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Foreground Predictions for the Cosmic Microwave Background Power Spectrum from Measurements of Faint Inverted Radio Sources at 5 GHz

We present measurements of a population of matched radio sources at 1.4 and 5 GHz down to a flux limit of 1.5 mJy in 7 sq. degs. of the NOAO Deep Field South. We find a significant fraction of sources with inverted spectral indices that all have 1.4 GHz fluxes less than 10 mJy, and are therefore too faint to have been detected and included in previous radio source count models that are matched at multiple frequencies. Combined with the matched source population at 1.4 and 5 GHz in 1 sq. deg. in the ATESP survey, we update models for the 5 GHz differential number counts and distributions of spectral indices in 5 GHz flux bins that can be used to estimate the unresolved point source contribution to the cosmic microwave background temperature anisotropies. We find a shallower logarithmic slope in the 5 GHz differential counts than in previously published models for fluxes < 100 mJy as well as larger fractions of inverted spectral indices at these fluxes. Because the Planck flux limit for resolved sources is larger than 100 mJy in all channels, our modified number counts yield at most a 10% change in the predicted Poisson contribution to the Planck temperature power spectrum. For a flux cut of 5 mJy with the South Pole Telescope and a flux cut of 20 mJy with the Atacama Cosmology Telescope we predict a ~30% and ~10% increase, respectively, in the radio source Poisson power in the lowest frequency channels of each experiment relative to that predicted by previous models.