The effect of the ionosphere on ultra-low-frequency radio-interferometric observations

Context. The ionosphere is the main driver of a series of systematic effects that limit our ability to explore the low-frequency (<1 GHz) sky with radio interferometers. Its effects become increasingly important towards lower frequencies and are particularly hard to calibrate in the low signal-to-noise ratio (S/N) regime in which low-frequency telescopes operate. Aims. In this paper we characterise and quantify the effect of ionospheric-induced systematic errors on astronomical interferometric radio observations at ultra-low frequencies (<100 MHz). We also provide guidelines for observations and data reduction at these frequencies with the LOw Frequency ARray (LOFAR) and future instruments such as the Square Kilometre Array (SKA). Methods. We derive the expected systematic error induced by the ionosphere. We compare our predictions with data from the Low Band Antenna (LBA) system of LOFAR. Results. We show that we can isolate the ionospheric effect in LOFAR LBA data and that our results are compatible with satellite measurements, providing an independent way to measure the ionospheric total electron content (TEC). We show how the ionosphere also corrupts the correlated amplitudes through scintillations. We report values of the ionospheric structure function in line with the literature. Conclusions. The systematic errors on the phases of LOFAR LBA data can be accurately modelled as a sum of four effects (clock, ionosphere first, second, and third order). This greatly reduces the number of required calibration parameters, and therefore enables new efficient calibration strategies