Foreground-Induced Biases in CMB Polarimeter Self-Calibration
  Precise polarisation measurements of the cosmic microwave background (CMB)
require accurate knowledge of the instrument orientation relative to the sky
frame used to define the cosmological Stokes parameters. Suitable celestial
calibration sources that could be used to measure the polarimeter orientation
angle are limited, so current experiments commonly `self-calibrate.' The
self-calibration method exploits the theoretical fact that the $EB$ and $TB$
cross-spectra of the CMB vanish in the standard cosmological model, so any
detected $EB$ and $TB$ signals must be due to systematic errors. However, this
assumption neglects the fact that polarized Galactic foregrounds in a given
portion of the sky may have non-zero $EB$ and $TB$ cross-spectra. If these
foreground signals remain in the observations, then they will bias the
self-calibrated telescope polarisation angle and produce a spurious $B$-mode
signal. In this paper we estimate the foreground-induced bias for various
instrument configurations and then expand the self-calibration formalism to
account for polarized foreground signals. Assuming the $EB$ correlation signal
for dust is in the range constrained by angular power spectrum measurements
from Planck at 353 GHz (scaled down to 150 GHz), then the bias is negligible
for high angular resolution experiments, which have access to CMB-dominated
high $\ell$ modes with which to self-calibrate. Low-resolution experiments
observing particularly dusty sky patches can have a bias as large as
$0.5^\circ$. A miscalibration of this magnitude generates a spurious $BB$
signal corresponding to a tensor-to-scalar ratio of approximately
$r\sim2\times10^{-3}$, within the targeted range of planned experiments.
