Evaluating star formation rates at z = 5

¹ Observatoire Astronomique de Strasbourg, Université de Strasbourg, CNRS, UMR 7550, 67000, Strasbourg, France
² Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000, Gent, Belgium
³ Institut d’Astrophysique de Paris, Sorbonne Université, CNRS, UMR 7095, 98 bis bd Arago, 75014, Paris, France
⁴ Department of Astronomy and Yonsei University Observatory, Yonsei University, Seoul, 03722, Republic of Korea
⁵ Korea Astronomy and Space Science Institute, 776, Daedeokdae-ro, Yuseong-gu, Daejeon, 34055, Republic of Korea

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 January 2026
Accepted: 1 April 2026

Abstract

Inferring the star formation rates (SFR) in high-redshift galaxies remains challenging because of observational limitations or uncertainties in calibration methods that link luminosities to SFRs. We used two state of the art hydrodynamical simulations, NEWHORIZON and NEWCLUSTER, post-processed with the radiative transfer code SKIRT, to investigate the systematic uncertainties and biases in the inferred SFRs for z = 5 galaxies, an epoch in which galaxies build up their stellar mass. We created synthetic observables for widely used tracers: the Hα nebular line, the [C II] 158 μm fine-structure line, the total infrared (IR) continuum luminosity, and hybrid (IR + UV). We find that Hα-inferred SFRs, time-averaged over 10 Myr, are sensitive to the choice of calibration and exhibit substantial scatter driven by dust attenuation, viewing angle, and dust-to-metal ratio. A steeper attenuation curve reduces this scatter significantly, but does not fully eliminate systematic uncertainties. IR continuum-based SFRs trace intrinsic SFRs time-averaged over 100 Myr timescales when a well-sampled continuum emission between rest frames 8 and 1000 μm is available, and they underestimate them with typical approaches when IR data are limited. Nevertheless, IR SFRs display a considerable scatter, largely due to UV photon leakage and strong variations in the star formation history. When UV data are available, hybrid (IR + UV) SFRs provide a more robust estimate, reducing scatter compared to IR-based SFRs while avoiding explicit attenuation corrections. Finally, we derived a [C II]–SFR relation finding a steeper relation than previous studies, but with significant scatter linked to gas density and metallicity. Overall, IR-, hybrid-, and [C II]-based tracers remain more robust than Hα against variations in optical depth.