstract

We measure the total stellar halo luminosity using red giant branch (RGB) stars selected from Gaia data release 2. Using slices in magnitude, colour and location on the sky, we decompose RGB stars belonging to the disc and halo by fitting 2-dimensional Gaussians to the Galactic proper motion distributions. The number counts of RGB stars are converted to total stellar halo luminosity using a suite of isochrones weighted by age and metallicity, and by applying a volume correction based on the stellar halo density profile. Our method is tested and calibrated using Galaxia and N-body models. We find a total luminosity (out to 100 kpc) of L_halo = 7.9 +/- 2.0 x 10^8 L_Sun excluding Sgr, and L_halo = 9.4 +/- 2.4 x 10^8 L_Sun including Sgr. These values are appropriate for our adopted stellar halo density profile and metallicity distribution, but additional systematics related to these assumptions are quantified and discussed. Assuming a stellar mass-to-light ratio appropriate for a Kroupa initial mass function (M*/L = 1.5), we estimate a stellar halo mass of M*_halo = 1.4 +/- 0.4 x 10^9 M_Sun. This mass is larger than previous estimates in the literature, but is in good agreement with the emerging picture that the (inner) stellar halo is dominated by one massive dwarf progenitor. Finally, we argue that the combination of a ~10^9 M_Sun mass and an average metallicity of <[Fe/H]> ~ -1.5 for the Galactic halo points to an ancient (~10 Gyr) merger event.

Figures

Figures reproduced from arXiv: 1908.02763 by the authors.

Figure 1
Figure 1. Colour magnitude diagrams (CMDs) and proper motion distributions for the Galaxia models and GDR2. In all panels, only stars with high latitude (|b| > 30◦ ) are shown. Panel (a): Apparent magnitude vs. colour for stars in Galaxia. Here, the halo component is from an N-body model (Halo-7, see main text). The dashed lines indicate the colour range used in this work to select red giant branch stars. Photometric and astr… view at source ↗
Figure 2
Figure 2. Slices in Galactic longitude and latitude used to fit the disc/halo components. Each bin is fitted separately. The colour coding indicated is adopted throughout the paper. The Sgr leading and trailing arms are shown. When Sgr is excluded, stars lying within 12 deg of these tracks are omit￾ted. Stars in close proximity to the LMC and/or SMC are excluded in our analysis. namics of the globular cluster population in ac… view at source ↗
Figure 3
Figure 3. The mean (first and third panels) and dispersion (second and fourth panels) of the Galaxia model proper motions in Galactic coordinates as a function of GBP − GRP colour. Blue and red lines indicates the halo and disc components, respectively. Different magnitude bins are shown with different linestyles, and each row shows a different bin in Galactic longitude. The sequences are very similar for bins above and below… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Left columns: Extreme deconvolution (XD) fits to the Galaxia proper motion distributions in bins of GBP − GRP colour. The solid red and blue lines show the true disc and halo distributions, and the dashed lines show the XD fits. Here, we use the true Galaxia model valu…
Figure 5
Figure 5. Figure 5: The estimated number of halo RGB stars in the Galaxia models from the XD fitting (namp) relative to the true number (ntrue) as a function of colour. Here, we have combined results from all eleven BJ05 haloes and show the median and 16/84 percentiles. Each panel indicat…
Figure 6
Figure 6. Figure 6: Left columns: Extreme deconvolution (XD) fits to the GDR2 proper motion distributions in bins of GBP − GRP colour. The dashed red and blue lines show the estimated disc and halo distributions. Here, we use the Galaxia model values to initialize the XD fit. Right column…
Figure 7
Figure 7. Figure 7: The mean (first and third panels) and dispersion (second and fourth panels) of the GDR2 model proper motions in Galactic coordinates as a function of GBP − GRP colour. Blue and red lines indicates the estimated halo and disc components, respectively. Different magnitud…
Figure 8
Figure 8. Figure 8: Top: The relation between total luminosity and number of RGB stars per colour bin. Here, we have used a set of weighted PARSEC isochrones assuming uniform ages in the range 10-14 Gyr, and a metal￾licity distribution with h[Fe/H]i = −1.5, σ([Fe/H]) = 0.5. Bottom: The to…
Figure 9
Figure 9. Figure 9: The estimated (total) stellar halo luminosity as a function of colour. Each panel shows a different magnitude bin. For each colour, magnitude bin, there are 8 bins on the sky. The colour coding is the same as in [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: The estimated luminosity for the Galaxia+N-body haloes rel￾ative to the true values as a function of stellar halo luminosity. Here, the “total” luminosity is defined within 100 kpc. The right-inset panel shows the PDF for the Lhalo,est − Lhalo,true /Lhalo,true values…
Figure 11
Figure 11. Figure 11: The estimated (total) stellar halo luminosity as a function of colour. Each panel shows a different magnitude bin. For each colour, magnitude bin, there are 8 bins on the sky. The colour coding is the same as in [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: Left: The total halo luminosity derived with various stellar halo density profiles relative to the fiducial density profile assumption. Note here we adopt a single isochrone model with age T = 10 Gyr and metallicity [Fe/H]= −1.5. We use the range of density profiles s…
Figure 13
Figure 13. Figure 13: Left: The stellar halo mass fraction (M⋆ halo/M⋆ gal) as a function of galaxy mass. We show the simulated Auriga galaxies, and observational estimates from Ghosts (Harmsen et al. 2017), Dragonfly (Merritt et al. 2016), and M31 (Sick et al. 2015; Harmsen et al. 2017). …
Figure 12
Figure 12. Figure 12: AD is supported by a Royal Society University Research Fel￾lowship. AD also acknowledges the support from the STFC grant ST/P000541/1. JLS acknowledge the support of the Leverhulme and Newton Trusts. This work has made use of data from the European Space Agency (ESA) …

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Forward citations

Cited by 1 Pith paper

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    Using a bias-free sample of 4,232 halo giants, the H3 Survey finds the Milky Way's stellar halo has a mean metallicity of [Fe/H] = -1.2 with no gradient between 6 and 100 kpc.

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Pith tools

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