BeyondPlanck XIV. Intensity foreground sampling, degeneracies and priors
  We present the intensity foreground algorithms and model employed within the
BeyondPlanck analysis framework. The BeyondPlanck analysis includes a limited
set of frequency channels, and it is therefore particularly sensitive to
parameter degeneracies. We discuss various priors that are introduced to break
these degeneracies, and we improve the previous $Planck$-based
$\texttt{Commander}$ component separation implementation in four specific ways
that are all designed to improve stability and computational efficiency for
weakly constrained posterior distributions. These are 1) joint foreground
spectral parameter and amplitude sampling, building on ideas from Miramare; 2)
component-based monopole determination; 3) joint spectral parameter and
monopole sampling; and 4) application of informative spatial priors for
component amplitude maps. We find that the only spectral parameter with a
significant signal-to-noise ratio using the current BeyondPlanck data set is
the peak frequency of the anomalous microwave emission component, for which we
find $\nu_{\mathrm{p}}=25.3\pm0.5$ GHz; all others must be constrained through
external priors. Future work will aim at integrating many more data sets into
this analysis, both map and time-ordered based, and thereby gradually
eliminating the currently observed degeneracies in a controlled manner with
respect to both instrumental systematic effects and astrophysical degeneracies.
This work will be organized within the Open Science-based Cosmoglobe community
effort.
