Validation Solutions to the Full-Sky Radio Interferometry Measurement Equation for Diffuse Emission

TL;DR

This paper develops analytical solutions for the Radio Interferometry Measurement Equation (RIME) for diffuse sky emission, enabling validation of simulations crucial for detecting the Cosmic Dawn 21 cm signal amidst foreground contamination.

Contribution

It introduces analytically-defined diffuse emission patterns with closed-form RIME solutions, facilitating validation of observational models and simulations in low-frequency radio astronomy.

Findings

Analytical RIME solutions for diffuse emission patterns

Validation of RIME integrals against simulated data

Differences behave as expected with sky resolution and baseline variations

Abstract

Low-frequency radio observatories are reaching unprecedented levels of sensitivity in an effort to detect the 21 cm signal from the Cosmic Dawn. High precision is needed because the expected signal is overwhelmed by foreground contamination, largely from so-called diffuse emission -- a non-localized glow comprising Galactic synchrotron emission and radio galaxies. The impact of this diffuse emission on observations may be better understood through detailed simulations, which evaluate the Radio Interferometry Measurement Equation (RIME) for a given instrument and sky model. Evaluating the RIME involves carrying out an integral over the full sky, which is naturally discretized for point sources but must be approximated for diffuse emission. The choice of integration scheme can introduce errors that must be understood and isolated from the instrumental effects under study. In this paper, we present several analytically-defined patterns of unpolarized diffuse sky emission for which the RIME integral is manageable, yielding closed-form or series visibility functions. We demonstrate the usefulness of these RIME solutions for validation by comparing them to simulated data, and show that the remaining differences behave as expected with varied sky resolution and baseline orientation and length.