Synchrotron spectral index and interstellar medium densities of star-forming galaxies

The spectral index of synchrotron emission is an important parameter in understanding the properties of cosmic ray electrons (CREs) and the interstellar medium (ISM). We determine the synchrotron spectral index ($\alpha_{\rm nt}$) of four nearby star-forming galaxies, namely NGC 4736, NGC 5055, NGC 5236 and NGC 6946 at sub-kpc linear scales. The $\alpha_{\rm nt}$ was determined between 0.33 and 1.4 GHz for all the galaxies. We find the spectral index to be flatter ($\gtrsim -0.7$) in regions with total neutral (atomic + molecular) gas surface density, $\Sigma_{\rm gas} \gtrsim \rm 50~M_\odot pc^{-2}$, typically in the arms and inner parts of the galaxies. In regions with $\Sigma_{\rm gas} \lesssim \rm 50~M_\odot pc^{-2}$, especially in the interarm and outer regions of the galaxies, the spectral index steepens sharply to $<-1.0$. The flattening of $\alpha_{\rm nt}$ is unlikely to be caused due to thermal free--free absorption at 0.33 GHz. Our result is consistent with the scenario where the CREs emitting at frequencies below $\sim0.3$ GHz are dominated by bremsstrahlung and/or ionization losses. For denser medium ($\Sigma_{\rm gas} \gtrsim \rm 200~M_\odot pc^{-2}$), having strong magnetic fields ($\sim 30~\mu$G), $\alpha_{\rm nt}$ is seen to be flatter than $-0.5$, perhaps caused due to ionization losses. We find that, due to the clumpy nature of the ISM, such dense regions cover only a small fraction of the galaxy ($\lesssim5$ percent). Thus, the galaxy-integrated spectrum may not show indication of such loss mechanisms and remain a power-law over a wide range of radio frequencies (between $\sim 0.1$ to 10 GHz).