A sensitivity and array-configuration study for measuring the power spectrum of 21cm emission from reionization

Telescopes aiming to measure 21cm emission from the Epoch of Reionization must toe a careful line, balancing the need for raw sensitivity against the stringent calibration requirements for removing bright foregrounds. It is unclear what the optimal design is for achieving both of these goals. Via a pedagogical derivation of an interferometer's response to the power spectrum of 21cm reionization fluctuations, we show that even under optimistic scenarios first-generation arrays will yield low-signal-to-noise detections, and that different compact array configurations can substantially alter sensitivity. We explore the sensitivity gains of array configurations that yield high redundancy in the uv-plane - configurations that have been largely ignored since the advent of self-calibration for high-dynamic-range imaging. We first introduce a mathematical framework to generate optimal minimum-redundancy configurations for imaging. We contrast the sensitivity of such configurations with high-redundancy configurations, finding that high-redundancy configurations can improve power-spectrum sensitivity by more than an order of magnitude. We explore how high-redundancy array configurations can be tuned to various angular scales, enabling array sensitivity to be directed away from regions of the uv-plane (such as the origin) where foregrounds are brighter and instrumental systematics are more problematic. We demonstrate that a 132 antenna deployment of the Precision Array for Probing the Epoch of Reionization observing for 120days in a high-redundancy configuration will, under ideal conditions, have the requisite sensitivity to detect the power spectrum of the 21cm signal from reionization at a 3σ level at k < 0.25 h Mpc^-1 in a bin of Δln k = 1. We discuss the tradeoffs of low- versus high-redundancy configurations.