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 polarization maps. An axion field coupled to electromagnetism predicts a nearly frequency-independent birefringence angle, beta nu = beta, while Faraday rotation from local magnetic fields and Lorentz violating theories predict a cosmic birefringence angle that is proportional to the frequency, nu, to the power of some integer n, beta(nu) proportional to nu(n). In this work, we first sampled beta(nu) individually for each polarized HFI frequency band in addition to the 70 GHz channel from the LFI. We also constrained a power law formula for the birefringence angle, beta(nu) = beta(0) (nu/nu(0))(n), with nu(0) = 150 GHz. For a nearly full-sky measurement, f(sky) = 0.93, we find beta(0) = 0.26 degrees +/- 0.11 degrees (68% C.L.) and n = -0.45(-0.82)(+0.61) when we ignore the intrinsic EB correlations of the polarized foreground emission, and beta(0) = 0.33 degrees +/- 0.12 degrees and n = -0.37(-0.64)(+0.49) when we use a filamentary dust model for the foreground EB. Next, we used all the polarized Planck maps, including the 30 and 44 GHz 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 44 GHz frequency bands raises the measured values of beta(nu) and tightens n. At nearly full-sky, we measure beta(0) = 0.29-(0.11)degrees(+0.10)degrees and n = -0.35(-0.47)(+0.48). Assuming no frequency dependence, we measure beta = 0.33 degrees +/- 0.10 degrees. If our measurements have effectively mitigated the EB of the foreground, our constraints are consistent with a mostly frequency-independent signal of cosmic birefringence.