Abstract 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 αmed ∼ -0.9 to αmed∼ -0.8 ( Sν ∝ να), while S327 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 ≤ α < -1.0 ), steep spectrum sources (SSS, -1.0 ≤ α <-0.5 ) and flat spectrum sources (FSS, -0.5 ≤ α ≤ 0.0 ) is partly responsible for the spectral flattening. Another contribution to the spectral flattening comes from the variation of αmed of steep spectrum sources (α < -0.5) themselves which increases with decreasing flux densities. (3) The spectral flattening for faint sources (down to S327 ∼ 20 mJy) with steep spectra (α < -0.5) suggests that αmed 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.

Keywords radio continuum: general --- methods: statistical --- cosmology

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