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 $80\%$ 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 $0.89\pm0.22$ 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.
