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Foreground Model and Antenna Calibration Errors in the Measurement of the Sky-Averaged λ21 cm Signal at z~20

The most promising near-term observable of the cosmic dark age prior to widespread reionization (z~15-200) is the sky-averaged λ21 cm background arising from hydrogen in the intergalactic medium. Though an individual antenna could in principle detect the line signature, data analysis must separate foregrounds that are orders of magnitude brighter than the λ21 cm background (but that are anticipated to vary monotonically and gradually with frequency). Using more physically motivated models for foregrounds than in previous studies, we show that the intrinsic "spectral smoothness" of the foregrounds is likely not a concern, and that data analysis for an ideal antenna should be able to detect the λ21 cm signal after deprojecting a ~5th order polynomial in log(ν). However, we find that the foreground signal is corrupted by the frequency-dependent response of a real antenna. The frequency dependence complicates modeling of foregrounds commonly based on the assumption of spectral smoothness. Much of our study focuses on the Large-aperture Experiment to detect the Dark Age (LEDA), which combines both radiometric and interferometric measurements. We show that statistical uncertainty remaining after fitting antenna gain patterns to interferometric measurements does not compromise extraction of the λ21 cm signal for a range of cosmological models after fitting a 7th order polynomial to radiometric data. Our results generalize to most efforts to measure the sky-averaged spectrum.