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

Abstract

Detecting a signal from the Epoch of Reionisation (EoR) requires an exquisite understanding of galactic and extra-galactic foregrounds, low frequency radio instruments, instrumental calibration, and data analysis pipelines. In this work we build upon existing work that aims to understand the impact of calibration errors on 21-cm power spectrum (PS) measurements. It is well established that calibration errors have the potential to inhibit EoR detections by introducing additional spectral features that mimic the structure of EoR signals. We present a straightforward way to estimate the impact of a wide variety of modelling residuals in EoR PS estimation. We apply this framework to the specific case of broken dipoles in Murchison Widefield Array (MWA) to understand its effect and estimate its impact on PS estimation. Combining an estimate of the percentage of MWA tiles that have at least one broken dipole (15%-40%) with an analytic description of beam errors induced by such dipoles, we compute the residuals of the foregrounds after calibration and source subtraction. We find that that incorrect beam modelling introduces bias in the 2D-PS on the order of ∼ 10 3 mK 2 h −3 Mpc −3 , which is on the order of current lowest limits. Determining the accuracy of both current beam models and direction dependent calibration pipelines is therefore crucial in our search for an EoR signal.

The impact of tandem redundant/sky-based calibration in MWA Phase II data analysis

“…Redundant calibration takes advantage of the fact that any given correlation should depend only on relative positions of two antennas, which reduces a large number of unknowns when calibrating an redundant array. Redundant calibration is, to first order, sky-model-independent but may be contaminated by non-redundancy introduced through beam variation and antenna position errors (Orosz et al 2019; Joseph et al 2019). Joseph, Trott, & Wayth (2018) found that the position offsets introduce a phase bias of the calibration solutions.…”

Epoch of Reionization Power Spectrum Limits from Murchison Widefield Array Data Targeted at EoR1 Field

“…There have been many efforts in the community to understand about different systematics and the effective strategies to mitigate them; e.g. the residual power due to imperfect calibration models (Offringa et al 2015;Patil et al 2017;Procopio et al 2017;Morales et al 2018;Li et al 2019) and the spectral contamination from faint unmodeled sources (Barry et al 2016), excess power due to imperfect telescope beam models (Beardsley et al 2016;Li et al 2019;Barry et al 2019;Joseph et al 2020), the contamination due to RFI (Offringa et al 2015) and following possible contamination due to RFI excision (Offringa et al 2019), the introduced spectral structure due to instrumental chromaticity of interferometers (Trott & Wayth 2016) and the power bias due to ionospheric distortion effects (Jordan et al 2017;Trott et al 2018). Trott et al (2020) found that integrating beyond 300 observations (up to 820) did not significantly improve their results, implying the existence of a systematic floor of less than ∼ 26 hours.…”

“…By updating the beam model for each tile, we take into account the effect of any dead dipoles, if it contains any. Without this information, additional sources of error are included (Joseph et al 2020). Therefore, by flagging the dead dipoles within each tile, we obtain a less contaminated power spectrum as shown by red line.…”

“…While the correlator temporal resolution of 2013 and 2015 data is 0.5 s and 2 s respectively, the main difference between the data of these two seasons is due to the recording of dead dipoles (as discussed in section 3.7). There are ∼ 50 tiles with one dead dipole in 2015 data and the tiles with more than two dead dipoles are flagged (Joseph et al 2020). For the 2015 observations, the beam shape and visibility weights are adjusted if there is a dead dipole recorded, but that is not the case with 2013 observations.…”

“…Therefore, by developing suitable analysis approaches, they can be separated from the EoR signal in power space (Dillon et al 2014(Dillon et al , 2015aTrott et al 2016). The other major challenge is the systematic errors in calibration due to instrumental effects such as beam models (Joseph et al 2020) or spectral behaviour of electric components (Trott & Wayth 2016), imperfect sky models (Barry et al 2016;Byrne et al 2019;Zhang et al 2020), radio frequency interference (RFI) (Offringa et al 2015) and ionospheric distortions (Jordan et al 2017;Trott et al 2018;de Gasperin et al 2018). In addition, due to low SNR, we need to integrate over long observation times to average down the noise.…”