A measurement of the faint source correlation function in the GOODS and UDF surveys

We present a stable procedure for defining and measuring the two point angular autocorrelation function, w(θ) = [θ/θ₀(V)] ^-Γ, of faint (25 < V < 29), barely resolved and unresolved sources in the Hubble Space Telescope Great Observatories Origins Deep Survey and Ultra Deep Field data sets. We construct catalogues that include close pairs and faint detections. We show, for the first time, that, on subarcsec scales, the correlation function exceeds unity. This correlation function is well fit by a power law with index Γ ≈ 2.5 and a θ₀ = 10^-0.1(V-25.8) arcsec. This is very different from the values of Γ ≈ 0.7 and θ₀(r) = 10 ^-0.4(r-21.5) arcsec associated with the gravitational clustering of brighter galaxies. This observed clustering probably reflects the presence of giant star-forming regions within galactic-scale potential wells. Its measurement enables a new approach to measuring the redshift distribution of the faintest sources in the sky.