STRUCTURE ON THE LARGEST SCALES - CONSTRAINTS FROM THE ISOTROPY OF RADIO-SOURCE COUNTS

We show how the size of the largest scales of cellular structure in th e Universe may be deduced from the anisotropy of the sky distribution of extragalactic radio sources. Using a Voronoi tessellation to repres ent the skeleton structure of the galaxy distribution, together with a n evolving luminosity function for the mean space density of extragala ctic radio sources, we have calculated the source-count anisotropy exp ected as a function of tessellation scale rho(-1/3), radio-survey dept h and survey angular diameter. Deep pencil-beam surveys of opening ang le less than or similar to 0.1 rad provide strong limits on rho. We fi nd, for example, that, if the density parameter Omega = 1 and rho(-1/3 ) similar to 100 h(-1) Mpc, significant ( > root N) area-to-area fluct uations are expected for counts from pencil-beam surveys slightly deep er than the deepest yet achieved, S-1GHz < 0.1 mJy for a 0 degrees.5-d iameter survey, S-1GHz < 3 mJy for a 5 degrees-diameter survey. The an alysis demonstrates (a) the way in which deep radio-survey data can be used to constrain large-scale structure, and (b) the care which must be exercised in defining cosmologically representative samples of fain t radio sources. We review the isotropy (or otherwise) of (1) large-ar ea radio surveys, typically covering several steradians to similar to 1 Jy, and (2) pencil-beam radio surveys to mJy and mu Jy levels. Large -area surveys limit rho(-1/3) less than or similar to 250 h(-1) Mpc (i f Omega = 1). The counts from the 5C pencil-beam surveys (3000 sources in 10 fields to S-408MHz > 10 mJy) limit rho(-1/3) less than or simil ar to 150 h(-1) Mpc (for Omega = 1). A similar rho(-1/3) less than or similar to 100 h(-1) Mpc can be inferred from the isotropy (or margina l anisotropy) of deep VLA and WSRT radio surveys. We show how spectros copy of low-redshift (z < 0.4) optical identifications from deep penci l-beam surveys can be used to trace large-scale structure directly, an d we illustrate this with some results from the 5C12 surveys.