SHINONOME II: The role of LST-direction moving average and required sky model accuracy

Abstract Detecting the 21 cm power spectrum from the Cosmic Dawn requires extremely accurate calibration and substantial suppression of foreground emission. In this study, we analyze drift-scan observations in the Murchison Widefield Array ultra-low-frequency band (73.6–104.3 MHz) and demonstrate from real data that the gain autocorrelation functions have zero-crossing timescales of ∼2–3 h, while the Allan-deviation minima indicate characteristic stability timescales of ∼45 min for the gain amplitude and 1.3 h for the gain phase. Using simulations, we further evaluate how representative catalog errors—positional errors, flux-scale errors, and catalog incompleteness—induce frequency-dependent structures in the calibration gains and generate systematic power within the Epoch of Reionization window. The results show that the accuracy required for the calibration sky catalog depends on the assumed amplitude of the 21 cm signal. For strong absorption scenarios such as those suggested by EDGES, the signal remains detectable even with $\sim$0.1% flux-scale errors and arcsecond-level positional accuracy. However, for standard scenarios, we find that $\sim$0.01% flux-scale accuracy and ${\sim }0{_{.}^{\prime\prime}} 5$ positional accuracy are sufficient to achieve the required dynamic range. We also find that source completeness down to $1\, \mathrm{mJy}$ remains inadequate for achieving the necessary dynamic range for either the strong or weak standard 21 cm signal scenario, although it is sufficient for the EDGES-inspired exotic scenario. Motivated by the gain-stability timescale indicated by the Allan-deviation analysis, we apply a gain moving average in time (${\sim } 50$ min), which reduces the standard deviation of the gain by 30%–60% and partially relaxes the requirements on the calibration catalog. These results demonstrate that the accuracy of the calibration catalog is a key limiting factor for low-frequency 21 cm cosmology and indicate that future Cosmic Dawn observations will require next-generation catalogs with improved accuracy and depth.