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

¹ Istituto Nazionale di Astrofisica (INAF) – Osservatorio di Astrofisica e Scienza dello Spazio (OAS) Via Gobetti 101 I-40129 Bologna, Italy
² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM F-91191 Gif-sur-Yvette, France
³ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 3 I-35122 Padova, Italy
⁴ INAF – Osservatorio Astrofisico di Arcetri Largo E. Fermi 5 50125 Firenze, Italy
⁵ INAF – Astronomical Observatory of Trieste Via G.B. Tiepolo 11 I-34143 Trieste, Italy
⁶ IFPU – Institute for Fundamental Physics of the Universe Via Beirut 2 34151 Trieste, Italy
⁷ Institute for Physics, Laboratory for Galaxy Evolution and Spectral Modelling, Ecole Polytechnique Federale de Lausanne, Observatoire de Sauverny Chemin Pegasi 51 CH-1290 Versoix, Switzerland
⁸ School of Physics and Astronomy, Sun Yat-sen University, Zhuhai Campus 2 Daxue Road Xiangzhou District Zhuhai, China
⁹ Tianjin Normal University Binshuixidao 393 Tianjin, China
¹⁰ Max Planck Institut für Astronomie Königstuhl 17 D-69117 Heidelberg, Germany
¹¹ Purple Mountain Observatory, Chinese Academy of Sciences 10 Yuanhua Road Nanjing 210023, China
¹² Argelander-Institut für Astronomie, Universität Bonn Auf dem Hügel 71 53121 Bonn, Germany
¹³ Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, No. 1, Section 4 Roosevelt Road Taipei 106216, Taiwan, R.O.C.
¹⁴ SISSA Via Bonomea 265 34136 Trieste, Italy
¹⁵ IRA-INAF Via Gobetti 101 40129 Bologna, Italy
¹⁶ Cosmic Dawn Center (DAWN), Denmark
¹⁷ DTU-Space, Technical University of Denmark Elektrovej 327 DK-2800 Kgs. Lyngby, Denmark
¹⁸ Dipartimento di Fisica e Astronomia (DIFA), Universití di Bologna via Gobetti 93/2 I-40129 Bologna, Italy

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Received: 20 May 2025
Accepted: 12 November 2025

Abstract

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 “total” SFRF out to z ∼ 6. 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.