Systematic Effects in Interferometric Observations of the Cosmic Microwave Background Polarization

The detection of the primordial B-mode spectrum of the polarized cosmic microwave background (CMB) signal may provide a probe of inflation. However, observation of such a faint signal requires excellent control of systematic errors. Interferometry proves to be a promising approach for overcoming such a challenge. In this paper we present a complete simulation pipeline of interferometric observations of CMB polarization, including systematic errors. We employ two different methods for obtaining the power spectra from mock data produced by simulated observations: the maximum likelihood method and the method of Gibbs sampling. We show that the results from both methods are consistent with each other as well as, within a factor of six, with analytical estimates. Several categories of systematic errors are considered: instrumental errors, consisting of antenna gain and antenna coupling errors; and beam errors, consisting of antenna pointing errors, beam cross-polarization, and beam shape (and size) errors. In order to recover the tensor-to-scalar ratio, r, within a 10% tolerance level, which ensures the experiment is sensitive enough to detect the B-signal at r = 0.01 in the multipole range 28 < < 384, we find that, for a QUBIC-like experiment, Gaussian-distributed systematic errors must be controlled with precisions of |grms| = 0.1 for antenna gain, | rms| = 5 × 10−4 for antenna coupling, δrms ≈ 0. ◦7 for pointing, ζrms ≈ 0. ◦7 for beam shape, and μrms = 5 × 10−4 for beam cross-polarization. Although the combined systematic effects produce a tolerance level on r twice as large for an experiment with linear polarizers, the resulting bias in r for a circular experiment is 15% which is still on the level of desirable sensitivity.