Statistical analysis of the causes of excess variance in the 21 cm signal power spectra obtained with the Low-Frequency Array

¹ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
e-mail: hgan@astro.rug.nl
² LERMA (Laboratoire d’Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères), Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, 75014 Paris, France
³ The Netherlands Institute for Radio Astronomy (ASTRON), PO Box 2, 7990 AA Dwingeloo, The Netherlands
⁴ Max-Planck Institute for Astrophysics, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany
⁵ School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85281, USA
⁶ Astrophysics Research Center (ARCO), Department of Natural Sciences, The Open University of Israel, 1 University Road, PO Box 808, Ra’anana 4353701, Israel
⁷ Department of Physics, Technion, Haifa 32000, Israel
⁸ Department of Physics, Banwarilal Bhalotia College, GT Rd, Ushagram, Asansol, West Bengal 713303, India
⁹ Institute for Computational Science, University of Zurich, Winterthurerstraße 190, 8057 Zurich, Switzerland
¹⁰ Astronomy Centre, Department of Physics and Astronomy, University of Sussex, Pevensey II Building, Brighton BN1 9QH, UK
¹¹ The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, 10691 Stockholm, Sweden

Received: 16 December 2021
Accepted: 24 February 2022

Abstract

Context. The detection of the 21 cm signal of neutral hydrogen from the Epoch of Reionization (EoR) is challenging due to bright foreground sources, radio frequency interference (RFI), and the ionosphere as well as instrumental effects. Even after correcting for these effects in the calibration step and applying foreground removal techniques, the remaining residuals in the observed 21 cm power spectra are still above the thermal noise, which is referred to as the “excess variance.”

Aims. We study a number of potential causes of this excess variance based on 13 nights of data obtained with the Low-Frequency Array (LOFAR).

Methods. We focused on the impact of gain errors, the sky model, and ionospheric effects on the excess variance by correlating the relevant parameters such as the gain variance over time or frequency, local sidereal time (LST), diffractive scale, and phase structure–function slope with the level of excess variance.

Results. Our analysis shows that the excess variance, at the current level, is neither strongly correlated with gain variance nor the ionospheric parameters. Rather, excess variance has an LST dependence, which is related to the power from the sky. Furthermore, the simulated Stokes I power spectra from bright sources and the excess variance show a similar progression over LST with the minimum power appearing at LST bin 6h to 9h. This LST dependence is also present in sky images of the residual Stokes I of the observations. In very-wide sky images based on one night of observation after direction-dependent calibration, we demonstrate that the extra power comes exactly from the direction of bright and distant sources Cassiopeia A and Cygnus A with the array beam patterns.

Conclusions. These results suggest that the level of excess variance in the 21 cm signal power spectra is related to sky effects and, hence, it depends on LST. In particular, very bright and distant sources such as Cassiopeia A and Cygnus A can dominate the effect. This is in line with earlier studies and offers a path forward toward a solution, since the correlation between the sky-related effects and the excess variance is non-negligible.