Rethinking CMB foregrounds: systematic extension of foreground
  parameterizations
  Future high-sensitivity measurements of the cosmic microwave background (CMB)
anisotropies and energy spectrum will be limited by our understanding and
modeling of foregrounds. Not only does more information need to be gathered and
combined, but also novel approaches for the modeling of foregrounds,
commensurate with the vast improvements in sensitivity, have to be explored.
Here, we study the inevitable effects of spatial averaging on the spectral
shapes of typical foreground components, introducing a moment approach, which
naturally extends the list of foreground parameters that have to be determined
through measurements or constrained by theoretical models. Foregrounds are
thought of as a superposition of individual emitting volume elements along the
line of sight and across the sky, which then are observed through an
instrumental beam. The beam and line of sight averages are inevitable. Instead
of assuming a specific model for the distributions of physical parameters, our
method identifies natural new spectral shapes for each foreground component
that can be used to extract parameter moments (e.g., mean, dispersion,
cross-terms, etc.). The method is illustrated for the superposition of
power-laws, free-free spectra, gray-body and modified blackbody spectra, but
can be applied to more complicated fundamental spectral energy distributions.
Here, we focus on intensity signals but the method can be extended to the case
of polarized emission. The averaging process automatically produces
scale-dependent spectral shapes and the moment method can be used to propagate
the required information across scales in power spectrum estimates. The
approach is not limited to applications to CMB foregrounds but could also be
useful for the modeling of X-ray emission in clusters of galaxies.
