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Dependence of Multi-band Absolute Magnitudes and Color Indexes of the Tip of Red Giant Branch Stars on Metallicity in the Galactic Globular Clusters

T0 review · 5 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The I-band tip of the red giant branch is a constant candle only below [Fe/H] = -1.2; above it, the tip fades with metallicity, pushing the TRGB-calibrated Hubble constant to 70.86 ± 1.2 ± 0.9 km/s/Mpc.

desk verdict Low-metallicity M_I is solid, but the high-metallicity trend is mostly dust, not metallicity, and the abstract gets the sign wrong. read the letter →

arxiv 2502.03705 v2 pith:CCMGLHEA submitted 2025-02-06 astro-ph.SR astro-ph.GA

Zhenzhen Shao , Shu Wang , Biwei Jiang , Xiaofeng Wang , Zhishuai Ge , Haichang Zhu This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords tipoftheredgiantbranchglobularclustersmetallicitydistancescaleHubbleconstantGaiaDR3near-infraredphotometrystandardcandle
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

This paper asks whether the standard candle used for extragalactic distances, the tip of the red giant branch (TRGB), is truly independent of a star's metal content. By selecting 33 Galactic globular clusters and taking the reddest red-giant star in each cluster as the TRGB, the authors find that the I-band absolute magnitude is essentially constant at $-4.017 \pm 0.036 \pm 0.027$ mag for clusters with [Fe/H] $< -1.2$, but becomes fainter as metallicity rises above that threshold. If this is correct, distance measurements to metal-rich galaxies need a metallicity correction, and the value of the Hubble constant inferred from TRGB-calibrated supernovae shifts to $70.86 \pm 1.2 \pm 0.9$ km s$^{-1}$ Mpc$^{-1}$ — roughly one to two units higher than the canonical TRGB-based value. The paper also derives metallicity relations for the optical and near-infrared bands and for three color indexes, with the color relations showing less scatter than the magnitude relations.

What carries the argument

The central object is the tip of the red giant branch (TRGB), the point of maximum luminosity reached by low-mass stars before the helium flash. The key identification is geometric rather than statistical: the TRGB is selected as the reddest star on the red giant branch in the Gaia color-magnitude diagram, justified by the argument that higher opacity in metal-rich stars shifts radiation to longer wavelengths and makes the tip appear as the reddest, not the brightest, point of the branch. This selection feeds magnitude measurements in seven bands, which are then fitted against cluster metallicity with exponential and linear functions to produce relations such as $M_I = 10.47 \exp(3.92[\mathrm{Fe/H}]) - 4.017$.

What would settle it

A direct spectroscopic metallicity measurement of the individual TRGB stars in a dozen metal-rich clusters, together with a check of whether the reddest CMD star is the same star that shows the helium-flash luminosity discontinuity, would settle whether the steep drop in $M_I$ above [Fe/H] > -1.2 is real. Specifically, if the reddest star in clusters like NGC 6838 turns out to be an AGB star or a large-amplitude variable, the claimed metallicity dependence would weaken.

Watch

Extended reading notes

Core claim

The central discovery is that the metallicity independence of the TRGB standard candle holds only in the metal-poor regime. Using the reddest star of the red giant branch in the Gaia $G_{\rm BP}-G_{\rm RP}$ versus $G_{\rm RP}$ diagram as the TRGB, the authors calibrate absolute magnitudes in the $V$, $I$, $G_{\rm BP}$, $G_{\rm RP}$, $J$, $H$, and $K_{\rm S}$ bands for 33 Galactic globular clusters. They find $M_I$ is flat at $-4.017$ mag for [Fe/H] below $-1.2$ and fades with increasing metallicity above it, while the near-infrared magnitudes grow brighter with metallicity and the optical bands grow fainter. Applying the updated $M_I$ to Type Ia supernova calibrations yields $H_0 = 70.86 \pm 1.2 \pm 0.9$ km s$^{-1}$ Mpc$^{-1}$, and the paper argues that metal-rich galaxies such as the LMC require a metallicity correction that earlier TRGB work omitted.

Load-bearing premise

The reddest star on the red giant branch is the true TRGB, and in metal-rich clusters this reddest point is not contaminated by dusty AGB stars, foreground stars, or variable stars.

Editorial extensions

If this is right

  • TRGB distances to galaxies with [Fe/H] > -1.2 need a metallicity correction; ignoring it biases distances because the tip is fainter than assumed.
  • The I-band constancy that makes TRGB a standard candle is restricted to [Fe/H] < -1.2; the corresponding Hubble constant from SNe Ia calibrated with this $M_I$ is $70.86 \pm 1.2 \pm 0.9$ km/s/Mpc.
  • In near-infrared bands the metallicity trend reverses, so $J$ and $K_{\rm S}$ TRGB magnitudes are brighter for metal-rich clusters, consistent with stellar model predictions.
  • Color indexes such as $(G_{\rm BP}-G_{\rm RP})$, $(V-I)$, and $(J-K_{\rm S})$ show lower dispersion with metallicity than the absolute magnitudes, offering alternative calibrators.

Reading between the lines

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

  • If the reddest-star criterion is biased in metal-rich clusters (for example by picking circumstellar dust-enshrouded stars), the steep fading above [Fe/H] > -1.2 may be partly an extinction effect rather than a true luminosity-metallicity relation; the paper's own detection of infrared excess in two metal-rich TRGBs hints at this.
  • The claimed $H_0$ shift of about 1 to 2 km/s/Mpc depends on assuming that TRGB stars in the LMC and similar galaxies have the disk metallicity rather than the halo metallicity; a direct metallicity measurement of the actual TRGB stars used in the SNe Ia calibration would test this.
  • The color-metallicity relations with smaller scatter could serve as a metallicity indicator for partially resolved stellar populations, if calibrated on additional clusters.
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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

5 major / 4 minor

Summary. The paper identifies TRGB stars in 43 (later 33) Galactic globular clusters as the reddest stars in Gaia GBP−GRP versus GRP color-magnitude diagrams, computes absolute magnitudes in the GBP, GRP, V, I, J, H, and KS bands, and fits their dependence on metallicity. The central claim is that MI is nearly constant at −4.017 ± 0.036 ± 0.027 mag for [Fe/H] < −1.2 while becoming fainter for [Fe/H] > −1.2; this calibration is then transformed into H0 = 70.86 ± 1.2 ± 0.9 km/s/Mpc via the Riess et al. (2016) formula. The paper also presents color–metallicity relations and compares the KS-band behavior with stellar models.

Significance. If the low-metallicity MI value holds, it provides a useful TRGB zero point consistent with several independent calibrations and supports the use of TRGB as a standard candle. The claimed high-metallicity trend, if intrinsic, would require corrections to TRGB distances of metal-rich galaxies and would shift H0 by 1–2 km/s/Mpc. However, the high-metallicity portion rests on only six clusters, is partly attributed by the authors themselves to circumstellar dust, and is sensitive to the post-hoc rejection of 10 of 43 candidates. The paper is therefore valuable mainly for the metal-poor calibration and for the multi-band relations, while the headline metallicity correction for metal-rich systems is not yet established.

major comments (5)
  1. [Section 3.6, Eq. (4)] The paper states that 'the fainter TRGB magnitude in the metal-rich stars is most likely caused by circumstellar dust' and that excluding the two TRGBs with infrared excess 'shows that the trend ... slows down.' Yet Eq. (4) and the H0 application use the full fit as an intrinsic metallicity dependence. Please quantify the refit after excluding the two dusty stars, report whether a statistically significant slope remains for [Fe/H] > −1.2, and clearly separate the dust-affected regime from a dust-free metallicity calibration. As written, the recommendation to apply a metallicity correction to metal-rich galaxies conflates extinction/emission by circumstellar dust with a change in TRGB luminosity.
  2. [Abstract] The abstract says 'for [Fe/H] > −1.2, MI is found to become fainter with lower metallicity', but Eq. (4) and the body text state the opposite: higher metallicity corresponds to a fainter (larger) MI. This is a sign error in the abstract and must be corrected to match the actual fit and discussion.
  3. [Section 3.1 and Figure 4] The four gray points are excluded because they deviate by 3σ from the KS-band fit, and then the same fit is reported as the final relation. This is mildly circular: the fit defines the outliers, and the outliers define the fit. The subsequent physical justification (Section 3.4: these stars are warmer and may not have reached the TRGB) is helpful, but the rejection was not originally based on that criterion. Please show the fits with and without each rejected point, demonstrate stability of the high-metallicity slope, and report how many of the six clusters with [Fe/H] > −1.2 drive the effect. Given that one of the four rejected clusters, NGC 6366, is in the high-metallicity regime, the robustness of the high-metallicity claim is not established.
  4. [Section 2 and Section 3.2] The identification of the TRGB as the single reddest star in the CMD is not validated for metal-rich clusters, where AGB contamination and variability are more common. The paper itself finds that 2 of 43 candidates are AGB stars and 4 are large-amplitude variables, and it reports that using the second-reddest star shifts MI by 0.029 mag. Please apply an edge-detection or luminosity-function method to at least a few clusters (e.g., NGC 5904 and a metal-rich cluster) to confirm that the reddest-star criterion indeed selects the RGB tip rather than an AGB or a dusty variable, and quantify how the selection bias varies with metallicity.
  5. [Section 3.3] The derived H0 = 70.86 ± 1.2 ± 0.9 km/s/Mpc is a direct algebraic transform of MI through Eq. 9 of Riess et al. (2016) with only the TRGB magnitude varied; it is therefore a restatement of the calibration and not an independent check. The comparison with the LMC predicted MI = −3.7 mag versus measured −4.04 mag is dismissed on the assertion that previous LMC TRGB measurements drew on metal-poor halo stars, but no evidence for that assertion is provided. Please either remove the H0 discussion or explicitly present it as a sensitivity illustration, and support the LMC metallicity argument with references or data.
minor comments (4)
  1. [Units] The Hubble constant units are written inconsistently as 'kms^{-1}Mpc^{-1}' in the abstract and text; please use consistent spacing, e.g., 'km s^{-1} Mpc^{-1}'.
  2. [Table 1] The notation for excluded stars (asterisk and plus sign) is explained only in the table caption; please clarify in the text of Section 2 that '∗' denotes LPV/AGB removal and '+' denotes the four 3σ outliers, and make clear that the final sample used for fitting has 33 stars.
  3. [Figure 7] The single deviant point NGC 6121 is visible in Figure 7 but not identified in the figure; please label it in the figure so the discussion in Section 3.5 is directly tied to the plot.
  4. [References] Cerny et al. (2020) is cited as 'arXiv' with no arXiv number; Bellazzini et al. (2004) is incomplete. Please complete the reference list for the journal submission.

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity: the central M_I and H0 values are derived from external photometry, distances, and a standard transformation; the only mild self-referential step is a 3-sigma outlier rejection based on the fit itself, which is partly offset by an independent temperature check.

  1. other [Section 3.1, Figure 4 (text near 'In the KS band panel of Figure 4...')]
    "In the KS band panel of Figure 4, there are four gray points that significantly deviate from the trend line. These outliers fall outside the 3 σ range of our fitting and are therefore excluded. The fitting in the other bands or intrinsic colors also eliminates these points."

    The 3-sigma cutoff is computed from the residuals of the very fit that is being constructed; after removing the worst-fitting points, the same functional forms are refit to the surviving 33 stars. Thus the reported residuals and final relations (Eqs. 1-6) are not fully independent of the outlier-selection step. The loop is partially mitigated by the independent argument in Section 3.4 that the excluded stars are warmer and 'may not have reached the TRGB stage', but the statistical criterion itself remains fit-defined. This does not undermine the central metal-poor M_I anchor (-4.017), which is consistent with external calibrations, nor the H0 value, which is a direct transformation of M_I via the Riess et al. (2016) relation rather than a separately fitted input.

full rationale

The paper's main derivation chain is self-contained against external data: TRGB candidates are selected from Gaia DR3 photometry with membership probabilities from Vasiliev & Baumgardt (2021); absolute magnitudes are computed using distances from Baumgardt & Vasiliev (2021), reddening from Harris (2010), and an extinction law from Wang & Chen (2019). The M_I = -4.017 +/- 0.036 +/- 0.027 mag plateau at [Fe/H] < -1.2 is a fitted value, but it is not circularly defined: it is anchored to external photometric and astrometric measurements and agrees with independent previous calibrations (Freedman 2021; Dixon et al. 2023). The reported H0 = 70.86 +/- 1.2 +/- 0.9 km/s/Mpc is a direct application of the Riess et al. (2016) formula to this M_I, so it is a derived quantity rather than a prediction forced by the inputs. The only noticeable self-referential step is the 3-sigma outlier rejection in Section 3.1, where the fit defines which points are excluded before the final fit is made; this is a mild methodological loop but not a load-bearing one, especially because Section 3.4 supplies an independent temperature-based justification for excluding those stars. No load-bearing self-citation, no uniqueness theorem imported from the authors, and no renaming of known results were found. The paper's internal inconsistency about the sign of the high-metallicity trend (abstract vs. text) and the circumstellar-dust interpretation are correctness concerns, not circularity, and therefore do not raise the circularity score.

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

The paper's own contributions are the TRGB identifications and the fitted relations; everything else (distances, metallicities, reddening, extinction law, SNe Ia slope) is imported from external catalogs and papers. The fits carry many free parameters, and the outlier rejection is applied after seeing the relation, so the ledger reflects that the quantitative results are calibrated, not derived.

free parameters (5)
  • a0, a1, a2 in M_I fit (Eq. 4) = 10.47, 3.92, -4.017
    Least-squares fit to 33 globular clusters; the asymptotic value -4.017 is quoted as the constant TRGB magnitude.
  • Coefficients for M_GBP, M_GRP, M_V, M_J, M_KS fits (Eqs. 1-3, 5-6) = See Eqs. 1-6
    All are free parameters fitted to the same 33 clusters; the functional forms are chosen by comparing residuals in Table 2.
  • Coefficients for color-metallicity relations (Eqs. 7-9) = See Eqs. 7-9
    Fitted independently to the 33 TRGB colors.
  • LPV variability cutoff of 0.05 mag = 0.05 mag
    Threshold chosen to exclude four large-amplitude variables; motivated by Anderson et al. (2024) but applied by hand.
  • 3-sigma outlier rejection in the KS band = 3 sigma
    Four points are removed from all bands after exceeding 3 sigma in the KS fit; this is a post hoc selection applied after the relation is defined.
assumptions (5)
  • domain assumption Cluster distances from Baumgardt & Vasiliev (2021) are accurate.
    Used without modification in Section 3.1 to convert apparent magnitudes to absolute magnitudes.
  • domain assumption Metallicities and reddening from Harris (2010) are correct.
    The [Fe/H] values and E(B-V) are taken directly from this catalog in Section 3.1.
  • domain assumption The extinction law of Wang & Chen (2019) applies to all clusters.
    Used in Section 3.1 to deredden all band magnitudes; a different law would shift the absolute magnitude zero points.
  • ad hoc to paper The reddest star in the CMD is the TRGB.
    Central selection rule introduced in Section 2; it replaces the standard edge-detection method because globular clusters lack enough bright RGB stars.
  • domain assumption The SNe Ia slope ax in the Riess et al. (2016) H0 relation is unchanged.
    Used in Section 3.3 to convert the fitted M_I into a Hubble constant; the paper only varies M_I.

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Cite this review

Pith. "Pith review of Dependence of Multi-band Absolute Magnitudes and Color Indexes of the Tip of Red Giant Branch Stars on Metallicity in the Galactic Globular Clusters." pith.science (2026). https://pith.science/paper/CCMGLHEA

@misc{pith2026250203705,
  author       = {Pith},
  title        = {Pith review of: Dependence of Multi-band Absolute Magnitudes and Color Indexes of the Tip of Red Giant Branch Stars on Metallicity in the Galactic Globular Clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CCMGLHEA}},
  note         = {Machine review of arXiv:2502.03705}
}
abstract

The tip of red giant branch (TRGB) stars have attracted intensive attention in recent years because their $I$-band absolute magnitudes, $M_\rm I$, are often used for distance calibration in the Hubble constant measurements because of its almost independence on metallicity ([Fe/H]). However, a discrepancy exists between various studies and the theoretical stellar model predicts dependence of their luminosity on [Fe/H]. Here we present a careful study of the dependence of absolute magnitudes and color indexes on metallicity in optical and near-infrared bands. With the TRGB stars identified in 33 Galactic globular clusters by the reddest color in the $G_{\rm BP}-G_{\rm RP}$ vs. $G_{\rm RP}$ diagram, it is confirmed that $M_\rm I$ is almost constant of $-4.017 \pm 0.036 \pm 0.027$ mag when $[\rm Fe/H]<-1.2$, which would give $H_0=70.86\pm 1.2\pm0.9$ $\rm kms^{-1} Mp c^{-1}$ with this updated luminosity calibration for type Ia supernovae. However, for $[\rm Fe/H]>-1.2$, $M_\rm I$ is found to become fainter with lower metallicity, which would lead to a larger Hubble constant. In the optical $G_{\rm BP}, G_{\rm RP}$ and $V$ bands, the absolute magnitude of TRGB stars tends to increase with metallicity, while in the infrared $J, H$, and $K_{\rm S}$ bands, the variation with metallicity shows an inverse tendency. In addition, the analytical relations of the color indexes with metallicity are presented, which have smaller dispersion than those derived for the corresponding absolute magnitudes.

Figures

Figures reproduced from arXiv: 2502.03705 by the authors.

Figure 1
Figure 1. The color-magnitude diagram of NGC 5904. The green dots represent the stars with over a 50% probability of belonging to cluster, and the black dots are the selected stars with over a 90% probability of belonging to the cluster according to Vasiliev & Baumgardt (2021). The red point is the selected TRGB in this cluster as the reddest star on the red giant branch [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. The CMD of 43 globular clusters, with the red pentagrams in the maps representing our selected TRGBs [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. The variation of absolute magnitude in the GBP and GRP band with metallicity for the 43 TRGB candidates. The red line represents the fitting result, the gray circles and triangle indicate LPVs and AGBs, respectively, with error bars representing the photometric dispersion. The black dots represent the remaining TRGBs, and their error bars represent the photometric errors [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The relations of absolute magnitudes or intrinsic color indexes of TRGBs with [Fe/H]. In the KS band, four TRGBs (gray points) deviate from the fitting trend by 3σ and are therefore removed in all bands. The red line is the fit of the remaining stars (black points). Th…
Figure 5
Figure 5. Figure 5: The relations between Hubble constant (H0) and the I-band absolute magnitudes of TRGBs, as well as [Fe/H]. In the left panel, the red pentagram indicates our finalized H0 value and the corresponding [Fe/H]. In the right panel, the red line represents the H0 obtained fr…
Figure 6
Figure 6. Figure 6: The Teff vs. [Fe/H] diagram of TRGBs. The purple pentagrams, gray triangles, and blue circles are TRGBs with Teff taken from TESS, APOGEE and other observations in the literatures, respectively. The green circles indicate the four excluded sources (see Section 3.1 and …
Figure 7
Figure 7. Figure 7: The J − KS vs. MKS diagram. The TRGB (red square) shows a good linear relation between absolute magnitude and color index, which is in good agreement with the results from various stellar evolution models such as MARCS (blue crosses), PHOENIX (black crosses), PARSEC (b…
Figure 8
Figure 8. Figure 8: Spectral energy distributions of the 33 TRGBs. Two TRGBs with infrared excess are represented by different colored symbols, while the remaining stars are indicated by small gray circles [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.