Context. Star formation rate functions (SFRFs) give an instantaneous view of the distribution of star formation rates (SFRs) in galaxies at different epochs. They are a complementary and more stringent test for models than the galaxy stellar mass function, which gives an integrated view of the past star formation activity. However, the exploration of SFRFs has been limited thus far due to difficulties in assessing the SFR from observed quantities and probing the SFRF over a wide range of SFRs.
Aims: We overcome these limitations thanks to an original method that predicts the infrared luminosity from the rest-frame UV/optical color of a galaxy and then its SFR over a wide range of stellar masses and redshifts. We applied this technique to the deep imaging survey HSC-CLAUDS combined with near-infrared and UV photometry. We provide the first SFR functions with reliable measurements in the high- and low-SFR regimes up to z = 2 and compare our results with previous observations and four state-of-the-art hydrodynamical simulations.
Methods: The SFR estimates are based on the calibration of the infrared excess (IRX = L_IR/L_UV) in the NUVrK color-color diagram. We improved upon the original calibration in the COSMOS field by incorporating Herschel photometry, which allowed us to extend the analysis to higher redshifts and to galaxies with lower stellar masses using stacking techniques. Our NrK method leads to an accuracy of individual SFR estimates of σ ∼ 0.25 dex. We show that it reproduces the evolution of the main sequence up to z = 2 and the behavior of the attenuation (or ⟨IRX⟩) with stellar mass. In addition to the known lack of evolution of this relation up to z = 2 for galaxies with M_⋆ ≤ 10^10.3 M_⊙, we observe a plateau in ⟨IRX⟩ at higher stellar masses that depends on redshift.
Results: We measure the SFR functions and cosmic SFR density up to z = 2 for a mass-selected star-forming galaxy sample (with a mass limit of M_⋆ ≥ 2.10⁹ M_⊙ at z = 2). The SFR functions cover a wide range of SFRs (0.01 ≤ SFR ≤ 1000 M_⊙ yr⁻¹), providing good constraints on their shapes. They are well fitted by a Schechter function after accounting for the Eddington bias. The high-SFR tails match the far-infrared observations well, and show a strong redshift evolution of the Schechter parameter, SFR^⋆, as log₁₀(SFR⋆) = 5.8z + 0.76. The slope of the SFR functions, α, shows almost no evolution up to z = 1.5 − 2 with α = −1.3 ± 0.1. We compare the SFR functions with predictions from four state-of-the-art hydrodynamical simulations. Significant differences are observed between them, and none of the simulations are able to reproduce the observed SFRFs over the whole redshift and SFR range. We find that only one simulation is able to predict the fraction of highly star-forming galaxies at high z, 1 ≤ z ≤ 2. This highlights the benefits of using SFRFs as a constraint that can be reproduced by simulations; however, despite efforts to incorporate more physically motivated prescriptions for star-formation and feedback processes, its use remains challenging.