EMU/GAMA: Refining Dust Extinction Corrections for Hα Luminosity Functions Using Radio-Based Calibration

Abstract

We present a novel approach to correcting H$α$ luminosity functions for dust extinction by calibrating against radio-based star formation rates (SFRs), using data from the Evolutionary Map of the Universe (EMU) and Galaxy and Mass Assembly (GAMA) surveys. Accurate dust correction is essential for deriving SFRs from rest-frame UV-optical emission lines, particularly as the \textit{James Webb Space Telescope} extends such measurements to galaxies at $z>5$. While a luminosity dependence of dust obscuration has long been recognised, our method exploits the empirical relationship between obscured (H$α$) and unobscured (radio) SFRs to provide a dust correction that can be applied where traditional spectroscopic techniques, e.g. Balmer line based approaches, are unavailable. We apply the SFR based dust correction to 25 published H$α$ luminosity functions spanning $0<z<8$, and derive corresponding star formation rate densities (SFRDs). Adopting the locally calibrated H$α$--radio relation ends up with an overestimate of the cosmic SFRD by more than two orders of magnitude at $z\gtrsim1$. Motivated by the luminosity dependent relation in the local Universe, we introduce a new model where the luminosity dependence of the dust obscuration decreases with increasing redshift. This approach can reproduce observed SFRDs across cosmic time. These results highlight the potential of a radio-based calibration for dust correction, where a luminosity dependent correction would need to decline in strength with increasing redshift. This implies that the dust content or distribution in galaxies at early epochs differs substantially from that in the local Universe.

Figures (5)

• Figure 1: The BPT diagram, which uses the [OIII]/H$\beta$ and [NII]/H$\alpha$ emission line ratios, classifies galaxies as star-forming galaxies (SFGs), active galactic nuclei (AGNs), or composite sources. SFGs, represented by pink stars, lie below the dashed blue Kauffmann line; AGNs, represented by orange circles, are positioned above the solid blue Kewley line; and composite sources, shown as yellow diamonds, are located between the two diagnostic lines. These sources are drawn from the EMU and GAMA catalogues and were processed as described in § \ref{['sec:Data']}.
• Figure 2: The relationship between H$\alpha$ and $1.4$ GHz radio tracers of star formation. Four models are shown: the solid line is the best-fit relation to the local EMU-GAMA SFG sample, while the dashed line marks the 1:1 case, where H$\alpha$ and radio SFRs would be equal, making the 1:1 line the dust free line. The dotted and dot-dashed lines represent proposed interim models. For each model, the redshift interval over which its dust-corrected results align with the published SFRD measurements from Figure \ref{['fig:CSFD']} is indicated. The truncated equation for each model is shown here for reference but can be seen in full in Table \ref{['Tab: Models']}. The calibration from hopkins_toward_2001 is shown in orange.
• Figure 3: Published luminosity values, corrected for dust obscuration using the fitted SFR relation from Figure \ref{['fig:SFRComp']} (coloured symbols), along with the corresponding best-fit Schechter functions (dashed line), shown across six redshift bins. Where possible, raw luminosity data from these sources have been used; if necessary, published dust corrections were removed. Our fitted SFR-based dust correction relation (Model 4) was applied instead and new LFs were refitted, where the shaded region depicts the 95% confidence interval from 100,000 MCMC iterations. See §\ref{['Sec:lums']} for relevant published H$\alpha$ luminosity data.
• Figure 4: Cosmic SFRDs derived from dust-corrected luminosity functions using each of our four dust correction models, shown in Table \ref{['Tab: Models']}. These results are compared with recent dust-corrected measurements from covelo-paz_h_2024 and chiang2025cosmicinfraredbackgroundtomography in dashed and dot-dashed linesrespectively. The madau_cosmic_2014 relation is also shown in solid grey for comparison. Published dust-corrected star formation rate density (SFRD) values are shown in grey, with markers indicating the observational tracer: UV (circles), H$\alpha$ (triangles), infrared (squares), and radio (diamonds). The published data is compiled in Table \ref{['Tab:SFRD_combined']}.
• Figure 5: The SFRD from a spline fit to the step-function model for the SFRD evolution, illustrating the evolving dust correction derived from the fitted relationship between H$\alpha$ and radio SFR tracers. Here the symbols are the same as in Figure \ref{['fig:CSFD']}. The colors of the spline fit correspond to those in Figure \ref{['fig:CSFD']} for the model proposed in each redshift range, from the 'local Universe dust content' scenario of Model 4 to the 'dust-free' scenario of Model 1. The data points where the spline fit changes model are shown by the overlayed markers, where the marker type represents the model as shown in Figure\ref{['fig:CSFD']}.