Impacts and Statistical Mitigation of Missing Data on the 21 Cm Power Spectrum: A Case Study with the Hydrogen Epoch of Reionization Array

The precise characterization and mitigation of systematic effects is one of the biggest roadblocks impeding the detection of the fluctuations of cosmological 21 cm signals. Missing data in radio cosmological experiments, often due to radio frequency interference (RFI), pose a particular challenge to power spectrum analysis as this could lead to the ringing of bright foreground modes in the Fourier space, heavily contaminating the cosmological signals. Here we show that the problem of missing data becomes even more arduous in the presence of systematic effects. Using a realistic numerical simulation, we demonstrate that partially flagged data combined with systematic effects can introduce significant foreground ringing. We show that such an effect can be mitigated through inpainting the missing data. We present a rigorous statistical framework that incorporates the process of inpainting missing data into a quadratic estimator of the 21 cm power spectrum. Under this framework, the uncertainties associated with our inpainting method and its impact on power spectrum statistics can be understood. These results are applied to the latest Phase II observations taken by the Hydrogen Epoch of Reionization Array, forming a crucial component in power spectrum analyses as we move toward detecting 21 cm signals in the ever more noisy RFI environment.