Radio spectral index from NVSS and TGSS

I extract the radio spectral index, $\alpha$, from 541,195 common sources observed in the 150 MHz TIFR GMRT Sky Survey (TGSS) and the 1.4 GHz NRAO VLA Sky Survey (NVSS). This large common source catalogue covers about $80\mathrm{\%}$ of the sky. The flux density limits in these surveys are such that the observed galaxies are presumably hosts of active galactic nuclei (AGNs). I confirm the steepening of $\alpha$ with increasing flux density for this large sample and provide a parametric fit between $\alpha$ and flux density. Next, I divide the data into a low flux (LF) and a high flux (HF) density sample of roughly equal number of galaxies. The LF sample contains all galaxies below 100 mJy TGSS and 20 mJy NVSS flux density and the HF sample is all galaxies above 100 mJy TGSS and 20 mJy NVSS. I observe an increase in $\alpha$ with source size (TGSS measured), saturating for large sizes to $0.89\pm 0.22$ and $0.76\pm 0.21$ for the LF and HF sources, respectively. I discuss the observed results and possible physical mechanisms to explain observed $\alpha$ dependence with source size for LF and HF samples.