Framework for analysis of next generation, polarised CMB data sets in
  the presence of galactic foregrounds and systematic effects
  Reaching the sufficient sensitivity to detect primordial B-modes requires
modern CMB polarisation experiments to rely on new technologies, necessary for
the deployment of arrays thousands of detectors with a broad frequency coverage
and operating them for extended periods of time. This increased complexity of
experimental design unavoidably introduces new instrumental and systematic
effects, which may impact performance of the new instruments. In this work we
extend the standard data analysis pipeline by including a (parametric) model of
instrumental effects directly in the data model. We then correct for them in
the analysis, accounting for the additional uncertainty in the final results.
We embed these techniques within a general, end-to-end formalism for estimating
the impact of the instrument and foreground models on constraints on the
amplitude of the primordial B-mode signal. We focus on the parametric component
separation approach which we generalize to allow for simultaneous estimation of
instrumental and foreground parameters.
  We demonstrate the framework by studying the effects induced by an achromatic
half-wave plate (HWP), which lead to a frequency-dependent variation of the
instrument polarisation angle, and experimental bandpasses which define
observational frequency bands. We assume a typical Stage-3 CMB polarisation
experiment, and show that maps recovered from raw data collected at each
frequency band will unavoidably be linear mixtures of the Q and U Stokes
parameters. We then derive a new generalized data model appropriate for such
cases, and extend the component separation approach to account for it. We find
that some of the instrumental parameters, in particularly those describing the
HWP can be successfully constrained by the data themselves without need for
external information, while others, like bandpasses, need to be known with good
precision in advance.
