Detectability of tensor modes in the presence of foregrounds

TL;DR

This paper tackles the detectability of tensor (gravity-wave) B-modes in the CMB in the presence of Galactic foregrounds. It uses a Fisher-matrix framework with a quadratic estimator for the tensor-to-scalar ratio $T/S$, incorporating partial-sky E/B mixing from masks and foreground contamination, and implements two numerical strategies (exact and Monte Carlo) to compute the Fisher information under different sky fractions and dust-cleaning assumptions. The results show that the conventional $f_{sky}^{-1/2}$ scaling fails on the cut sky and, for $f_{sky}>0.7$, the scaling approaches $f_{sky}^{-2}$, implying that detecting $T/S$ at the $10^{-3}$ level requires tens of percent of the sky and extremely stringent foreground removal (dust polarized at or below $0.1\%$ of its intensity in the cleanest region; $10^{-4}$ may require ~70% sky and $0.01\%$ cleaning). These findings indicate foregrounds pose a substantial barrier to measuring primordial B-modes at low $T/S$, and they have direct implications for mission design and foreground characterization at observing frequencies like 90 GHz.

Abstract

In inflationary models, gravitational waves are produced and generate B-type polarization in the CMB. Since B polarization is only generated by gravity waves it does not suffer from the cosmic variance. A perfect decomposition of the CMB into B-modes and E-modes would require data from the entire sky, which in practice is not possible because of the foreground contaminants. This leads to mixing of E polarization into B, which introduces cosmic variance conta- mination of B polarization and reduces sensitivity to gravity wave amplitude even in absence of detector noise. We present numerical results for the uncertainty in the tensor-to-scalar ratio using the Fisher matrix formalism for various resolutions, using foreground models based on dust maps and assuming 90 GHz operating frequency. We find that the usual scaling delta(T/S) ~ f_sky^(-1/2) is significantly degraded and becomes delta(T/S) ~ f_sky^(-2) for f_sky>0.7. This dependence is affected only weakly by the choice of sky cuts. To achieve a T/S=10^(-3) detection at 3 sigma one needs to observe 15% of the sky as opposed to naive expectation of 0.3%. To prevent contamination over this large sky area at required level one must be able to remove polarized dust emission at or better than 0.1% of unpolarized intensity, assuming the cleanest part of the sky has been chosen. To achieve T/S=10^(-4) detection at 3 sigma one needs to observe 70% of the sky, which is only possible if dust emission is removed everywhere over this region at 0.01% level. Reaching T/S=10^(-2) should be easier: 1% of the sky is needed over which polarized emission needs to be removed at 1% of total intensity if the cleanest region is chosen. These results suggest that foreground contamination may make it difficult to achieve levels below T/S=10^(-3). (abridged)

Figures (8)

• Figure 1: The masks used for cutting the sky based on HEALPix resolution 3 galactic dust maps in Aitoff projection. Various levels of gray show the way the masks were built by adding areas with higher dust temperature. The units are of black body temperature.
• Figure 2: ${\rm w}C_l^{EE}$, ${\rm w}C_l^{BB}$ and the lensing + detector noise level after applying the Gaussian window for $T/S \simeq 1/2$. ${\rm w} C_l^{EE}$ is represented by the dashed line, ${\rm w} C_l^{BB}$ by the continuous line and the lensing + detector noise level by the thick horizontal line. These are the values used for resolution 6, where $l_{Ny} = 196$.
• Figure 3: ${\rm w}C_l^{BB}$ for two different values of the optical depth to the reionization $\tau$. The dashed line corresponds to a value of $\tau = 0.07$ and the continuous line to $\tau = 0.17$. The thick horizontal line is the lensing + detector noise level.
• Figure 4: $\triangle \left( \frac{T}{S} \right)$ as a function of sky fraction. The dashed line is computed based on the exact method for resolution 4, while the points with error bars are based on the Monte Carlo method for resolution 6 The continuous lines represent the theoretical scaling of $\triangle \left( \frac{T}{S} \right)$. The lower line corresponds to the idealized scaling $\triangle \left( \frac{T}{S} \right) \propto f_{sky}^{-1/2}$, while the upper line is $\triangle \left( \frac{T}{S} \right) \propto f_{sky}^{-2}$ and fits better the actual results for $f_{sky}>0.7$.
• Figure 5: The lines represent the fraction of the sky for which the polarized fraction of the dust thermal emission is less than the polarized signal, as defined in equation \ref{['b']}, assuming the polarized fraction of the dust thermal emission to be 1% (top), 0.1% (middle) and 0.01% (bottom). Dashed area is excluded if we require a detection of tensor-to-scalar ratio $\frac{T}{S}$ at a $3\sigma$ confidence. For example, to detect $T/S=10^{-3}$ at $3\sigma$ we need to observe 15% of the sky and if that is chosen to be the cleanest region of the sky then the dust polarization in this region needs to be cleaned at 0.1% level of its intensity.