Removal of Galactic foregrounds for the Simons Observatory primordial gravitational wave search

Upcoming observations from the Simons Observatory have been projected to constrain the tensor-to-scalar ratio, $r$, at the level of $\sigma(r)=$0.003. Here we describe one of the forecasting algorithms for the Simons Observatory in more detail, based on cleaning CMB polarization maps using a parametric model. We present a new code to perform this end-to-end forecast, and explore the assumptions in greater detail. If spatial uniformity of the spectral energy distribution of synchrotron radiation and thermal dust emission is assumed over the region planned for observations, covering almost a fifth of the sky, a bias of order 1--3$\sigma$ in $r$ is projected for foreground models consistent with current data. We find that by masking the most contaminated regions of sky, or by adopting more parameters to describe the spatial variation in spectral index for synchrotron and dust, such a bias can be mitigated for the foreground models we consider. We also explore strategies for testing whether the cleaned CMB polarization maps contain residual foreground contamination, including cross-correlating with maps tracing the foregrounds. This method also has applications for other CMB polarization experiments.