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.
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