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-f
orming 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).
We studied the total magnetic field strength in normal star-forming galaxies estimated using energy equipartition assumption. Using the well known radio--far infrared correlation we demonstrate that the equipartition assumption is valid in galaxies a
t sub-kpc scales. We find that the magnetic field strength is strongly correlated with the surface star formation rate in the galaxies NGC 6946 and NGC 5236. Further, we compare the magnetic field energy density to the total (thermal + turbulent) energy densities of gas (neutral + ionized) to identify regions of efficient field amplification in the galaxy NGC 6946. We find that in regions of efficient star formation, the magnetic field energy density is comparable to that of the total energy density of various interstellar medium components and systematically dominates in regions of low star formation efficiency.
