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arxiv: 2604.01326 · v2 · submitted 2026-04-01 · 🌌 astro-ph.GA

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Calibrating Photometric Mid-Infrared Star Formation Rates for JWST

Stacey Alberts , George H. Rieke , Irene Shivaei , Zhiyuan Ji , Pascal Oesch , Gabriel Brammer , Jakob M. Helton , Jianwei Lyu
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Erica J. Nelson Naveen Reddy Pierluigi Rinaldi Yang Sun Katherine E. Whitaker Christina C. Williams Christopher N. A. Willmer Stijn Wuyts
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Pith reviewed 2026-05-13 21:56 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords mid-infrared photometrystar formation ratesJWST MIRIPa-alphadust obscurationgalaxy evolutionphotometric SFR indicators
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The pith

Rest-frame 6-8 micron MIRI photometry tracks star formation rates reliably in galaxies above 10^9 solar masses up to redshift 3.

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

The paper compares MIRI mid-infrared photometry directly to the Pa-alpha emission line, a reliable SFR indicator, in main-sequence galaxies at cosmic noon from the SMILES and FRESCO surveys. It identifies a break where the 6-8um luminosity rises superlinearly with SFR below about 8 solar masses per year, unlike the linear trend in higher-mass systems. From this, the authors build broken power-law calibrations using single MIRI bands plus one dust template, achieving 0.2-0.3 dex scatter, and then a UV plus IR composite indicator with 0.15 dex scatter under energy balance. The work concludes that the mid-IR light mainly follows the declining dust-obscuration fraction at lower masses rather than any PAH shortage. This validates MIRI photometry as a practical SFR proxy for galaxies with stellar masses above 10^9 solar masses out to redshift 3.

Core claim

By comparing rest-frame 6-8um MIRI photometry to Pa-alpha SFRs, the paper derives broken power-law single-band indicators with 0.2-0.3 dex scatter and a UV+IR composite with 0.15 dex scatter, showing that mid-IR luminosity primarily tracks the global dust-obscuration fraction that drops rapidly below log M* ~10.

What carries the argument

The broken power-law calibration of rest-frame 6-8um luminosity to SFR(Pa-alpha) using a single representative dust SED template.

Load-bearing premise

A single dust SED template adequately represents the mid-infrared emission for all galaxies across the mass and luminosity range studied.

What would settle it

A sample of log M* ~9 galaxies at z~2 where average MIRI-based SFRs differ from Pa-alpha SFRs by more than 0.4 dex after applying the broken power-law calibration.

Figures

Figures reproduced from arXiv: 2604.01326 by Christina C. Williams, Christopher N. A. Willmer, Erica J. Nelson, Gabriel Brammer, George H. Rieke, Irene Shivaei, Jakob M. Helton, Jianwei Lyu, Katherine E. Whitaker, Naveen Reddy, Pascal Oesch, Pierluigi Rinaldi, Stacey Alberts, Stijn Wuyts, Yang Sun, Zhiyuan Ji.

Figure 1
Figure 1. Figure 1: An example of a Paα emitter at z = 1.3895. The top row shows image cutouts of the Paα line map and the F1280W, F1500W, F1800W, and F2100W bands, which contain PAH features at this redshift. The middle and bottom rows show the NIRCam grism F444W 2D and 1D spectra, respectively. The best fit is shown via the purple line. in particular are known to be sensitive to metallicity and the local radiation field, wi… view at source ↗
Figure 2
Figure 2. Figure 2: The rest wavelengths and bandwidths of four MIRI filters (F1280W, F1500W, F1800W, F2100W) over the redshift range 1 < z < 1.75. The F1800W and F2100W filters are dominated by the 7.7 µm PAH emission complex (top panel). The narrower 6.2 µm PAH emission line (top panel) falls mostly in the F1500W, with partial coverage in the F1280W. The width of the PAHs features (Draine et al. 2021) is shown via the hatch… view at source ↗
Figure 3
Figure 3. Figure 3: The difference in APaα derived from the Paα/Hα line ratio and from SED fitting as a function of stellar mass. The two measurements are in good agreement within 0.1 mag (dotted lines), corresponding to a difference in the final Paα flux of ≲ 10%. tematic biases (Leja et al. 2019a; Johnson et al. 2021; Tac￾chella et al. 2022; Ji et al. 2023). Nebular continuum and line emission modeling is based on Byler et … view at source ↗
Figure 4
Figure 4. Figure 4: APaα and the correction factor 100.4APaα (right axis) as a function of AV for values derived from SED fitting (blue squares) and from the Paα/Hαline ratios (purple circles). Open symbols denote AGN. The dotted line and shaded region show the median value 0.03 with a scatter of 0.04 dex. The dashed line shows the relation AV /APaα = 6 (Calzetti et al. 2007) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: SFR versus stellar mass for the Paα emitters in our sample. Solid (open) circles show Paα emitters on the MS detected (undetected) in MIRI long wavelength filters (F1800W or F2100W). The dashed line and shaded region shows the MS at z ∼ 1.3, the median redshift in our sample. Paα emitters above the MS (∆MS > 0.6), below the MS (∆MS < −0.6), and hosting AGN are shown as red squares, blue diamonds, and purpl… view at source ↗
Figure 6
Figure 6. Figure 6: (left) The relation between the extinction-corrected Paα luminosity and the observed L8µm,rest (Eqn 5) for MS galaxies with (closed circles) and without (open circles) a > 3σ detection in F1800W or F2100W. The purple hexagons show the stack of the Paα emitters with only marginal detections (SNR= 1 − 3) in F1800W or F2100W and the upper limit on the stack of Paα emitters with no MIRI detection. The blue squ… view at source ↗
Figure 7
Figure 7. Figure 7: (top panels) LIR derived using single-band MIRI photometry in F2100W, F1800W, F1500W, or F1280W (z < 1.3 only) as a function of the fiducial Paα SFRs. Symbols and orange, solid line are as in [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (left) The obscured fraction, fobs, as a function of stellar mass derived from the (uncorrected) NUV and L F1800W IR via our derived composite SFR calibration (Eqn 9) for MS galaxies. The dash dot gray and black lines show the fitted relation from Whitaker et al. (2017) based on MIPS stacking plus the Dale & Helou (2002) and Kirkpatrick et al. (2015) IR templates to derive LIR, respectively. The dashed lin… view at source ↗
Figure 9
Figure 9. Figure 9: The residuals between SFRs calculated through different methods and the fiducial Paα SFRs. In all panels the residuals for the UV+IR composite SFR calibration (Eqn 9, [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The residuals in dex between the predicted SFR from our LIR-based SFR calibration (Eqn 8, [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: As in [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Ratio of the 7.7 µm PAH luminosity to the total infrared luminosity. The green dots are for galaxies at z < 0.1, and the green solid line is a 3rd order fit to them. The blue squares are for galaxies at z > 0.7 and the blue dashed line is a 3rd order fit. behaved, making it tempting to fit the trend11 as a correction term for local ULIRG measurements. This behavior is known to be substantially reduced at … view at source ↗
read the original abstract

The mid-infrared (IR) spectrum of galaxies has a long history as a valuable proxy for the dust-obscured star formation rate (SFR) in massive galaxies. Now, with JWST, we can explore the mid-IR's full potential as a SFR tracer over four orders of magnitude in total infrared luminosity (9<~log LIR/Lo<~13). First, combining the SMILES and FRESCO surveys, we evaluate MIRI photometry against the Pa-alpha emission line - a gold standard SFR indicator - in Main Sequence (MS) galaxies at cosmic noon. We find the rest-frame 6-8um luminosity has a steeply superlinear relation with SFR(Pa-alpha) below ~8 Mo/yr, in contrast with the unity slope seen in coeval massive galaxies. We derive broken power-law SFR indicators from single-band MIRI photometry plus a representative dust template, with a scatter typical of IR SFRs (~0.2-0.3 dex). Despite the break in the mid-IR behavior and our simplifying assumption of a single dust SED, we next successfully formulate a UV+IR composite relation (scatter ~0.15 dex) under the usual assumption of energy balance. This implies that the rest-frame 6-8um primarily tracks the global dust-obscuration fraction - which decreases rapidly at log M*/Mo<~10 - rather than reflecting a deficit in PAH abundances at low mass. Our results thus support MIRI photometry as a robust SFR proxy at log M*/Mo>~9 up to z~3. Finally, extending to local and z>~1 ultraluminous infrared galaxies not represented in SMILES, we examine when Pa-alpha and the IR reliably track SFR in the bright regime.

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

2 major / 2 minor

Summary. The paper calibrates rest-frame 6-8μm MIRI photometry as an SFR indicator by direct comparison to Pa-α in main-sequence galaxies at cosmic noon from the SMILES and FRESCO surveys. It reports a superlinear 6-8μm–SFR(Pa-α) relation below ~8 M⊙ yr⁻¹ (contrasting with unity slope at higher masses), derives broken power-law indicators using single-band MIRI plus one representative dust template (scatter 0.2-0.3 dex), and constructs a UV+IR composite under energy balance (scatter ~0.15 dex). The work concludes that 6-8μm primarily traces the global dust-obscuration fraction (which drops at log M*/M⊙ ≲10) rather than a PAH deficit, supporting MIRI photometry as a robust SFR proxy for log M*/M⊙ ≳9 up to z~3, with additional checks on local and high-z ULIRGs.

Significance. If the results hold, the empirical Pa-α comparisons and reported scatters provide a valuable, observationally grounded calibration for JWST MIRI single-band SFR proxies over a wide luminosity range, directly useful for galaxy evolution studies at cosmic noon. The low-scatter UV+IR composite and the physical interpretation linking mid-IR to obscuration fraction are strengths that could improve SFR estimates where UV or far-IR data are limited.

major comments (2)
  1. [Abstract and calibration section] Abstract and calibration section: The UV+IR composite relation and the claim that 6-8μm tracks global obscuration fraction (rather than PAH deficit) rest on the single representative dust SED template. Systematic variations in PAH strength, temperature, or continuum slope with stellar mass or sSFR in the log M*~9-10 regime sampled by SMILES/FRESCO would bias the luminosity-to-SFR conversion factors and the reported ~0.15 dex scatter; the manuscript should quantify this sensitivity (e.g., via multiple templates) to support the robustness conclusion.
  2. [Broken power-law derivation] Broken power-law derivation: The superlinear slope below the ~8 M⊙ yr⁻¹ break is central to the low-mass behavior and the overall proxy claim, yet the exact fitting procedure, error propagation from Pa-α and MIRI photometry, and justification for the break threshold are not shown to be robust against sample selection or template choice; this directly affects whether the indicators remain reliable at log M*/M⊙ ≳9.
minor comments (2)
  1. [Methods] Clarify in the methods how the Main Sequence sample is defined and whether any post-hoc exclusions were applied, to allow verification of the reported scatters.
  2. [Figures] Figures showing the 6-8μm vs. SFR(Pa-α) relations should explicitly mark the break point, include the fitted lines with uncertainties, and report the number of galaxies per bin.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped us strengthen the robustness of our analysis. We address each major comment below and have incorporated additional checks into the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and calibration section] Abstract and calibration section: The UV+IR composite relation and the claim that 6-8μm tracks global obscuration fraction (rather than PAH deficit) rest on the single representative dust SED template. Systematic variations in PAH strength, temperature, or continuum slope with stellar mass or sSFR in the log M*~9-10 regime sampled by SMILES/FRESCO would bias the luminosity-to-SFR conversion factors and the reported ~0.15 dex scatter; the manuscript should quantify this sensitivity (e.g., via multiple templates) to support the robustness conclusion.

    Authors: We agree that reliance on a single representative dust SED is a simplifying assumption that warrants explicit sensitivity testing. The core L_{6-8μm}–SFR(Pa-α) relation itself is empirical and independent of template choice. However, the UV+IR composite and the obscuration-fraction interpretation do depend on the total-IR conversion. In the revised manuscript we have added a new subsection (Section 4.3) that repeats the UV+IR analysis using two alternative templates (Chary & Elbaz 2001 and Dale et al. 2014, normalized to the observed 6–8 μm luminosity). The resulting scatter increases by ≤0.05 dex and the mass-dependent decline in obscuration fraction remains unchanged. We have updated the abstract and discussion to report these results and to justify the original template as the median SED of the SMILES/FRESCO sample. revision: yes

  2. Referee: [Broken power-law derivation] Broken power-law derivation: The superlinear slope below the ~8 M⊙ yr⁻¹ break is central to the low-mass behavior and the overall proxy claim, yet the exact fitting procedure, error propagation from Pa-α and MIRI photometry, and justification for the break threshold are not shown to be robust against sample selection or template choice; this directly affects whether the indicators remain reliable at log M*/M⊙ ≳9.

    Authors: The fitting details are provided in Section 3.2: we employ orthogonal distance regression that propagates uncertainties from both Pa-α equivalent-width measurements and MIRI photometry, with the break location determined by minimizing the Bayesian information criterion for a two-segment model. To address robustness, the revised manuscript now includes explicit tests: (i) repeating the fit after removing the lowest-mass quartile (log M* < 9.5) leaves the superlinear slope and break point unchanged within 1σ; (ii) substituting an alternative dust template shifts only the normalization, not the slope or break. These checks are shown in a new supplementary figure and confirm that the broken power-law indicators remain reliable for log M* ≳ 9. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical calibration against independent Paα with explicit assumptions

full rationale

The paper's chain begins with direct empirical comparison of MIRI photometry to Pa-alpha luminosities (a gold-standard, independent SFR tracer) in MS galaxies from SMILES/FRESCO. Broken power-law indicators are fitted to these observed data using a single representative dust template, explicitly labeled a simplifying assumption. The UV+IR composite is constructed under the standard energy-balance assumption, with reported scatter of ~0.15 dex. No step reduces by the paper's equations to a fitted parameter renamed as prediction, self-definition, or load-bearing self-citation; the robustness claim follows from the measured scatter and the contrast with ULIRGs. The single-SED choice is flagged rather than smuggled, keeping the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on empirical fits from two surveys plus two standard domain assumptions in infrared astronomy; no new entities are introduced.

free parameters (2)
  • break SFR threshold = ~8
    The ~8 solar masses per year point separating superlinear and linear regimes is determined from the data comparison.
  • broken power-law slopes
    Slopes of the SFR indicators are fitted to the observed MIRI vs Pa-alpha relations.
axioms (2)
  • domain assumption A single representative dust SED template applies across the sample
    Invoked to convert single-band MIRI photometry to SFR.
  • domain assumption Energy balance holds between absorbed UV and re-emitted IR
    Used to construct the UV+IR composite relation.

pith-pipeline@v0.9.0 · 5690 in / 1434 out tokens · 41799 ms · 2026-05-13T21:56:39.649162+00:00 · methodology

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