The observed total star formation rate function up to z \sim 6: complementary UV and IR contributions and comparison with state-of-the-art galaxy formation models

TL;DR

This study combines UV and IR star formation rate functions up to redshift 6 to provide a comprehensive view of galaxy star formation, revealing the limitations of models at high redshift and the importance of both contributions.

Contribution

It presents the first combined total star formation rate function up to z~6, integrating UV and IR data, and compares these with state-of-the-art galaxy formation models.

Findings

UV and IR SFRFs are mostly complementary, covering different SFR ranges.

Models agree with observations at z<2.5 but underestimate high SFR galaxies at higher redshifts.

UV and IR alone cannot fully account for the total star formation rate density across all redshifts.

Abstract

We investigate how the obscured IR-derived and the dust-corrected UV star formation rate functions (SFRFs) compare with each other, and with predictions from state-of-the-art theoretical models of galaxy formation and evolution. We derive the IR-SFRF from the ALMA A$^3$COSMOS survey, by converting the IR luminosity functions (IR-LFs) into SFRF after correcting for AGN contribution. Similarly, we obtain the UV SFRFs from literature UV LFs, corrected for dust-extinction. First, we fit the two SFRFs independently via a MCMC approach, then we combine them to obtain the first estimate of the total SFRF out to $z \sim 6$. Finally, we compare this SFRF with the predictions of a set of theoretical models. We derived the UV (dust-extinction corrected, from literature UV-LFs) and IR SFRFs (from Herschel and ALMA IR-LFs) at $0.5 < z < 6$ , finding that they are mostly complementary, covering different ranges in star formation rate (SFR$ < 10-100$ M$_{\odot}$yr$^{-1}$ for the UV-corrected and SFR$ > 100$ M$_{\odot}$yr$^{-1}$ for the IR). From the comparison of the total SFRF with model predictions we find an overall good agreement at $z < 2.5$, with increasing difference at higher redshifts, with all models missing the galaxies that are forming stars with the highest SFRs. We finally obtained the UV (dust-corrected), IR and total star formation rate densities (SFRDs), finding that there are no redshift ranges where UV and IR alone are able to reproduce the whole total SFRD.