An empirical technique for assessing the instrumental errors of 21 centimeter emission line Zeeman splitting measurements

We illustrate a technique for empirically assessing the instrumental errors in 21 cm emission line Zeeman splitting measurements. For altitude-azimuth mounted telescopes this technique can be applied to many positions, but for equatorial telescopes it can be applied only at the celestial poles. Here we apply the technique with the equatorially mounted Hat Creek 85 foot (26 m) telescope by measuring the apparent circular polarization of the 21 cm line in emission toward the north celestial pole (NCP) and its variation with ''right ascension'' as the polarized beam pattern rotated with respect to the sky. The first and second Fourier components of this variation are equal to the instrumental errors contributed by beam squint and linear polarization, respectively. For the Hat Creek telescope at the NCP, we show that the dominant instrumental error is beam squint. We compare the empirical determination of the beam squint error with the value calculated from the measured beam squint. At the NCP, the instrumental error is fairly small compared to the actual field strength. The NCP has a somewhat larger velocity gradient than is typical, and the beam squint of the Hat Creek Radio Observatory telescope at the NCP was unusually large; we conclude that most measurements of Zeeman splitting in emission made with this telescope are reliable.