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

The paper tackles how to coherently combine obscured IR-derived and dust-corrected UV star formation rate functions to recover the total star formation rate density up to $z \sim 6$. By deriving $SFR_{IR}$ from ALMA A$^3$COSMOS IR-LFs and $SFR_{UV}$ from UV-LFs with dust corrections, and fitting them with redshift-evolving Schechter forms via MCMC, the authors construct a total SFRF and compare it with state-of-the-art hydrodynamical simulations and semi-analytical models. They find that IR and UV traces are largely complementary, with the UV sampling $SFR \lesssim 10-100$ $M_\odot$ yr$^{-1}$ and the IR tracing $SFR \gtrsim 100$ $M_\odot$ yr$^{-1}$, and that the total SFRD is best reproduced by combining both tracers, albeit with models underpredicting the brightest high-SFR systems at $z \gtrsim 2.5$. The cosmic SFRD peaks near $z_{\rm peak} \sim 2.6$, and the authors provide a new Madau-like fit to the total SFRD, noting consistency with recent FIR+UV studies and highlighting the ongoing need to refine feedback and dust physics in simulations. Overall, the work demonstrates the necessity of joint UV+IR analyses to recover the full star formation history and provides robust benchmarks for current 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.

Figures (8)

• Figure 1: Density (normalized to 1) distributions of the IR-SFR obtained through SED fitting for total A3COSMOS sample (cyan) and for the sub-sample considered in this work (teal).
• Figure 2: Upper panel: UV and IR SFRFs at different redshifts. Data points are plotted in cyan (UV) and red (IR), while the best fit is shown as blue and red curves for the UV and IR datasets, respectively. Lower panel: product between volume density ($\Phi$) and SFR in each redshift bin: this is the quantity that we integrate to obtain the SFRD. The UV (blue area) and the IR (red area) SFR density distributions are compared at different redshifts as function of the SFR. Both curves are normalize to have the peak of the UV at 1.
• Figure 3: Combined SFRF best-fit. The UV and IR data points are shown as in Figure \ref{['fig:SFRF_points_fit']}. Blue empty circles are the UV points not used to obtain the combined fit, which is shown as yellow area, corresponding to the 16th and 84 percentiles from the MCMC.
• Figure 4: Observed SFRF compared with the prediction from simulations and SAMs. The yellow area represents the observed data used for the fit. The best-fit curve is reported in black. The purple dashed line represents the SFRF from the EAGLE simulation; the pink dashed curve is the result from the SIMBA simulation and the magenta line is from the IllustrisTNG katsianis2017eaglekatsianis2021simba. The limegreen and green dotted curves are the prediction by Hirschmann2016sam and fontanot2020sam, from the GAEA SAM. Finally, the cyan dotted curves are the predictions by parente2023dust_sam.
• Figure 5: Fraction of the combined SFRD, at each redshift, recovered by UV (light blue and blue histograms) and IR (red histograms) data. The blue filled histograms represent the fraction recovered by the observed UV (i.e., without dust correction), while the dashed light blue histograms correspond to the dust corrected UV). We note that the UV and IR fractions do not sum up to 1, as each SFRD is obtained by integrating the respective best-fit SFR function.