Power Spectrum Sensitivity and the Design of Epoch of Reionization Observatories

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Abstract
Recent theoretical developments for observing the Epoch of Reionization (EOR) have concentrated on the power spectrum signature of redshifted 21 cm emission. These studies have demonstrated the great potential of statistical EOR observations, however, the sensitivity calculations for proposed low frequency radio arrays have been highly approximate. The formalism developed for interferometric measurements of the cosmic microwave background can be extended to three dimensions to naturally incorporate the line-of-sight information inherent in the EOR signal. In this paper we demonstrate how to accurately calculate the EOR power spectrum sensitivity of an array, and develop scaling relationships which can be used to guide the design of EOR observatories. The implications for antenna distribution, antenna size, and correlator requirements on the EOR sensitivity are detailed.
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