Beyond stacking: a maximum-likelihood method to constrain radio source counts below the detection threshold

Abstract

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. We show that it is possible to accurately constrain the number counts of the simulated distribution down to one-tenth of the flux noise rms with just a sky area of 100 deg2. We then test the application of our method using data from the Faint Images of the Radio Sky at Twenty-Centimetres survey (FIRST). We extract flux densities from the FIRST map, sensitive to 150 μJy beam−1 (1 σ), using the positional information from a catalogue in the same field, also acquired at the same frequency, sensitive to 12 μJy beam−1 (1 σ). Implementing our method, with known source positions, we are able to recover the right differential number counts of the noise-dominated FIRST map fluxes down to a flux-density level which is one-tenth the FIRST detection threshold.