Sample variance, source clustering and their influence on the counts of faint radio sources

The shape of the curves defined by the counts of radio sources per unit area as a function of their flux density was one of the earliest cosmological probes. Radio source counts continue to be an area of astrophysical interest as they can be used to study the relative populations of galaxy types in the Universe (as well as investigate any cosmological evolution in their respective luminosity functions). They are also a vital consideration for determining howsource confusion may limit the depth of a radio interferometer observation, and are essential for characterizing the extragalactic foregrounds in cosmicmicrowave background experiments. There is currently no consensus as to the relative populations of the faintest (sub-mJy) source types, where the counts show a turn-up. Most of the source count data in this regime are gathered from multiple observations that each use a deep, single pointing with an interferometric radio telescope. These independent count measurements exhibit large amounts of scatter (factors of the order of a few) that significantly exceeds their respective stated uncertainties. In this paper, we use a simulation of the extragalactic radio continuum emission to assess the level at which sample variance may be the cause of the scatter. We find that the scatter induced by sample variance in the simulated counts decreases towards lower flux density bins as the raw source counts increase. The field-to-field variations make significant contributions to the scatter in the measurements of counts derived from deep observations that consist of a single pointing, and could even be the sole cause at >100 μJy. We present a method for evaluating the flux density limit that a radio survey must reach in order to reduce the count uncertainty induced by sample variance to a specific value. We also derive a method for correcting Poisson errors on source counts from existing and future deep radio surveys in order to include the uncertainties due to the cosmological clustering of sources. A conclusive empirical constraint on the effect of sample variance at these low luminosities is unlikely to arise until the completion of future large-scale radio surveys with next-generation radio telescopes. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.