2025MNRAS.540..984O

This study investigates the radio spectral properties of K$_{S}$-selected star-forming galaxies (SFGs) in the XMM-LSS (multimirror mission large-scale structure) field using extensive multiwavelength data. By employing various diagnostics, SFGs are distinguished from quiescent galaxies and AGN across seven redshift bins ($\rm {0.1\le \, {\rm z}\, \le \, 3.0}$). The broad-band radio frequency spectral energy distribution is analysed at observer-frame frequencies from 144 to 1500 MHz using median stacking techniques correcting for median flux boosting. We investigate the relationship between the radio spectral index, $\alpha$ (where $S\propto \nu ^{\alpha }$) and redshift (z). Our analysis reveals no significant inverse correlation between $\alpha$ and z, indicating that the radio spectrum remains independent with varying redshift. We fit the stacked median radio SEDs with a power law (PL), curved power law (CPL), and double power-law (DPL) models. For the DPL and CPL models, we observe a consistent steepening of the low-frequency spectral index across all redshift bins. For the CPL model, the curvature term q is greater than zero in all redshift bins. Model comparisons indicate that spectra are generally well fitted by all the models considered. At 1500 MHz, SFGs display both a steep synchrotron component and a flat free-free emission component, with a thermal fraction consistently around 11 per cent to 18 per cent. Further deep radio observations, with higher resolution to better deal with source blending and confusion noise and wider frequency coverage to better separate non-thermal and thermal radio emission, are required to reveal the detailed physical processes, thus clarifying the nature of radio sources.