Calibration requirement for Epoch of Reionization 21-cm signal observation -- III. Bias and variance in uGMRT ELAIS-N1 field power spectrum

Abstract: Power spectrum of \HI 21-cm radiation is one of the promising probes to study large scale structure of the universe and understand galaxy formation and evolution. The presence of foregrounds, that are orders of magnitude larger in the same frequency range of the redshifted 21-cm signal has been one of the largest observational challenges. The foreground contamination also hinders the calibration procedures and introduces residual calibration errors in the interferometric data. It has been shown that the calibration errors can introduce bias in the 21-cm power spectrum estimates and introduce additional systematics. In this work, we assess the efficacy of 21-cm power spectrum estimation for the uGMRT Band-3 observations of the ELAIS-N1 field. We first evaluate the statistics of the residual gain errors and perform additional flagging based on these statistics. We then use an analytical method to estimate the bias and variance in the power spectrum. We found that (a) the additional flagging based on calibration accuracy help reduce the bias and systematics in the power spectrum, (b) the majority of the systematics at the lower angular scales, $\ell < 6000$, are due to the residual gain errors, (c) for the uGMRT baseline configuration and system parameters, the variance is always higher than the bias in the power spectrum estimates. Based on our analysis we observe that for an angular multipole of $\ell \sim3000$, $2000$ hours of `on source time' is required with the uGMRT to detect redshifted 21-cm signal at $3-\sigma$ significance from a redshift of $2.55$. In this work we only consider the power spectrum measurement in the plane of the sky, an assessment of residual gain statistics and its effect on multifrequency angular power spectrum estimation for the uGMRT and the SKA like telescopes will be presented in a companion paper.