The Simons Observatory: gain, bandpass and polarization-angle
  calibration requirements for B-mode searches
  We quantify the calibration requirements for systematic uncertainties for
next-generation ground-based observatories targeting the large-angle $B$-mode
polarization of the Cosmic Microwave Background, with a focus on the Simons
Observatory (SO). We explore uncertainties on gain calibration, bandpass center
frequencies, and polarization angles, including the frequency variation of the
latter across the bandpass. We find that gain calibration and bandpass center
frequencies must be known to percent levels or less to avoid biases on the
tensor-to-scalar ratio $r$ on the order of $\Delta r\sim10^{-3}$, in line with
previous findings. Polarization angles must be calibrated to the level of a few
tenths of a degree, while their frequency variation between the edges of the
band must be known to ${\cal O}(10)$ degrees. Given the tightness of these
calibration requirements, we explore the level to which residual uncertainties
on these systematics would affect the final constraints on $r$ if included in
the data model and marginalized over. We find that the additional parameter
freedom does not degrade the final constraints on $r$ significantly, broadening
the error bar by ${\cal O}(10\%)$ at most. We validate these results by
reanalyzing the latest publicly available data from the BICEP2/Keck
collaboration within an extended parameter space covering both cosmological,
foreground and systematic parameters. Finally, our results are discussed in
light of the instrument design and calibration studies carried out within SO.
