Framework For Analysis Of Next Generation, Polarized Cmb Data Sets In The Presence Of Galactic Foregrounds And Systematic Effects

Reaching the sufficient sensitivity to detect primordial B-modes requires modern CMB polarization experiments to rely on new technologies, necessary for the deployment of arrays of 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 in turn 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 in detail the effects induced by an achromatic half-wave plate (HWP), which lead to a frequency-dependent variation of the instrument polarization angle, and experimental bandpasses which define observational frequency bands. We assume a typical Stage-3 CMB polarization 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 particular 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. We also show that if the assumed model is an accurate description of the HWP and we have sufficient information about bandpasses, our approach can successfully correct for these effects. In particular, we recover the tensor-toscalar ratio r down to the precision levels typical of Stage-3 experiments, which aim at setting a (1 sigma) upper limit on r of similar to 10(-3) if r = 0.