Impact of star formation history on the measurement of star formation rates

Context. Measuring star formation across the Universe is key to constraining models of galaxy formation and evolution. Yet, determining the star formation rate (SFR) of galaxies remains a challenge.
Aims: In this paper we investigate in isolation the impact of a variable star formation history on the measurement of the SFR.
Methods: We combine 23 state-of-the-art hydrodynamical simulations of 1 <z< 2 galaxies on the main sequence with the cigale spectral energy distribution modelling code. This allows us to generate synthetic spectra every 1 Myr for each simulation, taking the stellar populations and the nebular emission into account. Using these spectra, we estimate the SFR from classical estimators, which we compare with the true SFR we know from the simulations.
Results: We find that except for the Lyman continuum, classical SFR estimators calibrated over 100 Myr overestimate the SFR from ~25% in the far-ultraviolet to ~65% in the U band. Such biases are due to 1) the contribution of stars living longer than 100 Myr, and 2) variations of the SFR on timescales longer than a few tens of Myr. Rapid variations of the SFR increase the uncertainty on the determination of the instantaneous SFR, but have no long term effect.
Conclusions: The discrepancies between the true and estimated SFR may explain at least part of the tension between the integral of the SFR density and the stellar mass density at a given redshift. To reduce possible biases, we suggest using SFR estimators calibrated over 1 Gyr rather than the usually adopted 100 Myr timescales.