The Radio Spectral Energy Distribution and Star Formation Calibration in MIGHTEE-COSMOS Highly Star-forming Galaxies at 1.5 &lt; <i>z</i> &lt; 3.5

Abstract Studying the radio spectral energy distribution (SED) of distant galaxies is essential for understanding their assembly and evolution over cosmic time. We present rest-frame radio SEDs of a sample of 160 star-forming galaxies at 1.5 &lt; z &lt; 3.5 in the Cosmic Evolution Survey field as part of the MeerKAT International GHz Tiered Extragalactic Exploration project. MeerKAT observations combined with archival Very Large Array and Giant Metrewave Radio Telescope data allow us to determine the integrated mid-radio ( ν = 1–10 GHz) continuum (MRC) luminosity and magnetic field strength. A Bayesian method is used to model the SEDs and to separate the free–free and synchrotron emission. We also calibrate the star formation rate (SFR) in radio both directly through SED analysis and indirectly through the infrared–radio correlation (IRRC). With a mean value of α nt ≃ 0.7, the synchrotron spectral index flattens with both redshift and specific SFR, indicating that cosmic rays are more energetic in the early Universe due to higher star formation activity. The magnetic field strength increases with redshift, B ∝ (1 + z ) (0.7±0.1) , and SFR as B ∝ SFR 0.3 , suggesting a small-scale dynamo acting as its main amplification mechanism. Taking into account the evolution of the SEDs, the IRRC is redshift invariant, and it does not change with stellar mass at 1.5 &lt; z &lt; 3.5, although the correlation deviates from linearity. Similarly, we show that the SFR traced using the integrated MRC luminosity is redshift invariant.