The impact of diffuse Galactic emission on direction-independent gain calibration in high-redshift 21 cm observations

This study examines the impact of diffuse Galactic emission on sky-based direction-independent (DI) gain calibration using realistic forward simulations of Low-Frequency Array (LOFAR) observations of the high-redshift ̧enti metre signal of neutral hydrogen during the epoch of reionization (EoR). We simulated LOFAR observations between hertz using a sky model that includes a point source catalog and diffuse Galactic emission. The simulated observations were DI gain-calibrated with the point source catalog alone, utilizing the LOFAR-EoR data analysis pipeline. A full power spectrum analysis was conducted to measure the systematic bias (relative to thermal noise) caused by DI gain calibration using a point-source-only (PSO) sky model, when applied to simulated data that include both point sources and diffuse Galactic emission. These results were compared to a ground truth scenario, where both the simulated sky and the calibration model solely included point sources. Additionally, the cross-coherence between observation pairs was computed to determine whether the DI gain calibration errors are coherent or incoherent in specific regions of power spectrum space as a function of integration time. We find that DI gain calibration with a PSO sky model that omits diffuse Galactic emission introduces a systematic bias in the power spectrum for k_∥ bins of < 0.2 h Mpc . The power spectrum errors in these bins are coherent in time and frequency; therefore, the resulting bias could be mitigated during the foreground removal step using Gaussian process regression (GPR), as demonstrated in previous studies. In contrast, errors for k_∥ > 0.2 h Mpc are largely incoherent and average down as noise. We conclude that based on our analysis prior to foreground removal, missing diffuse Galactic emission in the sky model during DI gain calibration is unlikely to be a dominant contributor to the excess noise observed in the current LOFAR-EoR upper limits on the 21 cm signal power spectrum.