<i>Planck</i>early results. XIII. Statistical properties of extragalactic radio sources in the<i>Planck</i>Early Release Compact Source Catalogue

The data reported in Planck's Early Release Compact Source Catalogue (ERCSC) are exploited to measure the number counts (dN/dS ) of extragalactic radio sources at 30, 44, 70, 100, 143 and 217 GHz. Due to the full-sky nature of the catalogue, this measurement extends to the rarest and brightest sources in the sky. At lower frequencies (30, 44, and 70 GHz) our counts are in very good agreement with estimates based on WMAP data, being somewhat deeper at 30 and 70 GHz, and somewhat shallower at 44 GHz. Planck's source counts at 143 and 217 GHz join smoothly with the fainter ones provided by the SPT and ACT surveys over small fractions of the sky. An analysis of source spectra, exploiting Planck's uniquely broad spectral coverage, finds clear evidence of a steepening of the mean spectral index above about 70 GHz. This implies that, at these frequencies, the contamination of the CMB power spectrum by radio sources below the detection limit is significantly lower than previously estimated.