# Fundamental uncertainty levels of 21cm power spectra from a delay analysis

## TL;DR

This paper quantifies the sample variance in 21cm power spectrum measurements from EoR experiments, highlighting its dependence on array design and implications for data analysis.

## Contribution

It provides the first detailed analysis of sample variance levels in delay-transform based 21cm power spectrum estimators for redundant arrays.

## Key findings

- Sample variance can reach 20-30% for individual baselines.
- Combining multiple baselines reduces variance to 1-3%.
- Results inform observing strategies and parameter constraints.

## Abstract

Several experimental efforts are underway to measure the power spectrum of 21cm fluctuations from the Epoch of Reionization (EoR) using low-frequency radio interferometers. Experiments like the Hydrogen Epoch of Reionization Array (HERA) and Murchison Widefield Array Phase II (MWA) feature highly-redundant antenna layouts, building sensitivity through redundant measurements of the same angular Fourier modes, at the expense of diminished UV coverage. This strategy limits the numbers of independent samples of each power spectrum mode, thereby increasing the effect of sample variance on the final power spectrum uncertainty. To better quantify this effect, we measure the sample variance of a delay-transform based power spectrum estimator, using both analytic calculations and simulations of flat-spectrum EoR-like signals. We find that for the shortest baselines in HERA, the sample variance can reach as high as 20%, and up to 30% for the wider fields-of-view of the MWA. Combining estimates from all the baselines in a HERA- or MWA-like 37 element redundant hexagonal array can lower the variance to $1-3$% for some Fourier modes. These results have important implications for observing and analysis strategies, and suggest that sample variance can be non-negligible when constraining EoR model parameters from upcoming 21cm data.