Systematic effects induced by half-wave plate precession into measurements of the cosmic microwave background polarization

Context. The primordial B-mode signal in the cosmic microwave background (CMB) represents the smoking gun of cosmic inflation, and measuring it is the main goal of current experimental effort. The most accessible method for measuring polarization features of the CMB radiation is a Stokes polarimeter based on the rotation of a half-wave plate (HWP). Aims. Current observational cosmology is starting to be limited by systematic effects. A Stokes polarimeter with a rotating HWP has the advantage of mitigating a long list of potential systematics by modulating the linearly polarized component of the radiation, but the rotating HWP itself may introduce new systematic effects that must be under control. This represents one of the most critical parts in the design of a B-mode experiment. It is therefore mandatory to take all the systematic effects into account that the instrumentation can induce. We here present, simulate, and analyze the spurious signal arising from the precession of a rotating HWP. Methods. We first derived an analytical formula to describe the systematic effect that is induced by the HWP precession on the propagating radiation, using the 3D generalization of the Müller formalism. We then performed several numerical simulations that show the effect induced on the Stokes parameters by this systematic. We also derived and discuss the effect on B-modes as measured by a satellite experiment. Results. We derive the analytical formula for the Stokes parameters from a Stokes polarimeter where the HWP follows a precessional motion with an angle θ0. We show the result depending on the HWP inertia tensor, spinning speed, and on θ0. The result of numerical simulations is reported as a simple time-line of the electric fields. Finally, assuming that the entire sky is observed with a satellite mission, we analyze the effect on B-mode measurements. Conclusions. The effect is not negligible at the sensitivity of current B-mode experiments, therefore this systematic needs to be carefully considered for future experiments.