Evolution of the infrared luminosity function and its corresponding dust-obscured star formation rate density out to z~6

TL;DR

This work advances the understanding of infrared galaxy evolution by constructing the FIR luminosity function (LF) out to $z \sim 6$ using a novel combination of faint-end stacking (via the $L_{\rm IR}$–$M_{\star}$ relation) and bright-end ALMA data (AS2UDS). The LF is modeled with a Schechter function, fixing the faint-end slope at $\alpha=-0.26$ and tracing redshift evolution through $L_{\star} \propto z^{1.38}$ and a double-power-law $\Phi_{\star}(z)$ that remains constant up to $z\approx 2.24$ before steeply declining as $z^{-4.95}$. Integrating the evolving LF yields the dust-obscured SFR density, $\rho_{\rm SFR}$, which peaks around $z\sim 2$ and diminishes toward $z\sim 6$, with the DSFG contribution dropping to $<25\%$ by that epoch and UV-visible star formation becoming dominant at $z>4$. The results favor a dust-poor early Universe scenario and provide important constraints for galaxy formation models, illustrating the growing importance of combining deep, wide FIR data with high-resolution ALMA follow-ups to map star formation across cosmic time.

Abstract

We present a new determination of the evolving far-infrared galaxy luminosity function (FIR LF) and the resulting inferred evolution of dust-obscured star-formation rate density (SFRD) out to redshift z~6. To establish the evolving co-moving number density of FIR-bright objects, we make use of the high-resolution ALMA follow-up study (AS2UDS), of the JCMT SCUBA-2 Cosmology Legacy Survey (S2CLS) sub-mm imaging in the UKIDSS UDS survey field. In order to estimate the contributions of faint/low-mass sources we implement a method in which the faint-end of the IR LF is inferred by stacking (in stellar mass and redshift bins) the optical/near-infrared samples of star-forming galaxies into the appropriate FIR Herschel and sub-mm JCMT maps. Using this information we determine the faint-end slope of the FIR LF in two intermediate redshift bins (where it can be robustly established) and then adopt this result at all other redshifts. The evolution of the characteristic luminosity of the galaxy FIR LF, L*, is found to be increase monotonically with redshift, evolving as z^1.38+-0.07, while the characteristic number density is well fitted by double power-law function, constant at z<2.24 and declining as z^-4.95+-0.73 at higher redshifts. The evolution of the corresponding dust-obscured star-formation rate density was then calculated and is here compared with the results from a number of recent studies in the literature. Our analysis confirms that dust-obscured star-formation activity dominates SFRD at cosmic noon, but then becomes progressively less important with increasing redshift: while dusty star-forming galaxies are still found out to the highest redshifts explored here, UV-visible star formation dominates at z>4, and dust-obscured activity contributes <25% of SFRD by z~6.

Figures (8)

• Figure 1: Infrared luminosity-stellar mass relation determined through stacking the optical/near-IR mass-complete samples of McLeod_2021 in the FIR Herschel and JCMT maps, adopted from Koprowski_2024. The stacked $L_{\rm IR}$ values are used here to determine the faint-end portion of the IR LF, as explained in Section \ref{['sec:lf1']}.
• Figure 2: Infrared luminosity function found in this work at different redshift bins, as indicated in the plot. The faint-end data (Table \ref{['tab:fe']}), determined through stacking (see Section \ref{['sec:lf1']} for details) is depicted by black points with horizontal error bars. The remaining bright-end data (Table \ref{['tab:be']}), found using the ALMA follow-up data of the S2CLS UKIDSS UDS sources (AS2UDS; Stach_2019) are also shown (Section \ref{['sec:lf2']}). The best-fit Schechter functions of Equation \ref{['eq:sch']} are represented by dashed black lines with the gray area representing $1\sigma$ uncertainties. The faint-end slope was determined at two low redshift bins and the more accurate result, $\alpha=-0.26\pm 0.11$, adopted at all the remaining redshifts, as explained in Section \ref{['sec:lf4']}.
• Figure 3: Redshift evolution of the Schechter function parameters found in this work. The values determined at each redshift (Table \ref{['tab:pars']}) are shown as black points, with the best fit functions (Equations \ref{['eq:parsf']} and \ref{['eq:parsfv']}) depicted by black solid lines. For details see Section \ref{['sec:lf4']}.
• Figure 4: Redshift evolution of the functional form of the IR LF found in this work (Equations \ref{['eq:sch']}, \ref{['eq:parsf']} and \ref{['eq:parsfv']}).
• Figure 5: Functional form of the infrared luminosity function found in this work (black solid line). For comparison we show the individual data found in other literature studies (Magnelli_2013Gruppioni_2013Wang_2019Dudzeviciute_2020Traina_2024 and Fujimoto_2024). For detailed discussion see Section \ref{['sec:lf4']}.