Empirical Covariance Modeling for 21 cm Power Spectrum Estimation: A Method Demonstration and New Limits from Early Murchison Widefield Array 128-Tile Data

The separation of the faint cosmological background signal from bright astrophysical foregrounds remains one of the most daunting challenges of mapping the high-redshift intergalactic medium with the redshifted 21 cm line of neutral hydrogen. Advances in mapping and modeling of diffuse and point source foregrounds have improved subtraction accuracy, but no subtraction scheme is perfect. Precisely quantifying the errors and error correlations due to missubtracted foregrounds allows for both the rigorous analysis of the 21 cm power spectrum and for the maximal isolation of the EoR window from foreground contamination. We present a method to infer the covariance of foreground residuals from the data itself in contrast to previous attempts at a priori modeling. We demonstrate our method by setting limits on the power spectrum using a 3 h integration from the 128-tile Murchison Widefield Array. Observing between 167 and 198 MHz, we find at 95% confidence a best limit of Delta^2(k) < 3.7 x 10^4 mK^2 at comoving scale k = 0.18 hMpc^-1 and at z = 6.8, consistent with existing limits.

Overcoming real-world obstacles in 21 cm power spectrum estimation: A method demonstration and results from early Murchison Widefield Array data

We present techniques for bridging the gap between idealized inverse covariance weighted quadratic estimation of 21 cm power spectra and the real-world challenges presented universally by interferometric observation. By carefully evaluating various estimators and adapting our techniques for large but incomplete data sets, we develop a robust power spectrum estimation framework that preserves the so-called EoR window and keeps track of estimator errors and covariances. We apply our method to observations from the 32-tile prototype of the Murchinson Widefield Array to demonstrate the importance of a judicious analysis technique. Lastly, we apply our method to investigate the dependence of the clean EoR window on frequency--especially the frequency dependence of the so-called wedge feature--and establish upper limits on the power spectrum from z = 6.2 to z = 11.7. Our lowest limit is Delta(k) < 0.3 Kelvin at 95% confidence at a comoving scale k = 0.046 Mpc^-1 and z = 9.5.