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An independent estimate of H(z) at z = 0.5 from the stellar ages of brightest cluster galaxies

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Pith's one-line read Using only the oldest, most massive galaxies in galaxy clusters, a cosmic-chronometer analysis of their 4000 Å break measures the expansion rate at z = 0.5 as 72.1 ± 33.9 (stat) ± 7.3 (syst) km/s/Mpc, independent of any cosmological model.

desk verdict Careful first BCG-only cosmic chronometer measurement; the metallicity systematic is understated, but the paper deserves serious review. read the letter →

arxiv 2506.03836 v1 pith:VHTNKGJJ submitted 2025-06-04 astro-ph.CO astro-ph.GA

S. Ilani Loubser , Adebusola B. Alabi , Matt Hilton , Yin-Zhe Ma , Xin Tang , Narges Hatamkhani , Catherine Cress , Rosalind E. Skelton
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S. Andile Nkosi
This is my paper · ORCID
classification astro-ph.COastro-ph.GA MSC 85A40
keywords galaxies:evolutionclusters:generaldistancesandredshiftscosmologicalparameterscosmicchronometersD4000nindexbrightestclustergalaxiesHubbleconstanttension
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 measure the expansion rate of the Universe at redshift $z=0.5$ by a route that assumes no cosmological model: the cosmic chronometer method, which reads the differential ageing of passively evolving galaxies from the strength of the 4000 Å break. The new ingredient is that the sample contains only brightest cluster galaxies (BCGs), the oldest and most massive galaxies, in a homogeneous, mass-selected cluster sample, which shrinks the systematic-error budget to about 10%. The result is $H(z=0.5)=72.1 \pm 33.9\ (\mathrm{stat}) \pm 7.3\ (\mathrm{syst})\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, where the 47% statistical uncertainty dominates. A sympathetic reader would care because this is an independent, cosmology-free probe of the Hubble constant that sits between measurements from the early universe and the local distance ladder, even though its current error bars are too large to arbitrate the Hubble tension.

What carries the argument

The load-bearing object is the narrow-band 4000 Å break index $\mathrm{D4000_n}$ — the ratio of continuum flux in the 4000--4100 Å band to that in the 3850--3950 Å band — which grows almost linearly with the age of a passively evolving stellar population. Its redshift derivative is measured from the stacked BCG spectra. The conversion from $\mathrm{D4000_n}$ to age is carried by the calibration factor $A(Z,M)$, the slope of the index--age relation computed from stellar population synthesis models, evaluated at a stellar metallicity of $1.5\,Z_\odot$. The key identity is $H(z) = -A(Z,M)/(1+z) \cdot dz/d\mathrm{D4000_n}$, which separates the statistically dominated observed slope from the model-dependent systematic calibration.

What would settle it

Obtain high signal-to-noise spectra of $z \approx 0.5$ BCGs with stellar population grids that extend beyond the current model boundary at $[M/H] = 0.4$ and measure the metallicity from gravity- and iron-sensitive indices; a recovered solar metallicity would shift the quoted $H(z)$ from 72.1 to 56.2 km s$^{-1}$ Mpc$^{-1}$. Alternatively, enlarge the BCG sample to roughly 2500 galaxies — which the authors estimate would cut the slope error to about 2% — and check whether the fitted $d\mathrm{D4000_n}/dz$ still equals $-0.45 \pm 0.21$ within the reduced error.

Watch

Extended reading notes

Core claim

The central discovery claimed is a cosmic-chronometer measurement of $H(z)$ built exclusively from brightest cluster galaxies. From 53 BCGs in massive, SZ-selected clusters at $0.3 < z < 0.7$, the authors stack spectra into 12 narrow redshift bins and measure the $\mathrm{D4000_n}$ index. A linear fit gives $d\mathrm{D4000_n}/dz = -0.45 \pm 0.21$, and stellar population models calibrate the index-age conversion at $A(Z,M) = 0.0498\ \mathrm{Gyr}^{-1}$ for $Z = 1.5\,Z_\odot$. Combining these through $H(z) = -A/(1+z) \cdot dz/d\mathrm{D4000_n}$ yields $H(z=0.5) = 72.1 \pm 33.9\ (\mathrm{stat}) \pm 7.3\ (\mathrm{syst})\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$; projecting to $z=0$ with a CMB+BAO prior on matter density gives $H_0 = 54.6 \pm 25.7\ (\mathrm{stat}) \pm 5.5\ (\mathrm{syst})\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$. The authors stress that the measurement is cosmology-independent apart from the FLRW metric and that its value is consistent, within its large errors, with both early- and late-universe probes.

Load-bearing premise

The load-bearing premise is that the BCGs' stellar metallicity is firmly super-solar, about $1.5\,Z_\odot$; if the true metallicity were solar, the central value of $H(z)$ would drop from 72.1 to 56.2 km s$^{-1}$ Mpc$^{-1}$, a shift about seven times larger than the quoted 3% metallicity systematic.

Editorial extensions

If this is right

  • If the central value stands, it gives a genuinely model-independent check on the expansion rate at $z=0.5$, directly comparable with future surveys and with model predictions in a regime between the local distance ladder and the CMB.
  • Demonstrating that a BCG-only sample reduces systematic errors to about 10% implies that the same approach, scaled to larger samples, could make cosmic chronometers competitive with distance-ladder and CMB precision without sharing their systematics.
  • The projected $H_0 = 54.6 \pm 25.7\ (\mathrm{stat}) \pm 5.5\ (\mathrm{syst})\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, while low, remains statistically consistent with both the CMB value of about 67 and the Cepheid distance-ladder value of about 73, so the measurement currently constrains neither side of the Hubble tension.
  • The 47% statistical uncertainty is the limiting factor; the authors quantify that reducing it to about 2% requires more than 50 stacked spectra per redshift bin, i.e., more than 2500 BCGs, which dedicated surveys could supply.
  • The work furnishes a data point at $z=0.5$ that can be combined with other cosmic-chronometer measurements to trace the expansion history across a wider redshift range than any single current sample covers.

Reading between the lines

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

  • An implication the authors leave implicit: the quoted central value carries the assumption that BCG metallicities sit at about 1.5 times solar; if a direct metallicity measurement instead found roughly solar abundances, the same data would report $H(z) \approx 56\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, so the numerical claim is only as good as the metallicity prior.
  • A testable extension of the authors' own logic: compare the slope of the BCG-only $\mathrm{D4000_n}$--redshift relation with the slope from more heterogeneous early-type galaxy samples over the same redshift range; a significant difference would indicate population mixing biases in standard cosmic-chronometer measurements.
  • A forward-looking consequence: once large BCG samples (thousands of spectra) reduce the statistical error below the roughly 10% systematic floor, further progress in stellar population synthesis models and libraries — rather than more data — becomes the binding constraint on cosmic-chronometer precision.
  • If the statistical error can be shrunk enough, the same BCG-only strategy could also provide a cosmology-independent test of the assumed FLRW geometry by comparing $H(z)$ at several redshifts against the integral constraints from BAO and supernovae.
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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

2 major / 4 minor

Summary. The paper uses the cosmic chronometer method with a sample of 53 brightest cluster galaxies from SZ-selected ACT clusters, observed with SALT, to measure H(z) at z = 0.5. The 53 BCGs are stacked into 12 redshift bins between z = 0.33 and z = 0.65, and a linear fit to the measured D4000n-z relation gives a slope m = dD4000n/dz = -0.45 ± 0.21. The slope is converted to H(z) using a stellar population calibration A(Z,M) = 0.0498 Gyr^-1 at Z = 1.5 Zsun, yielding H(z=0.5) = 72.1 ± 33.9 (stat) ± 7.3 (syst) km/s/Mpc. Using a Planck+BAO prior for Omega_m and Omega_Lambda, the projected H0 is 54.6 ± 25.7 ± 5.5 km/s/Mpc. The paper argues that the BCG-only sample reduces systematics, especially the stellar metallicity dependence, and that the measurement is statistically limited.

Significance. The paper provides a new, transparently analysed cosmic chronometer data point at z = 0.5 from a homogeneous, SZ-selected BCG sample. The statistical analysis is clear: TLS and MCMC fits to the D4000n-z relation agree, the D4000n measurements are made with a public tool on stacked spectra, and the paper includes explicit checks against young stellar components via the Ca II H/K ratio and emission-line inspection. If the stellar population calibration is accepted, this is a useful addition to the CC compilation and a step toward using BCGs to reduce population-mixing systematics. The current statistical uncertainty is large, so the main value is methodological rather than competitive for the Hubble tension.

major comments (2)
  1. [§5.1, Eq. (5), Table 2] The quoted 3% systematic error for stellar metallicity in Eq. (5) is not supported by the paper's own Table 2. Moving from the adopted Z = 1.5 Zsun to Z = 1.0 Zsun changes A(Z,M) from 0.0498 to 0.0388 and H(z) from 72.1 to 56.2 km/s/Mpc, a 22% downward shift, roughly seven times the quoted 3% metallicity term. The pPXF metallicity estimates in Section 3.1 and Appendix B saturate at the model boundary [M/H] = 0.4, and the paper itself cautions that these estimates should be interpreted with care. The convergence of A(Z,M) at high metallicity visible in Figure 8 protects only the high-Z side; the low-Z side is not constrained by the data. Because this calibration choice sets the central value, the systematic budget in Eq. (5) needs to be revised, for example by marginalising over a physically motivated prior on Z or by quoting H(z) as a range spanning Z = 1.0 to 2.0 Zsun (roughly 56 to 74.5 km/s/Mpc).
  2. [§5.2, Abstract, Conclusions] The abstract and conclusions state that using BCGs 'significantly reduced the systematic errors to 10%' and minimised the metallicity dependence of the method. This is inconsistent with the 22% sensitivity to the adopted metallicity shown in Table 2. Even if the total systematic error remains smaller than the 47% statistical error, the central value is not robust to the unmeasured metallicity, so the claimed 3% metallicity contribution and the associated wording should be corrected. The revised systematic budget, or a range of central values, should be reported before the final result in Eq. (6) is quoted as the main measurement.
minor comments (4)
  1. [§2.3] The text moves from 96 BCGs to 78 BCGs without an explicit sentence that the 18 BCGs at z > 0.7 are excluded before the stacking step; please state this clearly so the reader can follow the sample selection.
  2. [Table 1] Stack 8 has a very large uncertainty on the Ca II H/K ratio and an unusually high velocity dispersion with a large error, and the passive-galaxy check is inconclusive for this stack; a sentence on whether excluding or down-weighting stack 8 changes the fitted slope would be useful.
  3. [§5.4 and Fig. 10] The H0 projection uses Planck+BAO priors, so the statement that the result is 'consistent with both CMB and Cepheid measurements' should be qualified by noting that the comparison with the CMB is not fully independent; the paper is transparent about this in Section 5.4, but the abstract and Fig. 10 could state it more prominently.
  4. [Fig. 8 and Table 2] The notation for metallicity is inconsistent: the x-axis of Fig. 8 uses absolute Z, while the text and Table 2 use Z/Zsun; please unify the notation to avoid ambiguity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the H(z) estimate combines an independently measured D4000n-z slope with an external stellar-population calibration; the metallicity systematic is a robustness concern, not a circular step.

full rationale

The central claim (Eq. 6) is not equivalent to its inputs by construction. H(z) at z=0.5 is computed from Eq. (2) as -A(Z,M)/(1+z) * dz/dD4000n. The first factor is the fitted slope m = dD4000n/dz = -0.45 ± 0.21 (Eq. 4), obtained from 12 stacked BCG spectra (Section 3.2.3). The second factor is the stellar-population calibration A(Z,M) = 0.0498 Gyr^-1 at Z = 1.5 Zsun (Table 2), taken from MILES/Padova models and measured on mock spectra with the same PyLick procedure (Section 4). Neither input is defined in terms of the target Hubble parameter, and the calibration is external to the paper's own data. The systematic error budget (Section 5.1) combines literature estimates from Moresco et al. (2020) and model-to-model scatter; the calibration is varied over models, libraries, and IMFs rather than fitted to the target. The only cosmology-dependent step is the H0 projection in Section 5.4, which explicitly adopts Planck+BAO priors for Omega_m and Omega_Lambda; this is a disclosed model-dependent extrapolation, not part of the H(z) measurement, and the paper does not present it as an independent H0 constraint. Self-citations, such as Loubser et al. (2009) and Groenewald & Loubser (2014), support ancillary statements about BCG metallicities and star formation histories, but they are corroborated by external references (Lidman et al. 2012; Bellstedt et al. 2016; Contreras-Santos et al. 2022) and by the paper's own pPXF fits, so they are not the sole load-bearing evidence. A robustness caveat is that the quoted 3% metallicity systematic (Section 5.1) is not strongly supported by Table 2 if BCG metallicities were near solar, since H(z) would drop to 56.2 km/s/Mpc; however, this is an uncertainty-budget concern, not a circular derivation.

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

The central claim depends on one fitted slope and two chosen model quantities: the D4000n-age calibration A(Z,M) and the assumed BCG metallicity of 1.5 Z_sun. No new physical entities are introduced. The Planck+BAO Omega values are external priors used only for the H0 projection.

free parameters (3)
  • D4000n-z slope m = -0.45 ± 0.21 (dimensionless)
    Fitted to 12 stacked BCG spectra via MCMC and TLS (Eq. 4); H(z) is inversely proportional to this slope.
  • Stellar population calibration A(Z,M) = 0.0498 Gyr^-1 at Z = 1.5 Z_sun
    Chosen from MILES/Padova/Chabrier model grid; H(z) is directly proportional to A. Other models give different A, contributing to the systematic error.
  • Assumed BCG stellar metallicity = 1.5 Z_sun (nominal)
    Adopted for the central value; pPXF fits suggest [M/H] = 0.4 (2.5 Z_sun) at the model boundary. Using 1.0 or 2.0 Z_sun shifts H(z) between 56 and 75 km/s/Mpc.
assumptions (5)
  • standard math FLRW metric relation H(z) = -1/(1+z) dz/dt
    Eq. 1; minimal geometric assumption of the cosmic chronometer method.
  • domain assumption The 12 stacked BCG spectra represent a single passively evolving population with negligible recent star formation
    Validated by H/K < 1.2 and absence of emission lines (Section 3.2.1), but relies on the sample being homogeneous.
  • domain assumption D4000n-age relation is linear over D4000n 1.9-2.3 for the chosen models
    Section 4.2; the calibration A(Z,M) is the slope of a straight-line fit to model outputs.
  • domain assumption Stellar population synthesis models (MILES+Padova, BC03, M11, BC16) reliably map age and metallicity to D4000n
    Section 4; systematic spread across models is used to set the 6-7% model/library error, but the models themselves are not independently calibrated here.
  • domain assumption Flat LambdaCDM with Omega_m = 0.3122, Omega_Lambda = 0.6878 (Planck+BAO prior)
    Section 5.4; used only for projection to H0, not for the H(z) measurement.

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Pith. "Pith review of An independent estimate of H(z) at z = 0.5 from the stellar ages of brightest cluster galaxies." pith.science (2026). https://pith.science/paper/VHTNKGJJ

@misc{pith2026250603836,
  author       = {Pith},
  title        = {Pith review of: An independent estimate of H(z) at z = 0.5 from the stellar ages of brightest cluster galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VHTNKGJJ}},
  note         = {Machine review of arXiv:2506.03836}
}
abstract

Several cosmological observations (e.g., Cosmic Microwave Background (CMB), Supernovae Type Ia, and local distance ladder measurements such as Cepheids) have been used to measure the global expansion rate of the Universe, i.e., the Hubble constant, $H_{0}$. However, these precision measurements have revealed tensions between different probes that are proving difficult to solve. Independent, robust techniques must be exploited to validate results or mitigate systematic effects. We use the Cosmic Chronometer (CC) method, which leverages the differential age evolution of passive galaxies, to measure $H(z)$, without any assumption of the underlying cosmology. Unlike previous CC studies, we used only brightest cluster galaxies (BCGs), the oldest and most massive galaxies in the Universe, to construct a pure and homogeneous sample. In this work we used a sample of 53 BCGs in massive, Sunyaev-Zel'dovich selected galaxy clusters (0.3 $< z <$ 0.7) with Southern African Large Telescope (SALT) spectroscopic observations. We used optical spectra to measure D4000$_{\rm n}$ of the BCGs to obtain a new direct measurement of $H(z) = 72.1 \pm 33.9(\rm stat) \pm 7.3$(syst) km s$^{-1}$ Mpc$^{-1}$ at $z=0.5$. By using BCGs, we significantly reduced the systematic errors to 10% by minimising the stellar mass and metallicity dependence of the method. The dominant uncertainty, and limitation for our study, is statistical, and we need larger, homogeneous samples of the oldest, most massive galaxies. By using the $Planck$+BAO prior of $\Omega_{m}$ and $\Omega_{\Lambda}$, the projected Hubble constant is $H_{0}$ = $54.6 \pm 25.7(\rm stat) \pm 5.5$(syst) km s$^{-1}$ Mpc$^{-1}$, consistent with both CMB and Cepheid measurements.

Figures

Figures reproduced from arXiv: 2506.03836 by the authors.

Figure 1
Figure 1. A specstack stacked spectrum of five BCGs at z = 0.36 for illustration. The black line is the resultant stacked spectrum, and the blue indicate the 1σ error. The coloured lines in the back￾ground show the five individual, lower S/N, spectra. The SALT chip gaps can be seen at approximately 1/3 and 2/3 of the wave￾length range, and these regions are masked during measurements or full-spectrum fitting. all individual s… view at source ↗
Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Left: The BCG D4000n measurements are shown in blue for the 12 stacked spectra. In the background we also show individual D4000n measurements for early-type galaxies from Moresco et al. (2012) with black crosses. Our BCGs lie at the top end of the data as expected. The line and its surrounding dark gray and shallow gray regions are the best-fitting value of the slope and intercept parameters from the Markov chain Mo… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: We illustrate a mock spectrum generated using the MILES models (Vazdekis et al. 2010) with BaSTI isochrones (Hi￾dalgo et al. 2018) for a stellar metallicity of Z=0.03 and age of 14 Gyr. From the mock spectra we measure D4000n following the identical procedure in PyLick…
Figure 6
Figure 6. Figure 6: The BC16/MILES models for Chabrier and Salpeter IMFs at Z = 0.02 and 0.05, to illustrate the negligible effect of the IMF. 4 6 8 10 12 Age (Gyr) 1.7 1.8 1.9 2 2.1 2.2 2.3 D4000n 1 2 3 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: The D4000n – age relation for MILES models with Padova isochrones and a Chabrier IMF for metallicities Z = 0.008, Z = 0.019 (solar metallicity) and Z = 0.030 (indicated by 1, 2, and 3, respectively) fitted with lines as described in Section 4.2. the D4000n – age relati…
Figure 9
Figure 9. Figure 9: H(z) derived from the cosmic chronometers method at different redshifts. We use the data compiled by Moresco et al. (2022), and add the data from Tomasetti et al. (2023). Our estimate using only BCGs is shown with a blue star at z = 0.5. We indicate whether the measure…
Figure 10
Figure 10. Figure 10: H0 from all probes, similar to the compilation in Verde et al. (2019), supplemented with measurements from the detailed compilation presented in Di Valentino et al. (2021) (their figure 1), and updated with the latest measurements. We add our estimate in blue, and we …

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    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.