Frequency-Dependent Constraints on Cosmic Birefringence from the LFI and HFI Planck Data Release 4

We present new constraints on the frequency dependence of the cosmic birefringence angle from the Planck Data Release 4 polariza- tion maps. An axion field coupled to electromagnetism predicts a nearly frequency-independent birefringence angle, β ν = β , while Faraday rotation from local magnetic fields and Lorentz violating theories predict a cosmic birefringence angle that is proportional to the frequency, ν , to the power of some integer n , β ν ∝ ν n . In this work, we first sampled β ν individually for each polarized HFI frequency band in addition to the 70GHz channel from the LFI. We also constrained a power law formula for the birefringence angle, β ν = β 0 ( ν/ν 0 ) n , with ν 0 = 150GHz. For a nearly full-sky measurement, f sky = 0 . 93, we find β 0 = 0 . 26 ◦ ± 0 . 11 ◦ (68% C.L.) and n = − 0 . 45 + 0 . 61 − 0 . 82 when we ignore the intrinsic EB correlations of the polarized foreground emission, and β 0 = 0 . 33 ◦ ± 0 . 12 ◦ and n = − 0 . 37 + 0 . 49 − 0 . 64 when we use a filamentary dust model for the foreground EB . Next, we used all the polarized Planck maps, including the 30 and 44GHz frequency bands. These bands have a negligible foreground contribution from polarized dust emission and we thus treated them separately. Without any modeling of the intrinsic EB of the foreground, we generally find that the inclusion of the 30 and 44GHz frequency bands raises the measured values of β ν and tightens n . At nearly full-sky, we measure β 0 = 0 . 29 ◦ + 0 . 10 ◦ − 0 . 11 ◦ and n = − 0 . 35 + 0 . 48 − 0 . 47 . Assuming no frequency dependence, we measure β = 0 . 33 ◦ ± 0 . 10 ◦ . If our measurements have e ff ectively mitigated the EB of the foreground, our constraints are consistent with a mostly frequency-independent signal of cosmic birefringence.