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 interest, used to study the relative populations of galaxy types in the Universe (as well as investigate any cosmological evolution in luminosity functions). They are a vital consideration for determining how source confusion may limit the depth of a radio interferometer observation, and are essential for characterising extragalactic foregrounds in CMB experiments. There is currently no consensus as to the relative populations of the faintest (sub-mJy) source types, where the counts turn-up. Most of the source counts in this regime are gathered from multiple observations that each use a deep, single pointing with a radio interferometer. These independent measurements show large amounts of scatter (factors ~ a few) that significantly exceeds their stated uncertainties. In this article 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 are significant, and could even be the sole cause at >100 {\mu}Jy. We present a method for evaluating the flux density limit that a 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 counts in order to include the uncertainties due to the cosmological clustering of sources. An empirical constraint on the effect of sample variance at these low luminosities is unlikely to arise until the completion of new large-scale surveys with next-generation radio telescopes.