Radio spectral properties of star-forming galaxies in the MIGHTEE-COSMOS
  field and their impact on the far-infrared-radio correlation
  We study the radio spectral properties of 2,094 star-forming galaxies (SFGs)
by combining our early science data from the MeerKAT International GHz Tiered
Extragalactic Exploration (MIGHTEE) survey with VLA, GMRT radio data, and rich
ancillary data in the COSMOS field. These SFGs are selected at VLA 3GHz, and
their flux densities from MeerKAT 1.3GHz and GMRT 325MHz imaging data are
extracted using the "super-deblending" technique. The median radio spectral
index is $\alpha_{\rm 1.3GHz}^{\rm 3GHz}=-0.80\pm0.01$ without significant
variation across the rest-frame frequencies ~1.3-10GHz, indicating radio
spectra dominated by synchrotron radiation. On average, the radio spectrum at
observer-frame 1.3-3GHz slightly steepens with increasing stellar mass with a
linear fitted slope of $\beta=-0.08\pm0.01$, which could be explained by
age-related synchrotron losses. Due to the sensitivity of GMRT 325MHz data, we
apply a further flux density cut at 3GHz ($S_{\rm 3GHz}\ge50\,\mu$Jy) and
obtain a sample of 166 SFGs with measured flux densities at 325MHz, 1.3GHz, and
3GHz. On average, the radio spectrum of SFGs flattens at low frequency with the
median spectral indices of $\alpha^{\rm 1.3GHz}_{\rm
325MHz}=-0.59^{+0.02}_{-0.03}$ and $\alpha^{\rm 3.0GHz}_{\rm
1.3GHz}=-0.74^{+0.01}_{-0.02}$. At low frequency, our stacking analyses show
that the radio spectrum also slightly steepens with increasing stellar mass. By
comparing the far-infrared-radio correlations of SFGs based on different radio
spectral indices, we find that adopting $\alpha_{\rm 1.3GHz}^{\rm 3GHz}$ for
$k$-corrections will significantly underestimate the infrared-to-radio
luminosity ratio ($q_{\rm IR}$) for >17% of the SFGs with measured flux density
at the three radio frequencies in our sample, because their radio spectra are
significantly flatter at low frequency (0.33-1.3GHz).
