On the source counts of VLBI-detected radio sources and the prospects of all-sky surveys with current and next generation instruments

Abstract

We present an analysis of the detection fraction and the number counts of radio sources imaged with Very Long Baseline Interferometry (VLBI) at 1.4 GHz as part of the mJIVE-20 survey. From a sample of 24,903 radio sources identified by FIRST, 4,965 are detected on VLBI-scales, giving an overall detection fraction of $19.9\pm2.9~$per cent. However, we find that the detection fraction falls from around 50 per cent at a peak surface brightness of $80~mJy~beam^{-1}$ in FIRST to around 8 per cent at the detection limit, which is likely dominated by the surface brightness sensitivity of the VLBI observations, with some contribution from a change in the radio source population. We also find that compactness at arcsec-scales is the dominant factor in determining whether a radio source is detected with VLBI, and that the median size of the VLBI-detected radio sources is 7.7 mas. After correcting for the survey completeness and effective sky area, we determine the slope of the differential number counts of VLBI-detected radio sources with flux densities $S_{\rm 1.4~GHz} > 1~mJy$ to be $\eta_{\rm VLBI} = -1.74\pm 0.02$, which is shallower than in the cases of the FIRST parent population ($\eta_{\rm FIRST} = -1.77\pm 0.02$) and for compact radio sources selected at higher frequencies ($\eta_{\rm JBF} = -2.06\pm 0.02$). From this, we find that all-sky ($3\pi~sr$) surveys with the EVN and the VLBA have the potential to detect $(7.2\pm0.9)\times10^{5}$ radio sources at mas-resolution, and that the density of compact radio sources is sufficient (5.3~deg$^{-2}$) for in-beam phase referencing with multiple sources (3.9 per primary beam) in the case of a hypothetical SKA-VLBI array.