H I 21‐cm Cosmology and the Bispectrum: Closure Diagnostics in Massively Redundant Interferometric Arrays

Abstract

New, massively redundant low‐frequency arrays allow for a novel investigation of closure relations in interferometry. We employ commissioning data from the Hydrogen Epoch of Reionization Array to investigate closure quantities in this densely packed grid array of 14‐m antennas operating at 100 to 200 MHz. We investigate techniques that utilize closure phase spectra for redundant triads to estimate departures from redundancy for redundant baseline visibilities. We find a median absolute deviation from redundancy in closure phase across the observed frequency range of about 4.5°. This value translates into a nonredundancy per visibility phase of about 2.6°, using prototype electronics. The median absolute deviations from redundancy decrease with longer baselines. We show that closure phase spectra can be used to identify ill‐behaved antennas in the array, independent of calibration. We investigate the temporal behavior of closure spectra. The Allan variance increases after a 1‐min stride time, due to passage of the sky through the primary beam of the transit telescope. However, the closure spectra repeat to well within the noise per measurement at corresponding local sidereal times from day to day. In future papers in this series we will develop the technique of using closure phase spectra in the search for the H I 21‐cm signal from cosmic reionization.

Redundant-baseline calibration of the hydrogen epoch of reionization array

“…This result is consistent with other metrics of non-redundancy, e.g. closure phase (Carilli et al 2018). Likewise, this is consistent with the rough level of non-redundancy seen in the fiducial simulations of Orosz et al (2019), which take as inputs to their parameterized non-redundancy the construction tolerances of HERA dish and feed positioning.…”

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

“…Similar to how unmodeled diffuse emission created gain errors in sky calibration, these kinds of non-redundancies will create errors in redundant calibration and will appear at similar delays (Orosz et al 2019). Previous work showed that non-redundancy seems to be worse for short baselines (Carilli et al 2018), but quantifying this in more detail is still in progress (Dillon et al in prep.). The AR calibration gains also show significant power at τ 800 ns, which shows that redundant calibration is not immune to picking up cross coupling instrumental systematics.…”

Mitigating the effects of antenna-to-antenna variation on redundant-baseline calibration for 21 cm cosmology

“…We choose low, fiducial, and high error levels for each nonredundancy type, which we list in Table 1. These were chosen to represent realistic 4 antenna-to-antenna variations (Carilli et al 2018), with the condition that the resulting errors in visibilities are comparable for sources of non-redundancy at the same error level. To verify this, we show in Figure 2 the standard deviation of all the nominally redundant measurements of a single unique 14.6 m baseline.…”