Toward an Understanding of Foreground Emission in the BICEP2 Region

TL;DR

The paper evaluates foreground contamination, especially polarized dust, in the BICEP2 region by deploying multiple independent dust estimates and cross-template analyses. It demonstrates that dust polarization could either mimic or overwhelm the observed B-mode signal, and that current BICEP1/2 data cannot decisively distinguish between a primordial gravitational-wave origin and a foreground-dominated explanation. The work highlights the sensitivity of cross-correlation methods to polarization-angle noise and the need for Planck and Keck/Planck high-frequency data to resolve the origin. The findings motivate forthcoming multi-frequency observations to determine whether the BICEP2 signal is primordial or foreground-driven.

Abstract

BICEP2 has reported the detection of a degree-scale B-mode polarization pattern in the Cosmic Microwave Background (CMB) and has interpreted the measurement as evidence for primordial gravitational waves. Motivated by the profound importance of the discovery of gravitational waves from the early Universe, we examine to what extent a combination of Galactic foregrounds and lensed E-modes could be responsible for the signal. We reanalyze the BICEP2 results and show that the 100x150 GHz and 150x150 GHz data are consistent with a cosmology with r=0.2 and negligible foregrounds, but also with a cosmology with r=0 and a significant dust polarization signal. We give independent estimates of the dust polarization signal in the BICEP2 region using four different approaches. While these approaches are consistent with each other, the expected amplitude of the dust polarization power spectrum remains uncertain by about a factor of three. The lower end of the prediction leaves room for a primordial contribution, but at the higher end the dust in combination with the standard CMB lensing signal could account for the BICEP2 observations, without requiring the existence of primordial gravitational waves. By measuring the cross-correlations between the pre-Planck templates used in the BICEP2 analysis and between different versions of a data-based template, we emphasize that cross-correlations between models are very sensitive to noise in the polarization angles and that measured cross-correlations are likely underestimates of the contribution of foregrounds to the map. These results suggest that BICEP1 and BICEP2 data alone cannot distinguish between foregrounds and a primordial gravitational wave signal, and that future Keck Array observations at 100 GHz and Planck observations at higher frequencies will be crucial to determine whether the signal is of primordial origin. (abridged)

Figures (5)

• Figure 1: The left panel compares the Bicep2$\times$Bicep2 signal to two models: the best-fit lensed CMB plus gravitational wave model and the best-fit lensed CMB plus Galactic foregrounds model. The right panel compares the Bicep1$\times$Bicep2 signal to the same set of models with the same parameters. The shaded band (light blue) includes uncertainties on the amplitude of the dust obtained from the Bicep2$\times$Bicep2 fit, as well as uncertainties on the synchrotron amplitude and scaling with $\ell$. The black error bars in both panels include sample variance for a $\Lambda$CDM cosmology with $r=0.2$.
• Figure 2: Likelihood of the spectral index of the signal in antenna temperature given the $100\!\times\!150$ GHz Bicep1$\times$ Bicep2 and $150\!\times\!150$ GHz Bicep2 data. The red curve shows the posterior for the spectral index of the signal derived from a fiducial Gaussian approximation to the likelihood. As in the Bicep2 analysis no correction is applied for the lensing contribution. It lies very close to their published result. The blue curve uses a likelihood function corrected to account for CMB lensing. In both cases the fiducial model is a $\Lambda$CDM model with $r=0$. The green curve accounts for lensing and uses a Gaussian approximation to the likelihood that includes the variance associated with a foreground characterized by an angular power spectrum with $\ell(\ell+1)C_\ell^{BB}/2\pi=0.01\, \mu$K$^2$ at $\ell=46$, $\ell$-dependence consistent with dust, and spectral index $\beta$. The covariance matrix accounts for the correlations between the $100\!\times\!150$ GHz and $150\!\times\!150$ GHz data. Because our analysis accounts for CMB lensing, the likelihood function is broader than that computed in B2. The vertical lines in the plot denote the best-fit CMB prediction (black) and the best-fit foreground prediction (orange). The dashed line shows the 68% confidence interval. The null-hypothesis is not convincingly excluded, but a CMB spectrum provides a slightly better fit. However, the constraint on the spectral index is entirely driven by the second bandpower at $100\!\times\!150$ GHz.
• Figure 3: Predicted contribution of polarized dust emission to the $B$-mode angular power spectrum for our models discussed in section \ref{['sec:dust']}, and for the pre-Planck models studied by Bicep2 (blue) after taking into account the increase in polarization fraction. The range for the FDS, PSM, BSS, and LSA models, shown in blue, is based on a variation of the polarization fraction between 8 and 17%, while the range for the DDM-P1 and DDM-P2 models is based on our set of 96 models (see section \ref{['sec:dust']}). The range for the Hi estimate reflects the uncertainty in the extrapolation to low column densities and the uncertainty in frequency extrapolation. The gray band shows the best-fit amplitude of $0.011 \pm 0.003 \, \mu$K$^2$ at $\ell = 46$ determined in section \ref{['sec:multi_fit']}. If the dust foreground amplitude lies in this gray band, then the best-fit model to the data will have a negligible gravitational wave contribution.
• Figure 4: Comparison of several predictions for the 150 GHz signal versus the reported Bicep2$\times$Bicep2 and the preliminary Bicep2$\times$ Keck measurements. The predictions are a combination of the dust polarization signal and the predicted lensing signal for standard cosmological parameters. Panel (a) is based on DDM-P1, which assumes that the dust polarization signal is proportional to the dust intensity (extrapolated from 353 GHz) times the mean polarization fraction (based on our CIB-corrected map; see section~\ref{['sec:dust']}). The band represents the 1$\sigma$ contours derived from a set of 48 DDM-P1 models. Panel (b) shows DDM-P2, with polarization fractions from our CIB-corrected map, and polarization direction based on starlight measurements, the PSM, or BoulangerESLAB. Panel (c) uses the column density of neutral hydrogen in the Bicep2 region inferred from the optical depth at 353 GHz to estimate the dust foreground. In this panel, the band reflects the uncertainty in the extrapolation of the scaling relation to low column densities as well as the uncertainty in the rescaling from 353 GHz to 150 GHz.
• Figure 5: The left panel shows the correlation matrix at $\ell=46$ for model 5 and four of the templates used in B2: the Planck Sky Model (PSM) Delabrouille2013, the Bi-Symmetric Spiral (BSS) and Logarithmic Spiral Arm (LSA) field models presented in ODea2012, and Model 8 of Finkbeiner1999 with $Q=U$. If the true sky looked like one of the models, then a measurement of the cross-correlation using another model would underestimate the signal by as much as a factor of 10. The correlations further decrease for higher multipoles. The right panel shows the correlation matrix at $\ell=46$ for a small subset of five DDM-P2 dust models. The polarization angles are taken to be (1) the average angle in the patch as inferred from starlight data; (2) the average angle taken from the PSM; (3) from the PSM at 5 degree resolution; and (4) from the PSM at 1 degree resolution. Model 5 is based on BoulangerESLAB and is a proxy for data. Even between "data-based" models and data, correlation coefficients below 50% are common, suggesting that low cross-power between the data-driven models and data do not establish that foregrounds are negligible.