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

Aims.
We investigated how the obscured IR-derived and 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. 

Methods.
We derived the IR SFRF from the ALMA A³COSMOS survey by converting the IR luminosity functions (IR LFs) into SFRFs after correcting for the active galactic nucleus (AGN) contribution. Similarly, we obtained the UV SFRFs from UV LFs in the literature, corrected for dust-extinction. First, we fit the two SFRFs independently via a Markov chain Monte Carlo (MCMC) approach, then we combined them to obtain the first estimate of the "totala"SFRF out to z6. Finally, we compared this SFRF with predictions of a set of theoretical models. Results. We derive the UV and IR SFRFs at 0.5 < z < 6, using dust-extinction-corrected UV LFs from the literature and IR LFs from Herschel and ALMA. We find that the two functions are largely complementary, covering different ranges in star formation rate (SFR < 10-100 M_˙yr^-1 for the UV-corrected, and SFR > 100 M_˙yr^-1 for the IR). From the comparison of the total SFRF with model predictions, we find overall good agreement at z < 2.5, with increasing difference at higher redshifts; all models miss the galaxies that form stars with the highest SFRs. Finally, we finally obtain the UV (dust-corrected), IR and total SFR densities (SFRDs), finding that there are no redshift ranges where UV and IR alone are able to reproduce the total SFRD.