Quantifying Suppression of the Cosmological 21-cm Signal due to Direction Dependent Gain Calibration in Radio Interferometers

TL;DR

This paper quantifies how direction dependent calibration in radio interferometers suppresses the cosmological 21-cm signal and proposes methods to minimize this suppression using prior information and smooth gain models.

Contribution

It provides an exact calculation of 21-cm signal suppression due to DDC and demonstrates how to reduce this effect with smooth gain functions and prior knowledge.

Findings

Low-order smooth gain functions limit signal suppression.

More incomplete sky models increase signal suppression.

Simulation results confirm theoretical predictions.

Abstract

The 21-cm signal of neutral hydrogen - emitted during the Epoch of Reionization - promises to be an important source of information for the study of the infant universe. However, its detection is impossible without sufficient mitigation of other strong signals in the data, which requires an accurate knowledge of the instrument. Using the result of instrument calibration, a large part of the contaminating signals are removed and the resulting residual data is further analyzed in order to detect the 21-cm signal. Direction dependent calibration (DDC) can strongly affect the 21-cm signal, however, its effect has not been precisely quantified. In the analysis presented here we show how to exactly calculate what part of the 21-cm signal is removed as a result of the DDC. We also show how a-priori information about the frequency behavior of the instrument can be used to reduce signal suppression. The theoretical results are tested using a realistic simulation based on the LOFAR setup. Our results show that low-order smooth gain functions (e.g. polynomials) over a bandwidth of ~10\,MHz - over which the signal is expected to be stationary - is sufficient to allow for calibration with limited, quantifiable, signal suppression in its power spectrum. We also show mathematically and in simulations that more incomplete sky models lead to larger 21-cm signal suppression, even if the gain models are enforced to be fully smooth. This result has immediate consequences for current and future radio telescopes with non-identical station beams, where DDC might be necessary (e.g. SKA-low).