The Effect of Baseline Layouts on the Epoch of Reionization Foreground Wedge: A Semianalytical Approach

Abstract

The 2D power spectrum is a cornerstone of the modern toolkit for analysis of the low-frequency radio interferometric observations of the 21 cm signal arising from the early universe. Its familiar form disentangles a great deal of systematic information concerning both the sky and telescope and is displayed as a foreground-dominated "brick" and "wedge" on large line-of-sight scales and a complementary "window" on smaller scales. This paper builds on many previous works in the literature that seek to elucidate the varied instrumental and foreground factors that contribute to these familiar structures in the 2D power spectrum. In particular, we consider the effects of uv sampling on the emergence of the wedge. Our results verify the expectation that arbitrarily dense instrument layouts in principle restore the missing information that leads to mode mixing and can therefore mitigate the wedge feature. We derive rule-of-thumb estimates for the required baseline density for complete wedge mitigation, showing that these will be unachievable in practice. We also discuss the optimal shape of the layout, showing that logarithmic regularity in the radial separation of baselines is favorable. While complete suppression of foreground leakage into the wedge is practically unachievable, we find that designing layouts that promote radial density and regularity is able to reduce the amplitude of foreground power by one to three orders of magnitude.