The residual gain errors add to the systematics of the radio interferometric observations. In case of the high dynamic range observations, these systematic effects dominates over the thermal noise of the observation. In this work, we investigate the effect of time-correlated residual gain errors in the estimation of the power spectrum of the sky brightness distribution in high dynamic range observations. Particularly, we discuss a methodology to estimate the bias in the power spectrum estimator of the redshifted 21-cm signal from neutral hydrogen in the presence of bright extragalactic compact sources. We find, that for the visibility-based power spectrum estimators, particularly those use nearby baseline correlations to avoid noise bias, the bias in the power spectrum arises mainly from the time correlation in the residual gain error. The bias also depends on the baseline distribution for a particular observation. Analytical calculations show that the bias is dominant for certain types of baseline pairs used for the visibility correlation. We perform simulated observation of extragalactic compact sources in the presence of residual gain errors with the Giant Metrewave Radio Telescope like array and estimate the bias in the power spectrum. Our results indicate that in order to estimate the redshifted 21-cm power spectrum, better calibration techniques, and estimator development are required.
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.
Statistics of the magnetic field disturbances in supernova remnants (SNRs) can be accessed using the second-order correlation function of the synchrotron intensities. Here we measure the magnetic energy spectra in the supernova remnant Cassiopeia-A by two-point correlation of the synchrotron intensities, using a recently developed unbiased method. The measured magnetic energy spectra in the vicinity of supernova remnant shocks are found to be a 2/3 power law over the decade of range scales, showing the developed trans-Alfvénic magnetohydrodynamic turbulence. Our results are globally consistent with the theoretical prediction of trans-Alfvénic Mach number in developed magnetohydrodynamic turbulence and can be explained by amplification of the magnetic field in the vicinity of SNR shocks. The magnetic energy spectra predict SNR Cassiopeia-A to have an additional subshock in the radio frequency observation along with forward and reverse shocks, with a radial window of the amplified magnetic field of ∼ 0.115 pc near the shocks.
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