Effects of model incompleteness on the drift-scan calibration of radio
  telescopes
  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 auto-correlations 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.
