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Abstract Radio free–free emission is considered to be one of the most reliable tracers of star formation in galaxies. However, as it constitutes the faintest part of the radio spectrum—being roughly an order of magnitude less luminous than radio synchrotron emission at the GHz frequencies typically targeted in radio surveys—the usage of free–free emission as a star formation rate tracer has mostly remained limited to the local universe. Here, we perform a multifrequency radio stacking analysis using deep Karl G. Jansky Very Large Array observations at 1.4, 3, 5, 10, and 34 GHz in the COSMOS and GOODS-North fields to probe free–free emission in typical galaxies at the peak of cosmic star formation. We find that z ∼ 0.5–3 star-forming galaxies exhibit radio emission at rest-frame frequencies of ∼65–90 GHz that is ∼1.5–2 times fainter than would be expected from a simple combination of free–free and synchrotron emission, as in the prototypical starburst galaxy M82. We interpret this as a deficit in high-frequency synchrotron emission, while the level of free–free emission is as expected from M82. We additionally provide the first constraints on the cosmic star formation history using free–free emission at 0.5 ≲ z ≲ 3, which are in good agreement with more established tracers at high redshift. In the future, deep multifrequency radio surveys will be crucial in order to accurately determine the shape of the radio spectrum of faint star-forming galaxies, and to further establish radio free–free emission as a tracer of high-redshift star formation. 

ABSTRACT We present specific star formation rates (sSFRs) for 40 ultraviolet (UV)-bright galaxies at z ∼ 7–8 observed as part of the Reionization Era Bright Emission Line Survey (REBELS) Atacama Large Millimeter/submillimeter Array (ALMA) large programme. The sSFRs are derived using improved star formation rate (SFR) calibrations and spectral energy distribution (SED)-based stellar masses, made possible by measurements of far-infrared (FIR) continuum emission and [C ii]-based spectroscopic redshifts. The median sSFR of the sample is $$18_{-5}^{+7}$$ Gyr−1, significantly larger than literature measurements lacking constraints in the FIR, reflecting the larger obscured SFRs derived from the dust continuum relative to that implied by the UV+optical SED. We suggest that such differences may reflect spatial variations in dust across these luminous galaxies, with the component dominating the FIR distinct from that dominating the UV. We demonstrate that the inferred stellar masses (and hence sSFRs) are strongly dependent on the assumed star formation history in reionization-era galaxies. When large sSFR galaxies (a population that is common at z > 6) are modelled with non-parametric star formation histories, the derived stellar masses can increase by an order of magnitude relative to constant star formation models, owing to the presence of a significant old stellar population that is outshined by the recent burst. The [C ii] line widths in the largest sSFR systems are often very broad, suggesting dynamical masses capable of accommodating an old stellar population suggested by non-parametric models. Regardless of these systematic uncertainties among derived parameters, we find that sSFRs increase rapidly toward higher redshifts for massive galaxies (9.6 < log (M*/M⊙) < 9.8), evolving as (1 + z)1.7 ± 0.3, broadly consistent with expectations from the evolving baryon accretion rates.