Tomaschitz, R. (2019). Partially polarized black-body radiation, Physica A 524, 130-146, DOI: 10.1016/j.physa.2019.03.014
Angular temperature fluctuations in a photon gas generate fractional polarization of the black-body spectrum. The spectral density consists of two Planckians with different temperature variables representing orthogonal polarization states. The angular-dependent fluctuating temperature variables can be inferred from the Stokes parameters which have been measured, over the full solid angle, for the cosmic microwave background (CMB) radiation. The polarization matrix of a partially polarized photon gas is obtained by way of a unitary transformation of the annihilation and creation operators. The radiation is decomposed into a totally polarized and an unpolarized intensity component, and the polarization fraction is calculated, which is very small, of order ~10-7, for the nearly isotropic CMB radiation. Spatial energy density autocorrelations induced by polarization and temperature anisotropy are derived and isotropized by an angular average. These correlations are long-range, exhibiting power-law decay proportional to 1/r6 at large distance, and much stronger than the energy density correlation of an ideal photon gas which decays proportional to 1/r8. As for the CMB radiation, the spatial energy density correlations are calculated from analytic Gaussian fits to the measured temperature and polarization power spectra, including the crossover from the short-distance regime to the asymptotic power-law decay.
description: Roman Tomaschitz (2019) Partially polarized black-body radiation, Physica A 524, 130.
Keywords: Polarized photon gas; Polarization fraction; Stokes parameters of anisotropic black-body radiation; Multipole expansion of angular fluctuations; Spatial energy density correlations; Cosmic microwave background radiation
Black-body radiation can be fractionally polarized due to angular-dependent temperature fluctuations.
The spectral density of a partially polarized photon gas is derived and related to the Stokes parameters.
Spatial energy density correlations induced by temperature and polarization anisotropy are derived.
Analytic Gaussian representations of polarization power spectra are obtained via least-squares fits.
Long-range correlations of the microwave background radiation are calculated from angular power spectra.