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

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 Low-Frequency Array-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 cannot be easily removed by foreground removal or avoidance methods. Our analysis suggests that sidelobes of residual sources due to the chromatic point spread function (PSF) and ionospheric scintillation cannot 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. 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 modelled sources. We predict that the excess noise will reduce with more observation time in the same way as the thermal noise does. We also discuss possible solutions such as using only long baselines to calibrate the interferometric gain solutions as well as simultaneous multifrequency calibration along with their benefits and shortcomings.