A Sensitivity and Array-Configuration Study for Measuring the Power Spectrum of 21cm Emission from Reionization

TL;DR

This study evaluates how different array configurations of radio telescopes affect the sensitivity to detect the 21cm power spectrum from the Epoch of Reionization, highlighting the advantages of high-redundancy setups.

Contribution

It introduces a mathematical framework for designing optimal array configurations and demonstrates that high-redundancy arrays significantly improve sensitivity for 21cm reionization measurements.

Findings

High-redundancy configurations can enhance sensitivity by over an order of magnitude.

A 132-antenna high-redundancy array can detect the 21cm power spectrum at 3σ significance in 120 days.

Optimal array design involves tuning configurations to target specific angular scales while mitigating foregrounds.

Abstract

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-SNR 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 where instrumental systematics are more problematic. We demonstrate that a 132-antenna deployment of the Precision Array for Probing the Epoch of Reionization (PAPER) observing for 120 days 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 3\sigma level at k<0.25h Mpc^{-1} in a bin of \Delta ln k=1. We discuss the tradeoffs of low- versus high-redundancy configurations.