Ionospheric effect on the synthetic Epoch of Reionization observations with the SKA1-Low

The redshifted $21$\,cm signal of neutral hydrogen can be used as a direct probe of the intergalactic medium during Cosmic Dawn\,(CD) and Epoch of Reionization\,(EoR). However, detecting this inherently weak signal has numerous challenges. The major ones include accurate foreground removal from low-frequency radio observations and systematics arising from instrumental effects. The Earth's ionosphere poses a major obstacle at these low radio frequencies. Thus, a systematic study of ionospheric effects on these sensitive low-frequency observations is critical, given that the construction of the Square Kilometre Array (SKA1-Low) is in full progress. We use the end-to-end pipeline, called {\sc 21cme2e}, to study the effect of time-varying ionospheric corruption on the $21$\,cm power spectrum recovery. We use two models: a) a catalogue-based model focused on source position shift due to the refractive effect of the ionosphere and b) a realistic ionospheric condition generated using Kolmogorov's turbulence model. We assess the effect of the imperfections thus generated on the extraction of \HI\ $21$\,cm signal power spectrum. Our study shows that beyond ``median ionospheric offset" ($\theta_{\text{MIO}} \lesssim 0.1''$), the $21$\,cm signal from the EoR is unaffected by residual ionospheric effects. Our study emphasizes the need for the development of efficient ionospheric calibration algorithms for the upcoming SKA1-Low observations to extract the \HI\ $21$\,cm power spectra from the CD/EoR.