Correlation-function analysis has become the standard way of quantifying the clustering of different populations of astronomical sources. Much of the interest in this type of analysis stems from its potential to constrain the spectrum of density fluctuations present in the early universe and thus, to constrain the physics of the early universe. While it is the spatial correlation function that is directly related to the power spectrum, the angular correlation function of galaxies in optical surveys has been used to infer the spatial correlation function when redshift information was not available. These inferred values have later been shown to agree with measured values of the spatial correlation (cf Groth & Peebles, 1977 and Davis & Peebles, 1983). In addition, in all but the deepest optical surveys, the amplitude of the angular galaxy-galaxy correlation function (A, in , ) is found to scale with the depth of the survey as described in Peebles (1980). Very faint galaxies might have a slightly flatter slope, but the fact that A generally scales in this well-understood way supports the use of the angular correlation function as a probe of large-scale structure (and thus, a probe of the density fluctuation spectrum in the early universe.)
Optical surveys covering large regions of sky have provided much information on large-scale structure out to a redshift of . In addition, `pencil-beam' surveys have given some information on structure at redshifts beyond this. Radio surveys, however, generally sample much larger volumes of space than any optical surveys and so have the potential to provide information on much larger physical scales. It has been thought that the broad luminosity function of radio sources might, however, wash out any spatial correlations in the angular projection. This idea was supported by the work of Webster (1976) who determined the angular power spectrum of the 4C and GB radio surveys and by the work of Masson (1979) who determined the angular correlation function for the 6C catalog. The catalogs they used contained only the very brighest radio sources and neither found any evidence for clustering. More recently, however, Peacock & Nicholson (1991) have shown that bright radio sources (flux density, S>2 Jy) in a narrow redshift band (0.01<z<0.1) are spatially correlated, the sources showing the power-law behaviour . Shaver & Pierre (1989) also found some evidence of clustering towards the supergalactic plane for radio sources with z<0.02. In addition, marginal detections of a non-zero angular correlation function have been found for sources with S>35 mJy in the Green Bank 4.85 GHz survey (Kooiman, Burns & Klypin 1995; Sicotte 1995), suggesting that spatial correlations will indeed show up in the angular projection if a survey goes to faint enough fluxes.
The FIRST survey is 50 times more sensitive than any previous radio survey and thus provides an excellent opportunity to investigate the angular correlation function of faint sources and to explore the possibility of inferring spatial information from this measurement. In section 2, we describe the catalog of sources used in the study. We then outline the methods we have adopted to compute the angular correlation function and the errors thereon (§ 3). Section 4 presents the results for the catalog as a whole, as well as for various subsamples; in section 5 we compare our results with previous work and outline a preliminary approach to obtaining information on the spatial correlation of radio sources. In section 6 we summarize our conclusions.