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We study the effects of astrophysical foregrounds on the ability of CMBB-mode polarization experiments to constrain the primordial tensor-to-scalarratio, r. To clean the foreground contributions we use parametric, maximumlikelihood component separation technique, and consider experimental setupsoptimized to render a minimal level of the foreground residuals in therecovered CMB map. We consider nearly full-sky observations, include twodiffuse foreground components, dust and synchrotron, and study cases with andwithout calibration errors, spatial variability of the foreground properties,and partial or complete B-mode lensing signal removal.  In all these cases we find that in the limit of very low noise level and inthe absence of the intrumental or modeling systematic effects, the foregroundresiduals do not lead to a limit on the lowest detectable value of r. But theneed to control the foreground residuals will play a major role in determiningthe minimal noise levels necessary to permit a robust detection of r < 0.1 andtherefore in optimizing and forecasting the performance of the future missions.For current and proposed experiments noise levels, the foreground residuals arefound non-negligible and potentially can affect our ability to set constraintson r. We also show how the constraints can be significantly improved on byrestricting the post component separation processing to a smaller sky area.This procedure applied to a case of a COrE-like satellite mission is shown toresult potentially in over an order of magnitude improvement in the detectablevalue of r. With sufficient knowledge of the experimental bandpasses as well asforeground component scaling laws, our conclusions are found to be independenton the assumed overall normalization of the foregrounds and only quantitativelydepend on specific parametrizations assumed for the foreground components.

Astrophysical foregrounds and primordial tensor-to-scalar ratio constraints from CMB B-mode polarization observations