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

The gist: This work provides the first empirical determination of the average dust attenuation law for star-forming galaxies over the redshift range 2 < z < 7 based on JWST spectroscopy.

Methodology and Data

The researchers combined JWST/NIRSpec spectroscopy from the JADES survey with deep multi-wavelength photometry from ASTRODEEP-JWST catalogs to derive the attenuation curve The methodology adopted relies on the empirical approach introduced by Calzetti et al. (1994) and refined by Battisti et al. (2016), which uses the relation between nebular reddening and stellar continuum reddening This approach allows for a direct spectroscopic constraint on the average attenuation law of star-forming galaxies in the early Universe The analysis starts with 4086 targets available in the JADES DR3 release, selecting 584 sources with available Hα and Hβ fluxes After crossmatching with photometric catalogs, they found 504 objects spanning a redshift interval of z ∼ 0.6 − 6.9

Derivation of the Attenuation Law

The selective attenuation curve is derived by dividing the mass selected sample into four bins of Balmer optical depth τlB and constructing average spectral templates The selective attenuation curve is defined as Qn,r(λ) = τn,r(λ) / ∆τlB, where ∆τlB = τlB,n − τlB,r Using the four stacked spectral templates constructed in Sect. 5.3, they derived the wavelength-dependent selective attenuation curve Qeff(λ) This effective curve Qeff(λ) is well described by a third-order polynomial over 0.16 µm ≤ λ ≤ 1.14 µm

Key Findings on the Attenuation Curve

The resulting attenuation curve spans the rest-frame range 0.16–1.14 µm and is well described by a smooth function The normalization factor RV was derived by extrapolating the long-wavelength behavior and imposing k(λn) = 0 at λn = 2.85 µm, yielding RV = 3.98 ± 0.16 The resulting attenuation law is remarkably consistent with the local starburst attenuation relation of C00, both in slope and in normalization However, the curve appears systematically flatter in the ultraviolet compared to several empirical determinations at intermediate redshift

Physical Interpretations

The difference between their derived curve and previous empirical determinations suggests that the UV region of the selective attenuation curve Qeff(λ) shows a dependence on sSFR, with higher sSFR values corresponding to a flatter Qe f f(λ) The absence of a significant UV bump at 2175 Å in the derived attenuation curve may indicate that the small carbonaceous grains responsible for the bump are either less abundant or more efficiently destroyed in the interstellar medium of high-redshift galaxies This absence is consistent with scenarios where dust in early galaxies is dominated by large grains produced in core-collapse supernova ejecta

Implications for Galaxy Evolution

The results suggest that the ensemble-average attenuation behavior of star-forming galaxies over 2 < z < 7 remains broadly similar from the local Universe up to z ∼ 7 The lack of strong evolution in the attenuation properties suggests that the physical mechanisms regulating dust production and distribution are already established at early cosmic times The similarity of the average curve to the C00 relation and to the average curve of Markov et al. (2024) across 2 < z < 12 may reflect that the C00 curve itself represents an empirical mean attenuation curve for local starburst galaxies Future JWST observations will enable this issue to be explored further by combining spectroscopic constraints on nebular attenuation with spatially resolved imaging and far-infrared measurements

Normalization and Scaling

The scaling factor f, which takes into account the differential attenuation between ionized gas and stellar continuum, is defined so that k(B) − k(V) = 1 The value of f for their average selective attenuation curve is f = 3.778+0.411−0.228 This implies that in systems with higher sSFR the gas is more attenuated than the stars, leading to a systematically higher normalization of the total attenuation curve compared to previous works The final fit of the total attenuation curve is given by k(λ) = f Qeff(λ) + RV

Summary and Conclusions

In this work, they presented the first empirical determination of the average dust attenuation law for massive star-forming galaxies over the redshift range 2 < z < 7 using JWST spectroscopy Their main results can be summarized as finding a positive correlation between the UV continuum slope β and the Balmer optical depth τlB, consistent with expectations The effective curve Qeff(λ) is well described by a third-order polynomial over 0.16 µm ≤ λ ≤ 1.14 µm Their normalization RV = 3.98 ± 0.16 and the resulting attenuation law is remarkably consistent with the local starburst attenuation relation of C00, both in slope and in normalization Overall, their results provide the first direct empirical constraint on the average dust attenuation law of star-forming galaxies across 2 < z < 7 based on JWST spectroscopy

How it works

1. They combine NIRSpec spectra from the JADES survey with deep multi-wavelength photometry from ASTRODEEP-JWST catalogs

2. They use the Balmer decrement, defined as τlB = ln F(Hα)/F(Hβ) 2.75!, to trace dust attenuation in the ionized gas

3. They construct stacked spectral templates by grouping galaxies into bins of increasing dust content and averaging them

4. They derive the selective attenuation curve Qn,r(λ) = τn,r(λ) ∆τlB l, where ∆τlB = τlB,n − τlB,r

1. Gains an empirical method for deriving dust attenuation curves using JWST/NIRSpec spectroscopy combined with ASTRODEEP-JWST photometry to constrain "the average dust attenuation law of star-forming galaxies over the redshift range 2 < z < 7. This allows AI systems to model intrinsic galaxy properties, such as star formation rates, stellar masses, and metallicities," with significantly reduced uncertainty compared to previous indirect methods.

2. Enables robust modeling of galaxy SEDs using a Bayesian framework like Bagpipes by incorporating specific priors such as the delayed-τ model for the evolution of the Star Formation Rate (SFR), i.e. SFR(t) ∝ t exp(−t/τ) for the star formation history. This allows AI to simulate how intrinsic physical processes, like dust attenuation, affect observed spectra across different cosmic epochs.

3. Provides a quantitative measure of dust attenuation by deriving the selective and total attenuation curves through the relation between the reddening of the ionized gas (probed by the Balmer decrement) and the reddening of the stellar continuum. This capability allows AI to distinguish between extinction laws tracing individual sightlines versus those encoding the combined effect of dust and the relative spatial distribution of stars and dust within galaxies.

4. Allows for a systematic assessment of redshift evolution in dust properties by comparing derived curves with previous studies, noting that our curve appears systematically flatter in the ultraviolet compared to intermediate-redshift determinations. This enables AI to identify potential physical drivers, such as differences in dust–star geometry and grain-size distributions, influencing attenuation at high energies.

5. Facilitates the identification of the absence of specific dust features by showing that we find no significant evidence for a 2175 Å UV bump in the average attenuation curve. This allows AI systems to infer physical conditions, such as whether small carbonaceous grains are either not yet abundant or are efficiently destroyed in the interstellar medium at high redshift.

6. Enables the derivation of a normalization factor RV by extrapolating the long-wavelength behavior and imposing k(λn) = 0 at λn = 2.85 µm, yielding a result consistent with the local C00 relation, suggesting that the ensemble-average attenuation behavior of star-forming galaxies remains broadly similar from the local Universe up to z ∼ 7.