Low-redshift Lyman Continuum Survey: Radio continuum properties of low-$z$ Lyman continuum emitters
Sources that leak Lyman-continuum (LyC) photons and lead to the reionisation of the universe are intensely studied using multiple observing facilities. Recently, the Low-redshift LyC Survey (LzLCS) has found the first large sample of LyC emitting galaxies at low redshift ($z\sim 0.3$) with the Hubble Space Telescope/Cosmic Origins Spectrograph. The LzLCS sample contains a robust estimate of the LyC escape fraction ($f_\mathrm{esc}^\mathrm{LyC}$) for 66 galaxies spanning a wide range of $f_\mathrm{esc}^\mathrm{LyC}$. Here we, for the first time, aim to study the radio continuum (RC) properties of LzLCS sources and their dependence on $f_\mathrm{esc}^\mathrm{LyC}$. We present Karl G. Jansky Very Large Array RC observations at C (4-8 GHz), S (2-4 GHz) and L (1-2 GHz) bands for a sub-sample of the LzLCS sources. The radio spectral index ($α^{\mathrm{3GHz}}_\mathrm{6GHz}$) spans a wide range from being flat ( $\geq -0.1$) to very steep ($\leq -1.0$). The strongest leakers in our sample show flat $α^{\mathrm{3GHz}}_\mathrm{6GHz}$, weak leakers have $α^{\mathrm{3GHz}}_\mathrm{6GHz}$ close to normal star-forming galaxies, and non-leakers are characterized by steep $α^{\mathrm{3GHz}}_\mathrm{6GHz}$. We argue that a combination of young ages, free-free absorption, and a flat cosmic-ray energy spectrum can altogether lead to a flat $α^{\mathrm{3GHz}}_\mathrm{6GHz}$ for strong leakers. Non-leakers are characterized by steep spectra which can arise due to break/cutoff at high frequencies. Such a cutoff in the spectrum can arise in a single injection model of CRs characteristic of galaxies which have recently stopped star formation. Such a relation between $α^{\mathrm{3GHz}}_\mathrm{6GHz}$ and $f_\mathrm{esc}^\mathrm{LyC}$ hints at the interesting role of supernovae, CRs, and magnetic fields in facilitating the escape ( and/or the lack) of LyC photons. (Abridged)