Fundamental Limitations on the Calibration of Redundant 21 cm Cosmology Instruments and Implications for HERA and the SKA

Abstract

Precise instrument calibration is critical to the success of 21 cm cosmology experiments. Unmitigated errors in calibration contaminate the Epoch of Reionization (EoR) signal, precluding a detection. Barry et al. 2016 characterizes one class of inherent errors that emerge from calibrating to an incomplete sky model, however it has been unclear if errors in the sky model affect the calibration of redundant arrays. In this paper, we show that redundant calibration is vulnerable to errors from sky model incompleteness even in the limit of perfect antenna positioning and identical beams. These errors are at a level that can overwhelm the EoR signal and prevent a detection on crucial power spectrum modes. Finally, we suggest error mitigation strategies with implications for the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA).

Absolute Calibration Strategies for the Hydrogen Epoch of Reionization Array and Their Impact on the 21 cm Power Spectrum

“…Redundant calibration somewhat skirts the problem of an inadequate sky model, and indeed exploiting the power of redundant calibration was a motivating factor behind HERA's redundant design (Dillon & Parsons 2016). However, redundant calibration operates only within a specific subspace of the full antenna-based calibration equations, meaning a model of the sky is still fundamentally needed to fill in the few remaining degenerate modes (Liu et al 2010;Zheng et al 2014;Dillon et al 2018;Li et al 2018;Byrne et al 2019;Dillon et al in prep.). We discuss this in more detail for HERA in Section 5.…”

“…This will introduce spectrallydependent errors into the gain solutions at some level (Barry et al 2016;Ewall-Wice et al 2017) which we explore in the following section. This can be partially mitigated by self-calibration or redundant calibration, although redundant calibration still suffers from this effect to some degree (Byrne et al 2019).…”

“…where V measured ij is the raw data, V true ij is the true visibility that would be measured by an uncorrupted instrument, and g i and g j are the instrumental gains for antenna i and j, respectively . Recent work has shown how incomplete models in skybased calibration (Barry et al 2016;Ewall-Wice et al 2017;Byrne et al 2019) and non-redundancies in redundant calibration (Joseph et al 2018;Orosz et al 2019) can lead to gain calibration errors that contaminate the EoR window. Foreground and instrument simulations for HERA indicate that the fiducial EoR signal at k ∼ 0.2 h Mpc −1 is expected to be roughly 10 5 times weaker than the peak foreground amplitude at k ∼ 0 h Mpc −1 in the visibility (Thyagarajan et al 2016).…”

“…Redundant calibration has been hailed as a powerful alternative calibration strategy for 21 cm experiments that sidesteps some of the requirements of sky-based calibration (Liu et al 2010;Zheng et al 2014). However, redundant calibration still needs a sky model to pin down certain degenerate parameters it cannot solve for (Dillon et al 2018;Li et al 2018;Joseph et al 2018;Byrne et al 2019). In this work, we explore hybrid redundant-absolute calibration strategies using the hera cal package.…”

Calibration and 21-cm power spectrum estimation in the presence of antenna beam variations

“…absolute amplitudes and phase gradients see Wieringa (1992); Liu et al (2010) for more details. Byrne et al (2019) show that incomplete sky models fundamentally limit the accuracy of redundant calibration solutions due to limitations in sky model based calibration. We expect this to be exacerbated by beam modelling errors that push power further into the window.…”