Tomaschitz,
R. (2019). Partially polarized black-body radiation, *Physica A* **524**,
130-146, DOI: 10.1016/j.physa.2019.03.014

**Abstract **ScienceDirect

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/r^{6} at large distance, and much stronger than the
energy density correlation of an ideal photon gas which decays proportional to
1/r^{8}. 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

**Highlights**

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.

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