The Phoenix radio survey: The angular correlation function

Using the Phoenix radio survey, a homogeneous survey selected at 1.4 GHz and covering an area of ≈3deg², we analyse the clustering of the sub-mJy radio population using angular correlation function analysis. Extensive simulations are carried out to investigate the significance of the estimated angular correlation amplitudes. Our analysis show that for the S_1.4 > 0.5mJy sub-samples the radio source distribution is anisotropic at the 2σ significance level. Additionally, we estimate upper limits for the angular correlation amplitudes that, despite the large uncertainties, are in good agreement with the amplitude estimates for sources brighter than 1mJy, detected in the FIRST radio survey (Cress et al. 1997). Adopting a radio luminosity function and assuming an evolving spatial correlation function of the form ξ(r) = (r/r₀)-γ(1 + z)^-(3+ε), with the evolution parametrised by ε, we find an upper limit for the angular correlation length r₀ ≈ 9h^-1 Mpc for S_1.4 > 0.5mJy and γ = 2.1. This agrees well with the value r₀ ≈ 6 - 8h^-1 Mpc estimated from the FIRST radio survey for sources brighter than 1mJy. Additionally, we quantify the characteristics, in terms of areal coverage and limiting flux density, of future deep radio surveys to yield a significant correlation amplitude detection and to explore possible changes of the correlation amplitude with flux density.