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.
Despite decades of study, it remains unclear whether there are distinct radio-loud and radio-quiet populations of quasi-stellar objects (QSOs). Early studies were limited by inhomogeneous QSO samples, inadequate sensitivity to probe the radio-quiet population, and degeneracy between redshift and luminosity for flux-density-limited samples. Our new 6 GHz EVLA observations allow us for the first time to obtain nearly complete (97%) radio detections in a volume-limited color-selected sample of 179 QSOs more luminous than M_i = -23 from the Sloan Digital Sky Survey (SDSS) Data Release Seven in the narrow redshift range 0.2 < z < 0.3. The dramatic improvement in radio continuum sensitivity made possible with the new EVLA allows us, in 35 minutes of integration, to detect sources as faint as 20 microJy, or log[L_6 (W/Hz)] ~ 21.5 at z = 0.25, well below the radio luminosity, log[L_6 (W/Hz)] ~ 22.5, that separates star-forming galaxies from radio-loud active galactic nuclei (AGNs) driven by accretion onto a super-massive black hole. We calculate the radio luminosity function (RLF) for these QSOs using three constraints: (a) EVLA 6 GHz observations for log[L_6 (W/Hz)] < 23.5, (b) NRAO-VLA Sky Survey (NVSS) observations for log[L_6 (W/Hz)] > 23.5, and (c) the total number of SDSS QSOs in our volume-limited sample. We show that the RLF can be explained as a superposition of two populations, dominated by AGNs at the bright end and star formation in the QSO host galaxies at the faint end.
