Systematic biases in low-frequency radio interferometric data due to calibration: the LOFAR-EoR case

Abstract

The redshifted 21 cm line of neutral hydrogen is a promising probe of the Epoch of Reionization (EoR). However, its detection requires a thorough understanding and control of the systematic errors. We study two systematic biases observed in the LO-FAR EoR residual data after calibration and subtraction of bright discrete foreground sources. The first effect is a suppression in the diffuse foregrounds, which could potentially mean a suppression of the 21 cm signal. The second effect is an excess of noise beyond the thermal noise. The excess noise shows fluctuations on small frequency scales, and hence it can not be easily removed by foreground removal or avoidance methods. Our analysis suggests that sidelobes of residual sources due to the chromatic point spread function and ionospheric scintillation can not be the dominant causes of the excess noise. Rather, both the suppression of diffuse foregrounds and the excess noise can occur due to calibration with an incomplete sky model containing predominantly bright discrete sources. We show that calibrating only on bright sources can cause suppression of other signals and introduce an excess noise in the data. The levels of the suppression and excess noise depend on the relative flux of sources which are not included in the model with respect to the flux of modeled sources. We discuss possible solutions such as using only long baselines to calibrate the interferometric gain solutions as well as simultaneous multi-frequency calibration along with their benefits and shortcomings.

Upper Limits on the 21 cm Epoch of Reionization Power Spectrum from One Night with LOFAR

“…Because our calibration sky model only consists of relatively compact sources, this removal of diffuse emission occurs because of a "conspiracy" of the direction-dependent gains-or equivalently the directiondependent PSFs-convolving the sky model with extended low-level PSFs and removing structures in the data that are not part of the sky model. Whereas using too few calibration directions leaves artefacts around compact sources, using too many will remove structure (Patil et al 2016). This is opposite (not in contradiction) to the issue noted by Barry et al (2016), where an incomplete/inaccurate sky model in MWA data simulations causes gain errors on all baselines, which then leads to excess variance in the EoR 21 cm power spectrum.…”

“…This has been discussed and documented in detail in Patil et al (2016). Because our calibration sky model only consists of relatively compact sources, this removal of diffuse emission occurs because of a "conspiracy" of the direction-dependent gains-or equivalently the directiondependent PSFs-convolving the sky model with extended low-level PSFs and removing structures in the data that are not part of the sky model.…”

“…This leads to an increase of variance on the excluded baselines and a decrease on those that are included (see appendix in Patil et al 2016, for a mathematical description) and is related to a bias introduced in nonlinear optimization (Cook et al 1986;Laurent & Cook 1992). …”

“…The spectrally complex model of the brightest source (at frequencies below 130 MHz) in the field, 3C61.1 (Figure 1), still needs improvement using subarcsecond structural information from the European ∼1000 km baselines now available. The chromatic residual side-lobe noise from all these imperfectly calibrated sources will affect the frequency-dependent gain solution on a frequency scale that depends on the distance of the source from the phase center (see, e.g., Barry et al 2016;Patil et al 2016).…”

“…The three effects described in Section 4.4 lead to additional spectral fluctuations on short baselines (see Patil et al 2016).…”