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Accurately accounting for spectral structure in spectrometer data induced by instrumental chromaticity on scales relevant for detection of the 21-cm signal is among the most significant challenges in global 21-cm signal analysis. In the publicly available Experiment to Detect the Global Epoch of Reionization Signature low-band data set, this complicating structure is suppressed using beam-factor-based chromaticity correction (BFCC), which works by dividing the data by a sky-map-weighted model of the spectral structure of the instrument beam. Several analyses of these data have employed models that start with the assumption that this correction is complete. However, while BFCC mitigates the impact of instrumental chromaticity on the data, given realistic assumptions regarding the spectral structure of the foregrounds, the correction is only partial. This complicates the interpretation of fits to the data with intrinsic sky models (models that assume no instrumental contribution to the spectral structure of the data). In this paper, we derive a BFCC data model from an analytical treatment of BFCC and demonstrate using simulated observations that, in contrast to using an intrinsic sky model for the data, the BFCC data model enables unbiased recovery of a simulated global 21-cm signal from beam-factor chromaticity-corrected data in the limit that the data are corrected with an error-free beam-factor model.

 

We develop a Bayesian model that jointly constrains receiver calibration, foregrounds, and cosmic 21 cm signal for the EDGES global 21 cm experiment. This model simultaneously describes calibration data taken in the lab along with sky-data taken with the EDGES low-band antenna. We apply our model to the same data (both sky and calibration) used to report evidence for the first star formation in 2018. We find that receiver calibration does not contribute a significant uncertainty to the inferred cosmic signal ($\lt 1{{\ \rm per\ cent}}$), though our joint model is able to more robustly estimate the cosmic signal for foreground models that are otherwise too inflexible to describe the sky data. We identify the presence of a significant systematic in the calibration data, which is largely avoided in our analysis, but must be examined more closely in future work. Our likelihood provides a foundation for future analyses in which other instrumental systematics, such as beam corrections and reflection parameters, may be added in a modular manner.

 

ABSTRACT Precision calibration poses challenges to experiments probing the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn and Epoch of Reionization (z ∼ 30–6). In both interferometric and global signal experiments, systematic calibration is the leading source of error. Though many aspects of calibration have been studied, the overlap between the two types of instruments has received less attention. We investigate the sky based calibration of total power measurements with a HERA dish and an EDGES-style antenna to understand the role of autocorrelations in the calibration of an interferometer and the role of sky in calibrating a total power instrument. Using simulations we study various scenarios such as time variable gain, incomplete sky calibration model, and primary beam model. We find that temporal gain drifts, sky model incompleteness, and beam inaccuracies cause biases in the receiver gain amplitude and the receiver temperature estimates. In some cases, these biases mix spectral structure between beam and sky resulting in spectrally variable gain errors. Applying the calibration method to the HERA and EDGES data, we find good agreement with calibration via the more standard methods. Although instrumental gains are consistent with beam and sky errors similar in scale to those simulated, the receiver temperatures show significant deviations from expected values. While we show that it is possible to partially mitigate biases due to model inaccuracies by incorporating a time-dependent gain model in calibration, the resulting errors on calibration products are larger and more correlated. Completely addressing these biases will require more accurate sky and primary beam models.