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We present models to predict high frequency counts of extragalactic radiosources using physically grounded recipes to describe the complex spectralbehaviour of blazars, that dominate the mm-wave counts at bright fluxdensities. We show that simple power-law spectra are ruled out byhigh-frequency (nu>100 GHz) data. These data also strongly constrain modelsfeaturing the spectral breaks predicted by classical physical models for thesynchrotron emission produced in jets of blazars (Blandford & Konigl 1979;Konigl 1981). A model dealing with blazars as a single population is, at best,only marginally consistent with data coming from current surveys at high radiofrequencies. Our most successful model assumes different distributions of breakfrequencies, nu_M, for BL Lacs and Flat-Spectrum Radio Quasars (FSRQs). Theformer objects have substantially higher values of nu_M, implying that thesynchrotron emission comes from more compact regions; therefore, a substantialincrease of the BL Lac fraction at high radio frequencies and at bright fluxdensities is predicted. Remarkably, our best model is able to give a very goodfit to all the observed data on number counts and on distributions of spectralindices of extragalactic radio sources at frequencies above 5 and up to 220GHz. Predictions for the forthcoming sub-mm blazar counts from Planck, at thehighest HFI frequencies, and from Herschel surveys are also presented.

astronomy and astrophysics

High--frequency predictions for number counts and spectral properties of  extragalactic radio sources. New evidences of a break at mm wavelengths in  spectra of bright blazar sources