arxiv: 2604.09763 · v1 · submitted 2026-04-10 · 🌌 astro-ph.GA

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A first empirical derivation of the average dust attenuation law at 2<z<7

Giulia Rodighiero , Gaia Edes Esposito , Daniela Calzetti , Pietro Benotto , Michele Catone , Paolo Cassata , Giovanni Gandolfi , Laura Bisigello

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Stefano Carniani Alvio Renzini Irene Shivaei Benedetta Vulcani Annagrazia Puglisi

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:33 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords dust attenuationstar-forming galaxieshigh-redshift galaxiesJWST spectroscopyBalmer decrementattenuation curvestarburst galaxies

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The pith

The average dust attenuation law for star-forming galaxies at 2<z<7 follows the same slope and normalization as the local starburst relation.

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

The paper measures the wavelength-dependent dust attenuation affecting the light from distant galaxies by stacking their spectra and photometry according to the strength of their Balmer lines. This produces an average curve from the ultraviolet through the near-infrared that can be used to correct observed galaxy properties for dust effects. The authors find the curve is smooth, lacks a prominent 2175-angstrom bump, and matches the well-known Calzetti starburst law derived from nearby galaxies. This empirical result supplies a practical template for interpreting observations of early-universe galaxies where direct dust measurements remain scarce.

Core claim

Using NIRSpec spectroscopy and multi-wavelength photometry for a mass-selected sample of 120 galaxies at 2<z<7, the authors stack spectral energy distributions in bins of Balmer optical depth and recover a selective attenuation curve that spans rest-frame 0.16-1.14 microns, is described by a smooth function with normalization R_V=3.98, and is consistent in both slope and normalization with the local starburst attenuation law.

What carries the argument

Binning galaxies by measured Balmer decrement (H-alpha/H-beta) and stacking their spectral energy distributions to empirically derive the wavelength-dependent selective attenuation curve.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Galaxy evolution models could adopt the local starburst curve as a default dust template out to z=7 without large systematic error in average star-formation-rate estimates.
The absence of a strong UV bump suggests that dust grain properties in these high-redshift systems are on average similar to those in local starbursts.
Future surveys could test whether the same average law holds for lower-mass galaxies or for galaxies selected by different criteria such as Lyman-alpha emission.

Load-bearing premise

That the Balmer decrement measured in integrated spectra represents the average dust attenuation experienced by the stellar continuum light across the entire galaxy without major geometric or selection biases.

What would settle it

Finding that attenuation curves recovered from individual galaxy spectra or from different stacking methods differ substantially in slope or normalization from the stacked Balmer-decrement result.

Figures

Figures reproduced from arXiv: 2604.09763 by Alvio Renzini, Annagrazia Puglisi, Benedetta Vulcani, Daniela Calzetti, Gaia Edes Esposito, Giovanni Gandolfi, Giulia Rodighiero, Irene Shivaei, Laura Bisigello, Michele Catone, Paolo Cassata, Pietro Benotto, Stefano Carniani.

**Figure 1.** Figure 1: Distribution of SFR(Hα) as function of M⋆, color-coded by z; the blue line shows the Main Sequence (MS) at the mean redshift of the sample (Popesso et al. (2022)); the error bar in the lower-right corner indicates the typical uncertainty on the two quantities [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Figure 2: UV β slope as a function of the Balmer optical depth, τ l B . The color-bar represents the redshift z of each target. The black error-bar represents the mean error on the parameters β and τ l B ; the red line is our best linear fit (see details in the main text). parameters range dust AV [mag] 0, 6 nebular emission logU -4, -1 delayed-τ model age [Gyr] 0.001, 15 τ [Gyr] 0.01, 10 metallicity [Z⊙] 0, 2.5 mas… view at source ↗

**Figure 3.** Figure 3: Dependence of stellar mass on Balmer optical depth, τ l B (left), and on the UV continuum slope, β (right), for the sample of 301 galaxies at 1.86 < z < 7. The filled brown circles mark the sources included in the derivation of the attenuation law. The histogram on top of the left panel indicates the τ l B bins used to compute the corresponding average templates [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Specific star formation rate (based on Hα) as a function of the Balmer optical depth τ l B for the galaxies in our sample. Each point represents an individual source, while the error bar in the upper-left corner indicates the typical uncertainty on the two quantities. No strong correlation is observed, indicating that the range of attenuation probed by the sample is not primarily driven by variations in … view at source ↗

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 5.** Figure 5: Average spectral energy distributions (SEDs) in τ l B bins. The gray region shows the 1σ dispersion of the sample spectra in each bin. The vertical dotted lines delimit the central wavelength range that is common to all targets in the sample; the number of spectra contributing to each bin within this region is indicated. The outer regions correspond to wavelengths covered by more than 50% of the sources. T… view at source ↗

**Figure 7.** Figure 7: Effective selective attenuation curve Qeff(λ) derived in this work for galaxies at 2 < z < 7 (red dashed line; grey shaded region shows the 1σ dispersion of the fits obtained from the set of Qn,r(λ) templates shown in [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 9.** Figure 9: Average spectral templates in the four τ l B bins after extending the wavelength coverage using JWST/MIRI photometry. Colored points show the observed MIRI fluxes associated with the galaxies contributing to each bin, while the solid lines represent the stacked NIRSpec spectra normalized at 5500 Å. The inclusion of MIRI data allows the average SEDs to be traced up to ∼ 2.2 µm, reducing the extrapolation r… view at source ↗

**Figure 10.** Figure 10: Determination of RV from the long-wavelength extrapolation of the attenuation curve. The blue line shows the polynomial fit to f Qeff(λ) obtained using only the NIRSpec-based attenuation curve, while the red line includes the extension provided by the MIRI photometry. The vertical dashed line marks λ = 2.85 µm, where the condition k(λ) = 0 is imposed to derive RV . The comparison illustrates how the incl… view at source ↗

**Figure 11.** Figure 11: Comparison between the total attenuation curve derived in this work and previous attenuation and extinction relations. Left panel: attenuation curves expressed as k(λ) = Aλ/E(B − V) as a function of wavelength. Right panel: the same curves shown as A(λ)/A(V) versus 1/λ. Our result for galaxies at 2 < z < 7 (red dashed line) is compared with attenuation curves from C00, Battisti et al. (2016), Battisti et… view at source ↗

read the original abstract

Dust attenuation strongly affects the observed spectral energy distributions of galaxies, introducing significant uncertainties in the derivation of key physical properties such as star formation rates, stellar masses, and metallicities. While attenuation curves have been extensively studied in the local Universe and at intermediate redshift, direct spectroscopic constraints at earlier cosmic epochs have remained limited prior to JWST. We aim to derive the average dust attenuation law of star-forming galaxies over the redshift range 2<z<7. We combine NIRSpec spectroscopy from the JADES survey with deep multi-wavelength photometry from the ASTRODEEP catalogs. Using a mass-selected sample (log(M_\star/M_\odot) > 9) of 120 galaxies with reliable Balmer decrement (Ha/Hb), we construct stacked spectral energy distributions in bins of Balmer optical depth and derive the selective attenuation curve following the empirical methodology introduced by Calzetti et al. (2000). The wavelength coverage is further extended toward the near-infrared using MIRI photometry. The resulting attenuation curve spans the rest-frame range 0.16-1.14mu and is well described by a smooth function. We derive a normalization factor R_V=3.98, finding that the average attenuation law is consistent with the local starburst relation in both slope and normalization. Compared to several determinations at intermediate redshift, however, our curve appears systematically flatter in the ultraviolet. We find no significant evidence for a 2175A UV bump in the average attenuation curve. Our results provide the first empirical determination of the average dust attenuation law for star-forming galaxies at 2<z<7 based on JWST spectroscopy. Despite the diversity of attenuation properties observed in individual systems, the ensemble-average behavior remains consistent with the local starburst relation.

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.

Desk Editor's Note private letter to a colleague

This paper gives the first JWST spectroscopic empirical average dust attenuation curve at 2<z<7 by stacking Balmer decrements, landing close to the local Calzetti law but with the usual transferability questions.

read the letter

The main takeaway is that this work supplies the first empirical average dust attenuation law at 22. A reader focused on attenuation laws or high-redshift galaxy properties will get concrete numbers to compare against. It has enough new observational content and direct relevance to merit a serious referee rather than a desk reject, though the review should press on the robustness of the stacking against high-z geometry effects. I would send it to peer review.

Referee Report

2 major / 1 minor

Summary. The paper claims to provide the first empirical derivation of the average dust attenuation law for star-forming galaxies at 2<z<7. Using NIRSpec spectroscopy from the JADES survey combined with ASTRODEEP multi-wavelength photometry, the authors select a mass-limited sample of 120 galaxies (log M_*/M_⊙ > 9) with reliable Balmer decrements, bin them by Balmer optical depth, construct stacked SEDs (extended to MIRI), and derive the selective attenuation curve following the empirical Calzetti et al. (2000) stacking methodology. They report a normalization R_V=3.98, find the curve consistent with the local starburst law in slope and normalization, note a flatter UV slope than at intermediate redshifts, and report no significant 2175 Å bump.

Significance. If the central result holds, the work is significant because it supplies the first spectroscopy-driven empirical constraint on the ensemble-average dust attenuation law at these redshifts, directly addressing uncertainties in high-z SFR, stellar-mass, and metallicity estimates. The data-driven approach, use of JWST line ratios for binning, and extension to near-IR wavelengths via MIRI are clear strengths that build on an established local methodology while providing a falsifiable, observationally anchored curve.

major comments (2)

[§2] §2 (sample selection and binning): The exact boundaries of the Balmer optical depth bins and the full error-propagation procedure through the stacking and selective-attenuation calculation are not specified. These details are load-bearing for reproducing the reported R_V=3.98 and for assessing whether the derived curve shape is statistically robust.
[§4–5] §4–5 (results and discussion): The manuscript does not quantitatively address whether the assumption that the integrated Balmer decrement traces the average stellar-continuum attenuation remains valid at 2<z<7 given possible differences in dust geometry (clumpy distributions, differential attenuation between H II regions and older stars). This assumption is central to interpreting the recovered curve as an unbiased ensemble average and to the claim of consistency with the local starburst law.

minor comments (1)

[Abstract] Abstract: The S/N or quality threshold used to define 'reliable' Balmer decrements for the 120-galaxy sample is not stated; adding this would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and recommendation for minor revision. The comments highlight important points for reproducibility and interpretation, and we address each below.

read point-by-point responses

Referee: [§2] §2 (sample selection and binning): The exact boundaries of the Balmer optical depth bins and the full error-propagation procedure through the stacking and selective-attenuation calculation are not specified. These details are load-bearing for reproducing the reported R_V=3.98 and for assessing whether the derived curve shape is statistically robust.

Authors: We agree that these details are necessary for full reproducibility. In the revised manuscript we will explicitly list the Balmer optical depth bin boundaries in Section 2 and provide a complete description of the error propagation, including how measurement uncertainties on individual Balmer decrements and photometry are incorporated into the stacked SEDs and the final selective attenuation curve. revision: yes
Referee: [§4–5] §4–5 (results and discussion): The manuscript does not quantitatively address whether the assumption that the integrated Balmer decrement traces the average stellar-continuum attenuation remains valid at 2<z<7 given possible differences in dust geometry (clumpy distributions, differential attenuation between H II regions and older stars). This assumption is central to interpreting the recovered curve as an unbiased ensemble average and to the claim of consistency with the local starburst law.

Authors: We acknowledge that the validity of this assumption at high redshift is not quantitatively tested in the current version. A fully quantitative assessment would require detailed radiative-transfer simulations beyond the scope of this empirical study. In the revised manuscript we will add a dedicated paragraph in Section 5 that discusses the potential impact of clumpy dust geometries and differential attenuation between nebular and stellar light, cites relevant literature on high-z dust distributions, and clarifies the limitations while noting that the observed consistency with the local starburst curve provides empirical support for the ensemble-average result. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is data-driven from new observations

full rationale

The paper bins a new mass-selected sample of 120 galaxies (log M*>9) at 2<z<7 by observed Balmer optical depth from NIRSpec Ha/Hb, constructs stacked multi-band SEDs (including MIRI), and computes the selective attenuation curve directly from the differential extinction between bins using the standard empirical procedure of Calzetti et al. (2000). The output R_V=3.98 and the full 0.16-1.14 micron curve shape are therefore measured quantities, not parameters that were fitted to define the result or imported via self-citation. The subsequent comparison to the local starburst law is a post-hoc consistency check and does not enter the measurement chain. No step reduces by construction to its own inputs, and the central empirical claim rests on independent JWST spectroscopy and photometry rather than on any prior result by the same authors.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The measurement rests on standard astrophysical assumptions about dust and line emission rather than new postulates; the main additions are the new high-z data and the derived curve parameters.

free parameters (2)

R_V normalization factor = 3.98
Derived from the stacked data as the scaling that matches the selective attenuation curve to the observed optical depth.
Balmer optical depth bin boundaries
Chosen to divide the sample into groups for stacking; affects the resulting average curve.

axioms (2)

domain assumption The empirical methodology of Calzetti et al. (2000) for deriving selective attenuation from Balmer-binned stacks applies without modification at 2<z<7.
The paper explicitly follows this local-universe technique on the new JWST sample.
domain assumption The integrated Balmer decrement traces the average dust attenuation experienced by the stellar continuum light.
This underpins the binning step and the conversion from line optical depth to continuum attenuation.

pith-pipeline@v0.9.0 · 5675 in / 1622 out tokens · 64689 ms · 2026-05-10T16:33:16.399338+00:00 · methodology

discussion (0)

Reference graph

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