On the spectral index-flux density relation for large samples of radio sources

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 6C, Miyun, WENSS, B3, NVSS, GB87. Instrumental selection effects and the completeness of the catalogs are discussed. Based on the spectral indices calculated for about 200000 sources from the WENSS (327 MHz) and NVSS (1.4 GHz) catalogs, we obtained (1) The median spectral index increases from alpha(med) similar to -0-9 to alpha(med) similar to -0.8 (S-nu proportional to nu(alpha)), while S-327 flux densities decrease from 0.1 Jy down to 25 mJy. The median spectral indices nearly show no variation within the error bars when the flux density is larger than 0.1 Jy. (2) A dependence. of the fraction of ultra-steep spectrum sources (USS, -1.5 less than or equal to alpha less than or equal to -1.0), steep spectrum sources (SSS, -1.0 less than or equal to alpha less than or equal to -0.5) and flat spectrum sources (FSS, -0.5 less than or equal to alpha less than or equal to 0.0) is partly responsible for the spectral flattening. Another contribution to the spectral flattening comes from the variation of alpha(med) of steep spectrum sources (alpha < -0.5) themselves which increases with decreasing flux densities. (3) The spectral flattening for faint sources (down to S-327 similar to 20 mJy) with steep spectra (alpha < -0.5) suggests' that alphamed is correlated with luminosity rather than redshift according to the Condon' model. (4) A strong spectral selection effect occurs when spectral indices are calculated from samples with a large frequency separation.