A fast method for power spectrum and foreground analysis for 21 cm cosmology

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We develop and demonstrate an acceleration of the Liu and Tegmark quadratic estimator formalism for inverse variance foreground subtraction and power spectrum estimation in 21 cm tomography from OðN 3 Þ to OðN logNÞ, where N is the number of voxels of data. This technique makes feasible the megavoxel scale analysis necessary for current and upcoming radio interferometers by making only moderately restrictive assumptions about foreground models and survey geometry. We exploit iterative and Monte Carlo techniques and the symmetries of the foreground covariance matrices to quickly estimate the 21 cm brightness temperature power spectrum, Pðk k ; k ? Þ, the Fisher information matrix, the error bars, the window functions, and the bias. We also extend the Liu and Tegmark foreground model to include bright point sources with known positions in a way that scales as O½ðN logNÞ Â ðN point sourcesފ OðN 5=3 Þ. As a first application of our method, we forecast error bars and window functions for the upcoming 128-tile deployment of the Murchinson Widefield Array, showing that 1000 hours of observation should prove sufficiently sensitive to detect the power spectrum signal from the Epoch of Reionization.