Calibration requirements for Epoch of Reionization 21-cm signal observations – II. Analytical estimation of the bias and variance with time-correlated residual gains

Abstract

Observation of redshifted 21-cm signals from neutral hydrogen holds the key to understanding the structure formation and its evolution during the reionization and post-reionization era. Apart from the presence of orders of magnitude larger foregrounds in the observed frequency range, the instrumental effects of the interferometers combined with the ionospheric effects present a considerable challenge in the extraction of 21-cm signals from strong foregrounds. The systematic effects of time and frequency correlated residual gain errors originating from the measurement process introduce a bias and enhance the variance of the power spectrum measurements. In this work, we study the effect of time-correlated residual gain errors in the presence of strong foreground. We present a method to produce analytic estimates of the bias and variance in the power spectrum. We use simulated observations to confirm the efficacy of this method and then use it to understand various effects of the gain errors. We find that as the standard deviation in the residual gain errors increases, the bias in the estimation supersedes the variance. It is observed that an optimal choice of the time over which the gain solutions are estimated minimizes the risk. We also find that the interferometers with higher baseline densities are preferred instruments for these studies.

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

“…Manifestation of the time correlated residual gain errors as a bias in the power spectrum estimate is shown in [60]. It was observed by [61] that, with a few assumptions, the bias and excess variance in the time dependent residual gain errors can be analytically expressed for a known gain error model. In fact, this allows us to estimate the bias and variance in the power spectrum from a given observation, for which the gain error characteristics can be evaluated.…”

“…They find that the residual gain errors introduce bias in the TGE based power spectrum estimates and add to the systematics of the observation. Kumar et al (2022) [61] explore the effect of time-correlated residual gain errors in presence of strong foregrounds and thermal noise analytically and provide the mathematical expressions for bias and variance in the power spectrum measurements with a few assumptions.…”

“…In this work we explore the validity of the assumptions and simplification made by Kumar et al (2022) [61] using uGMRT observations of the ELAIS-N1 field at 300 − 500 MHz (data presented in Chakraborty et al (2019b) [55]). We thoroughly investigate various characteristics of residual gain errors and assumptions made in Kumar et al (2022) [61], to confirm the efficiency of their method and then use it to study the bias and excess variance in the power spectrum estimates of redshifted 21-cm signal. Rest of the paper is arranged in the following way.…”

Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator II: Cross-polarization power spectrum

“…The differences between the two estimates of 𝐶 ℓ (Δ𝜈) may arise due to polarized structure in the DGSE (Pen et al 2009b). Further, these differences may also arise from differences in the instrumental calibration of the two polarizations, instrumental polarization leakage due to asymmetry of the primary beam response and leakage from polarized point sources (Asad et al 2015;Van Eck et al 2018;Kumar et al 2022). Faraday rotation in the magnetized plasma causes a phase difference between the left and right circularly polarised components (Smirnov 2011), and this also can contribute to the difference in the Cross and Total 𝐶 ℓ (Δ𝜈).…”

Towards 21-cm intensity mapping at z = 2.28 with uGMRT using the tapered gridded estimator I: Foreground avoidance

“…Hence, we expect this excess noise to further contribute as excess power in the estimated power spectrum as residual foregrounds and systematics, as well as increase the error budget (the r.m.s. fluctuations) of the power spectrum estimated from the data (Kumar et al 2020(Kumar et al , 2022. Post four rounds of self-calibration (only phase), we have identified and subtracted out the compact and discrete sources with flux densities > 100𝜇Jy within an area of 1.8 deg 2 using the task UVSUB in CASA.…”