Foreground bias from parametric models of far-IR dust emission

We use simple toy models of far-IR dust emission to estimate the accuracy to which the polarization of the cosmic microwave background can be recovered using multi-frequency fits, if the parametric form chosen for the fitted dust model differs from the actual dust emission. Commonly used approximations to the far-IR dust spectrum yield CMB residuals comparable to or larger than the sensitivities expected for the next generation of CMB missions, despite fitting the combined CMB + foreground emission to precision 0.1% or better. The Rayleigh–Jeans approximation to the dust spectrum biases the fitted dust spectral index by $\Delta {\beta }_d=0.2$ and the inflationary B-mode amplitude by $\Delta r=0.03$. Fitting the dust to a modified blackbody at a single temperature biases the best-fit CMB by $\Delta r>0.003$ if the true dust spectrum contains multiple temperature components. A 13-parameter model fitting two temperature components reduces this bias by an order of magnitude if the true dust spectrum is in fact a simple superposition of emission at different temperatures, but fails at the level $\Delta r=0.006$ for dust whose spectral index varies with frequency. Restricting the observing frequencies to a narrow region near the foreground minimum reduces these biases for some dust spectra but can increase the bias for others. Data at THz frequencies surrounding the peak of the dust emission can mitigate these biases while providing a direct determination of the dust temperature profile.