Recovering redshifted 21-cm power spectrum: residual gain effects in radio interferometric Observations

Abstract

The power spectrum of H I 21-cm radiation is a key probe for studying the large-scale structure of the universe and the processes of galaxy formation and evolution. However, one of the major observational challenges is the contamination by foregrounds that are orders of magnitude brighter than the redshifted 21-cm signal in the same frequency range. Foreground contamination complicates calibration, introducing residual errors that bias power spectrum estimates and add systematics. In this work, we assess the efficacy of 21-cm power spectrum estimation using uGMRT Band-3 observations of the ELAIS-N1 field. By analyzing the statistics of residual gain errors and applying additional flagging based on these statistics, we demonstrate a significant reduction in bias and systematics. Our results show that systematics at lower angular scales (ℓ < 6000) primarily arise from residual gain errors and that standard deviation consistently exceeds the bias in power spectrum estimates. We estimate that approximately 2000 hours of on-source observation time is required to detect the 21-cm signal at a redshift of 2.55 with 3-σ significance at ℓ ≈ 3000.

Additionally, we explore the impact of frequency-dependent gain calibration errors on the EoR window in the k⊥-k∥ plane, finding significant contamination due to these errors. We also develop an analytical formula for the wedge structure, allowing wedge characterization directly from MAPS without simulations. These advancements provide critical insights into overcoming challenges in 21-cm cosmology for uGMRT and SKA-like telescopes. Further analysis of residual gain effects on multifrequency angular power spectra will be presented in a companion study.