New results on the spectral index–flux density relation from the WENSS/NVSS catalogs

We present new statistical results on the spectral index–flux density relation for large samples of radio sources using archival data of the most sensitive surveys, such as WENSS and NVSS. Instrumental selection effects and the completeness of the catalogs used in this study are discussed. Our main results are based on the spectral indices calculated for about 185 800 sources from the WENSS (327 MHz) and the NVSS (1.4 GHz) catalogs and are summarized as follows: (1) The median spectral index increases from to () for S327 flux densities decreasing from 0.1 Jy down to 23 mJy. The median spectral indices nearly show no variation within the error bars in the flux density range above 100 mJy up to several Jy. The median spectral index slightly increases again for S327 above several Jy. The new results confirm published models of the radio luminosity function (RLF) for sources with Jy and give constraints to the models for sources of , respectively. (2) A dependence of the fractions of ultra-steep-spectrum sources (USS, ), steep-spectrum sources (SSS, ) and flat-spectrum sources (FSS, ) is partly responsible for the spectral flattening. Another contribution to the spectral flattening comes from the variation of of steep-spectrum sources () themselves which increases with decreasing flux densities. (3) The spectral flattening for faint sources (down to ) with steep spectra () suggests that is correlated with luminosity rather than redshift according to the source evolution model of Condon ([CITE]).