Effects of Antenna Beam Chromaticity on Redshifted 21~cm Power Spectrum and Implications for Hydrogen Epoch of Reionization Array

Unaccounted for systematics from foregrounds and instruments can severely limit the sensitivity of current experiments from detecting redshifted 21~cm signals from the Epoch of Reionization (EoR). Upcoming experiments are faced with a challenge to deliver more collecting area per antenna element without degrading the data with systematics. This paper and its companions show that dishes are viable for achieving this balance using the Hydrogen Epoch of Reionization Array (HERA) as an example. Here, we specifically identify spectral systematics associated with the antenna power pattern as a significant detriment to all EoR experiments which causes the already bright foreground power to leak well beyond ideal limits and contaminate the otherwise clean EoR signal modes. A primary source of this chromaticity is reflections in the antenna-feed assembly and between structures in neighboring antennas. Using precise foreground simulations taking wide-field effects into account, we provide a framework to set cosmologically-motivated design specifications on these reflections to prevent further EoR signal degradation. We show HERA will not be impeded by such spectral systematics and demonstrate that even in a conservative scenario that does not perform removal of foregrounds, HERA will detect EoR signal in line-of-sight $k$-modes, $k_\parallel \gtrsim 0.2\,h$~Mpc$^{-1}$, with high significance. All baselines in a 19-element HERA layout are capable of detecting EoR over a substantial observing window on the sky.