Constraints on the clustering, biasing and redshift distribution of radio sources

We discuss how different theoretical predictions for the variance sigma(2) of the counts-in-cells distribution of radio sources can be matched to meas urements from the FIRST survey at different flux limits. The predictions ar e given by the integration of models for the angular correlation function w (theta) for three different functional forms of the redshift distribution N (z), different spatial correlation functions that match the observed presen t-day shape and by different evolutions of the bias b(z) with redshift. We also consider the two cases of open and flat universes. Although the predic ted w(theta) show substantial differences because of differences in the val ues of N(z), these differences are not significant compared to the uncertai nties in the current observations. It turns out that, independent of the ge ometry of the universe and the flux limit, the best fit is provided by mode ls with constant biasing at all times, although the difference between mode ls with epoch-independent bias and models with bias that evolves linearly w ith redshift is not very large. All models with strong evolution of bias wi th epoch are ruled out, as they grossly overestimate the amplitude of the v ariance over the whole range of angular scales sampled by the counts-in-cel ls analysis. As a further step we directly calculated w(obs)(theta) at 3 mJ y from the catalogue and matched it with our models for the angular correla tion function, in the hypothesis that the clustering signal comes from two different populations, namely AGN-powered sources and starbursting galaxies . The results are consistent with a scenario for hierarchical clustering wh ere the fainter starbursting galaxies trace the mass at all epochs, while t he brighter AGNs are strongly biased, with b(z) evolving linearly with reds hift, as suggested by some theories of galaxy formation and evolution.