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21cm tomography promises to be a powerful tool for estimating cosmologicalparameters, constraining the epoch of reionization, and probing the so-calleddark ages. However, realizing this promise will require the extraction of acosmological power spectrum from beneath overwhelmingly large sources offoreground contamination. In this paper, we develop a unified matrix-basedframework for foreground subtraction and power spectrum estimation, whichallows us to quantify the errors and biases that arise in the power spectrum asa result of foreground subtraction. We find that existing line-of-sightforeground subtraction proposals can lead to substantial mode-mixing as well asresidual noise and foreground biases, whereas our proposed inverse varianceforeground subtraction eliminates noise and foreground biases, gives smallererror bars, and produces less correlated measurements of the power spectrum. Wealso numerically confirm the intuitive belief in the literature that 21cmforeground subtraction is best done using frequency rather than angularinformation.

A Method for 21cm Power Spectrum Estimation in the Presence of Foregrounds