Line-of-Sight Extrapolation Noise in Dust Polarization
  The B-modes of polarization at frequencies ranging from 50-1000 GHz are
produced by Galactic dust, lensing of primordial E-modes in the cosmic
microwave background (CMB) by intervening large scale structure, and possibly
by primordial B-modes in the CMB imprinted by gravitational waves produced
during inflation. The conventional method used to separate the dust component
of the signal is to assume that the signal at high frequencies (e.g., 350 GHz)
is due solely to dust and then extrapolate the signal down to lower frequency
(e.g., 150 GHz) using the measured scaling of the polarized dust signal
amplitude with frequency. For typical Galactic thermal dust temperatures of
about 20K, these frequencies are not fully in the Rayleigh-Jeans limit.
Therefore, deviations in the dust cloud temperatures from cloud to cloud will
lead to different scaling factors for clouds of different temperatures. Hence,
when multiple clouds of different temperatures and polarization angles
contribute to the integrated line-of-sight polarization signal, the relative
contribution of individual clouds to the integrated signal can change between
frequencies. This can cause the integrated signal to be decorrelated in both
amplitude and direction when extrapolating in frequency. Here we carry out a
Monte Carlo analysis on the impact of this line-of-sight extrapolation noise,
enabling us to quantify its effect. Using results from the Planck experiment,
we find that this effect is small, more than an order of magnitude smaller than
the current uncertainties. However, line-of-sight extrapolation noise may be a
significant source of uncertainty in future low-noise primordial B-mode
experiments. Scaling from Planck results, we find that accounting for this
uncertainty becomes potentially important when experiments are sensitive to
primordial B-mode signals with amplitude r < 0.0015 .
