Ketron Mitchell-Wynne, Mario G. Santos, Jose Afonso, Matt J. Jarvis
We present a statistical method based on a maximum likelihood approach to constrain the number counts of extragalactic sources below the nominal flux-density limit of continuum imaging surveys. We extract flux densities from a radio map using positional information from an auxiliary catalogue and show that we can model the number counts of this undetected population down to flux density levels well below the detection threshold of the radio survey. We demonstrate the capabilities that our method will have with future generation wide-area radio surveys by performing simulations over various sky areas with a power-law dN/dS model. We generate a simulated power-law distribution with flux densities ranging from 0.1 \sigma to 2 \sigma, convolve this distribution with a Gaussian noise distribution rms of 10 micro-Jy/beam, and are able to recover the counts from the noisy distribution. We then demonstrate the application of our method using data from the Faint Images of the Radio Sky at Twenty-Centimeters survey (FIRST), acquired over 2 square degrees in the COSMOS field with the Very Large Array (VLA). We extract flux densities from the FIRST map, sensitive to 150 micro-Jy/beam (1 \sigma), using positional information from a catalogue in the same field, also acquired at the same frequency using the VLA, sensitive to 12 micro-Jy/beam (1 \sigma). Implementing our method, with known source positions, we are able to recover the differential number counts of the noise-dominated FIRST map fluxes down to a flux density level which is one-tenth the FIRST detection threshold. The method outlined in this paper can thus be used on the wealth of existing and forthcoming data at all wavelengths to extract real physical understanding of the sub-threshold source populations.
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http://arxiv.org/abs/1306.3536
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