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 vari ance 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.

15 Pages, 9 Figures, Accepted for Publication in MNRAS

References in corpus (19)

• Cosmology at Low Frequencies: The 21 cm Transition and the High-Redshift Universe
• Foreground simulations for the LOFAR - Epoch of Reionization Experiment
• On using visibility correlations to probe the HI distribution from the dark ages to the present epoch I: Formalism and the expected signal
• Foregrounds for redshifted 21 cm studies of reionization: GMRT 153 MHz observations
• Characterizing Foreground for redshifted 21-cm radiation: 150 MHz GMRT observations
• The multi-frequency angular power spectrum of the epoch of reionization 21 cm signal
• Multisource Self-calibration for Sensor Arrays
• Comparing Foreground Removal Techniques for Recovery of the LOFAR-EoR 21cm Power Spectrum
• Visibility based angular power spectrum estimation in low frequency radio interferometric observations
• Redundant-Baseline Calibration of the Hydrogen Epoch of Reionization Array
• Patterns of primary beam non-redundancy in close-packed 21 cm array observations
• Demonstrating the Tapered Gridded Estimator (TGE) for the Cosmological HI 21-cm Power Spectrum using $150\mathrm{MHz}$ GMRT observations
• The angular power spectrum measurement of the Galactic synchrotron emission in two fields of the TGSS survey
• A Tapered Gridded Estimator (TGE) for the Multi-Frequency Angular Power Spectrum (MAPS) and the Cosmological HI 21-cm Power Spectrum
• All sky angular power spectrum: I. Estimating brightness temperature fluctuations using TGSS 150 MHz survey
• Calibration Requirements for Epoch of Reionization 21-cm signal observations -- I. Effect of time-correlated gains
• Evidence of large scale energy cascade in the spiral galaxy NGC 5236
• An Image-based Tapered Gridded Estimator (ITGE) for the angular power spectrum
• Validating a novel angular power spectrum estimator using simulated low frequency radio-interferometric data

Cited by in corpus (5)

• Probing early universe through redshifted 21-cm signal: Modelling and observational challenges
• Towards 21-cm Intensity Mapping at $z=2.28$ with uGMRT using the Tapered Gridded Estimator I: Foreground Avoidance
• Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator III: Foreground removal
• Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator II: Cross-polarization power spectrum
• Calibration requirement for Epoch of Reionization 21-cm signal observation -- III. Bias and variance in uGMRT ELAIS-N1 field power spectrum