Galactic foreground constraints on primordial $B$-mode detection for ground-based experiments

Contamination by polarized foregrounds is one of the biggest challenges for future polarized cosmic microwave background (CMB) surveys and the potential detection of primordial $B$-modes. Future experiments, such as Simons Observatory (SO) and CMB-S4, will aim at very deep observations in relatively small ($f_{\rm sky} \sim 0.1$) areas of the sky. In this work, we investigate the forecasted performance, as a function of the survey field location on the sky, for regions over the full sky, balancing between polarized foreground avoidance and foreground component separation modeling needs. To do this, we simulate observations by an SO-like experiment and measure the error bar on the detection of the tensor-to-scalar ratio, $\sigma(r)$, with a pipeline that includes a parametric component separation method, the Correlated Component Analysis, and the use of the Fisher information matrix. We forecast the performance over 192 survey areas covering the full sky and also for optimized low-foreground regions. We find that modeling the spectral energy distribution of foregrounds is the most important factor, and any mismatch will result in residuals and bias in the primordial $B$-modes. At these noise levels, $\sigma(r)$ is not especially sensitive to the level of foreground contamination, provided the survey targets the least-contaminated regions of the sky close to the Galactic poles.