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arxiv: 2606.11594 · v1 · pith:6IKKJA45new · submitted 2026-06-10 · 🌌 astro-ph.SR · astro-ph.GA· astro-ph.IM

Empirical colour--effective temperature relations in the SDSS system from IRFM temperatures of GALAH and APOGEE stars

Zenghua Zhou , Luca Casagrande , Xiaobin Zhang , Jianping Xiong , Jiao Li , Yanjun Guo , Zhanwen Han , Xuefei Chen This is my paper

Pith reviewed 2026-06-27 08:44 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.GAastro-ph.IM
keywords stellar effective temperatureempirical colour-Teff relationsSDSS photometry2MASS photometryIRFMGALAHAPOGEEdwarfs and giants
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The pith

Empirical relations connect SDSS and 2MASS colors to effective temperature at 30-50 K precision on an IRFM scale from GALAH and APOGEE stars.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper calibrates updated empirical relations between stellar effective temperature and color indices from SDSS ugriz plus 2MASS JHKs photometry. It uses a combined sample of 3902 GALAH and 2535 APOGEE stars whose temperatures come from the homogeneous InfraRed Flux Method. Low-order polynomial fits with 3-sigma clipping produce both color-only and color-metallicity versions separately for dwarfs and giants. Long-baseline indices such as (g-Ks)0 and (g-z)0 reach internal precisions of roughly 30-50 K. The resulting calibrations supply a consistent way to estimate Teff from photometry when spectra are unavailable.

Core claim

The central claim is that empirical colour-Teff relations derived from SDSS and 2MASS photometry on an IRFM reference scale from GALAH and APOGEE stars deliver a homogeneous framework for temperature estimates, with performance that varies by colour index and reaches 30-50 K internal precision for the best long-baseline colours.

What carries the argument

Low-order polynomial models fitted with iterative 3-sigma clipping to the combined GALAH-APOGEE sample of dereddened colour indices versus IRFM Teff, applied separately for dwarfs, giants, and with or without metallicity terms.

Load-bearing premise

The IRFM effective temperatures derived for the GALAH and APOGEE stars form a homogeneous and sufficiently accurate reference scale against which the colour relations are calibrated.

What would settle it

A set of stars with independent Teff measurements from spectroscopy or asteroseismology, SDSS and 2MASS photometry, and no known zero-point issues that systematically deviate from the fitted relations by more than 50 K would falsify the claimed internal precision.

Figures

Figures reproduced from arXiv: 2606.11594 by Jianping Xiong, Jiao Li, Luca Casagrande, Xiaobin Zhang, Xuefei Chen, Yanjun Guo, Zenghua Zhou, Zhanwen Han.

Figure 1
Figure 1. Figure 1: Distribution of the combined GALAH and APOGEE samples in the Teff–log g plane, colour-coded by metallicity [Fe/H]. The dashed line indicates the adopted temperature￾dependent separation between dwarfs and giants. Stars within the buffer region around this boundary (shown in grey) are ex￾cluded from the calibration but retained for validation purposes. 10 1 10 2 10 3 Distance (pc) 0 100 200 300 400 Number D… view at source ↗
Figure 2
Figure 2. Figure 2: Distance distributions of the dwarf (green solid line) and giant (red dashed line) samples derived from Gaia parallaxes. Dwarfs are predominantly nearby, while giants probe larger dis￾tances. Corrections to the SDSS photometric zero-points are de￾rived as described in Zhou et al. (2026) and summarised in Section 2.3, with Gaia photometry used only to establish the reference sample. Here it suffices to say … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between effective temperatures derived from SDSS-based IRFM and the Gaia-based IRFM reference scale. Red and blue points represent the GALAH and APOGEE samples, respectively. The mean residual is ∼ −8 K, with no sig￾nificant trend as a function of Teff. provide precise stellar parameters, in particular metallicities, allowing us to explicitly account for metallicity effects in the colour–Teff re… view at source ↗
Figure 4
Figure 4. Figure 4: Metallicity distribution functions for the dwarf (blue solid line) and giant (orange dashed line) samples used in the calibration. • For Teff ≤ 5300 K, log g = 4.1; • For Teff ≥ 6000 K, log g = 3.5; • For 5300 < Teff < 6000 K, the boundary is linearly interpolated. To reduce cross-contamination between the two populations, a buffer region of width ∆ log g = 0.10 dex is introduced around this boundary. Star… view at source ↗
Figure 5
Figure 5. Figure 5: Colour-metallicity–Teff relations for dwarfs in a few selected long-baseline (top panels) and optical (bottom) indices. Points are colour-coded by metallicity [Fe/H]. Continuous curves correspond to the best-fitting polynomial relations evaluated at fixed percentiles (10, 50 and 90) of the sample metallicity distribution. Residual are defined as ∆Teff = T IRFM eff − T cal eff . Dashed horizontal lines show… view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Residual diagnostics for dwarfs (top row) and giants (bottom row). Each column corresponds to a colour index: (g − Ks)0 (left), (g − J)0 (centre), and (g − r)0 (right), representative of long-baseline, intermediate, and purely optical regimes. Scatter plots show residuals (∆Teff) as a function of metallicity, with their distribution shown by histograms. MNRAS 000, 1–10 (2026) [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 8
Figure 8. Figure 8: compares our calibrations with those of Pinson￾neault et al. (2012) and Huang et al. (2015) using SDSS colours only. Overall, good agreement is found with Pinson￾neault et al. (2012), with differences typically within ∼50 K, whereas offsets easily exceeding 100 K are appear in the (g − r)0 calibration of Huang et al. (2015) [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison between the colour–Teff relations derived in this work and the metallicity-dependent calibrations of Huang et al. (2015). The left-hand panels are for dwarfs and the right-hand panels for giants, respectively. The relations are shown for long-baseline optical–infrared colours (g − J)0, (g − H)0, and (g − Ks)0, evaluated at [Fe/H] = 0.0. Residuals are shown in the lower panels. calibrations, whil… view at source ↗
read the original abstract

Reliable estimates of stellar effective temperature ($T_{\mathrm {eff}}$) are fundamental to stellar population studies and Galactic astrophysics. However, the majority of stars observed in modern large-scale photometric surveys lack spectroscopic measurements, making empirical colour--$T_{\mathrm {eff}}$ relations essential tools. In this work, we present updated empirical colour--$T_{\mathrm {eff}}$ calibrations based on Sloan Digital Sky Survey (SDSS) $ugriz$ photometry combined with 2MASS $JHK_{\mathrm s}$ data. Effective temperatures are determined on a homogeneous InfraRed Flux Method (IRFM) scale using a combined sample of 3902 GALAH and 2535 APOGEE stars with high-quality photometry and well-characterised atmospheric parameters. Using this dataset, we establish empirical relations between $T_{\mathrm {eff}}$ and colour indices constructed from SDSS and 2MASS combinations. We provide both colour--metallicity--$T_{\mathrm {eff}}$ and colour--$T_{\mathrm {eff}}$ relations for dwarfs and giants. The calibrations are derived using low-order polynomial models with iterative $3\sigma$ clipping. Their performance depends on the adopted colour index, with long-baseline colours such as $(g-K_{\mathrm s})_0$ and $(g-z)_0$ achieving internal precisions of $\sim$30--50~K. Comparisons with previous calibrations show general agreement, with differences attributable to sample selection, photometric zero-points, and functional form. The resulting relations provide a homogeneous and internally consistent framework for estimating $T_{\mathrm {eff}}$ from SDSS and 2MASS photometry alone, and are well suited for application to large photometric surveys lacking spectroscopic information.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript derives empirical colour-Teff relations in the SDSS ugriz + 2MASS JHKs system by fitting low-order polynomials (with iterative 3σ clipping) to a combined sample of 3902 GALAH and 2535 APOGEE stars whose effective temperatures were placed on a homogeneous IRFM scale. Separate relations are provided for dwarfs and giants, both with and without explicit metallicity dependence; the authors report internal precisions of ~30-50 K for long-baseline colours such as (g-Ks)0 and (g-z)0, compare the new fits to earlier calibrations, and conclude that the relations supply a homogeneous framework for Teff estimation from photometry alone.

Significance. If the reference IRFM temperatures are shown to be internally consistent across the two surveys, the work supplies updated, survey-ready colour-Teff calibrations that could be directly applied to large photometric catalogues lacking spectroscopy. The approach follows standard empirical methods and the reported precisions are competitive with prior work, but the practical utility hinges on the homogeneity of the anchor scale.

major comments (1)
  1. [Abstract] Abstract: the central claim that the relations provide an 'internally consistent framework' rests on the assertion that the IRFM Teff values for the GALAH and APOGEE subsamples form a single homogeneous scale. No quantitative test for zero-point offsets (e.g., via overlapping stars, survey-specific photometric zero-points, or reddening assumptions) is described; any residual offset would shift the zero-points of every fitted polynomial and undermine the claimed internal consistency.
minor comments (1)
  1. [Abstract] The abstract does not state the Teff, log g, or [Fe/H] ranges spanned by the final sample; this information is needed to judge the domain of applicability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address the major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the relations provide an 'internally consistent framework' rests on the assertion that the IRFM Teff values for the GALAH and APOGEE subsamples form a single homogeneous scale. No quantitative test for zero-point offsets (e.g., via overlapping stars, survey-specific photometric zero-points, or reddening assumptions) is described; any residual offset would shift the zero-points of every fitted polynomial and undermine the claimed internal consistency.

    Authors: The referee correctly identifies that the manuscript does not include an explicit quantitative test for zero-point offsets between the GALAH and APOGEE samples. Although both sets of IRFM temperatures were derived using the same underlying method and calibrated to a common scale (as detailed in Section 2), we agree that demonstrating the absence of systematic offsets would strengthen the claim of homogeneity. We will revise the manuscript to include such a test, for example by identifying any stars in common between the two surveys and comparing their Teff values, as well as examining potential differences arising from photometric zero-points or reddening corrections. This addition will be incorporated in a revised version of the paper. revision: yes

Circularity Check

0 steps flagged

No circularity: direct empirical polynomial fits to external IRFM Teff scale

full rationale

The derivation consists of fitting low-order polynomials (with 3σ clipping) to Teff values obtained via the IRFM on independent GALAH and APOGEE spectroscopic samples, then presenting the resulting colour-Teff relations. No step reduces by the paper's own equations to a quantity defined in terms of the fitted coefficients; the relations are the output of the fit, not an input. No self-citation is invoked to justify uniqueness or to smuggle an ansatz, and the central claim of providing photometric Teff estimators does not collapse to a self-referential loop. The input Teff scale is treated as given external data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the input IRFM temperatures are homogeneous across the two surveys and that the photometric sample after quality cuts is representative; the polynomial coefficients themselves are free parameters fitted to the data.

free parameters (1)
  • polynomial coefficients for each color-Teff relation
    Low-order polynomial coefficients fitted by least-squares to the color-Teff data after iterative 3-sigma clipping.
axioms (2)
  • domain assumption IRFM temperatures from GALAH and APOGEE form a homogeneous reference scale
    Invoked when combining the two surveys to derive the relations.
  • domain assumption Reddening corrections and photometric zero-points are accurate for the selected stars
    Required to construct dereddened colors used in the fits.

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discussion (0)

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