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

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.