The brightness and spatial distributions of terrestrial radio sources

Faint undetected sources of radio-frequency interference (RFI) might become visible in long radio observations when they are consistently present over time. Thereby, they might obstruct the detection of the weak astronomical signals of interest. This issue is especially important for Epoch of Reionization (EoR) projects that try to detect the faint redshifted H I signals from the time of the earliest structures in the Universe. We explore the RFI situation at 30-163 MHz by studying brightness histograms of visibility data observed with Low-Frequency Array (LOFAR), similar to radio-source-count analyses that are used in cosmology. An empirical RFI distribution model is derived that allows the simulation of RFI in radio observations. The brightness histograms show an RFI distribution that follows a power-law distribution with an estimated exponent around -1.5. With several assumptions, this can be explained with a uniform distribution of terrestrial radio sources whose radiation follows existing propagation models. Extrapolation of the power law implies that the current LOFAR EoR observations should be severely RFI limited if the strength of RFI sources remains strong after time integration. This is in contrast with actual observations, which almost reach the thermal noise and are thought not to be limited by RFI. Therefore, we conclude that it is unlikely that there are undetected RFI sources that will become visible in long observations. Consequently, there is no indication that RFI will prevent an EoR detection with LOFAR.