Interpreting the HI 21-cm cosmology maps through Largest Cluster Statistics. Part II. Impact of the realistic foreground and instrumental noise on synthetic SKA1-Low observations

The Largest Cluster Statistics\,(LCS) analysis of the redshifted 21\,cm maps has been demonstrated to be an efficient and robust method for following the time evolution of the largest ionized regions\,(LIRs) during the Epoch of Reionization\,(EoR). The LCS can, in principle, constrain the reionization model and history by quantifying the morphology of neutral hydrogen\,(\HI) distribution during the different stages of the EoR. Specifically, the percolation transition of ionized regions, quantified and constrained via LCS, provides a crucial insight about the underlying reionization model. The previous LCS analysis of EoR 21\,cm maps demonstrates that the convolution of the synthesized beam of the radio interferometric arrays, e.g. SKA1-Low with the target signal, shifts the apparent percolation transition of ionized regions towards the lower redshifts. In this study, we present an optimal thresholding strategy to reduce this bias in the recovered percolation transition. We assess the robustness of LCS analysis of the 21\,cm maps, considering the effects of antenna-based gain calibration errors and instrumental noise for SKA1-Low. This analysis is performed using synthetic observations simulated by the \textsc{21cmE2E} pipeline, considering SKA1-Low AA4 configuration within a radius of 2\,km from the array centre. Our findings suggest that a minimum of $2000$\,hours of observation (SNR $\gtrapprox 3$) are required for the LCS analysis to credibly suppress the confusion introduced by thermal noise. Further, we also demonstrate that for a maximum antenna-based calibration error tolerance of $\sim 0.02\%$ (post calibration), the reionization history can be recovered in a robust and relatively unbiased manner using the LCS.