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.
