A Joint Analysis of BICEP2/Keck Array and Planck Data (1502.00612v2)

Abstract: We report the results of a joint analysis of data from BICEP2/Keck Array and Planck. BICEP2 and Keck Array have observed the same approximately 400 deg$^2$ patch of sky centered on RA 0h, Dec. $-57.5\deg$. The combined maps reach a depth of 57 nK deg in Stokes $Q$ and $U$ in a band centered at 150 GHz. Planck has observed the full sky in polarization at seven frequencies from 30 to 353 GHz, but much less deeply in any given region (1.2 $\mu$K deg in $Q$ and $U$ at 143 GHz). We detect 150$\times$353 cross-correlation in $B$-modes at high significance. We fit the single- and cross-frequency power spectra at frequencies $\geq 150$ GHz to a lensed-$\Lambda$CDM model that includes dust and a possible contribution from inflationary gravitational waves (as parameterized by the tensor-to-scalar ratio $r$), using a prior on the frequency spectral behavior of polarized dust emission from previous \planck\ analysis of other regions of the sky. We find strong evidence for dust and no statistically significant evidence for tensor modes. We probe various model variations and extensions, including adding a synchrotron component in combination with lower frequency data, and find that these make little difference to the $r$ constraint. Finally we present an alternative analysis which is similar to a map-based cleaning of the dust contribution, and show that this gives similar constraints. The final result is expressed as a likelihood curve for $r$, and yields an upper limit $r_{0.05}<0.12$ at 95% confidence. Marginalizing over dust and $r$, lensing $B$-modes are detected at $7.0\,\sigma$ significance.

• The paper presents a joint analysis of BICEP2/Keck and Planck CMB data using cross-correlation and multi-frequency techniques to constrain the tensor-to-scalar ratio $r < 0.12$ and quantify dust contamination.
• Analysis reveals a significant B-mode signal at 150 GHz which correlates with Planck high-frequency dust maps, indicating a strong dust contribution to the observed signal.
• This joint analysis highlights the importance of combining ground-based and satellite data to separate cosmological signals from foregrounds and refine constraints on primordial gravitational waves.

Analysis of Data from BICEP2, Keck Array, and Planck: Exploring $B$-Mode Polarization

BICEP2 and Keck Array (collectively BICEP2/Keck) collaborated with the Planck satellite to undertake a comprehensive analysis of $B$-mode polarization in the cosmic microwave background (CMB) radiation. This paper primarily leverages the deep-field observations from BICEP2/Keck and the all-sky coverage of Planck to constrain the cosmological parameter $r$, the tensor-to-scalar ratio, which could provide a direct window into primordial gravitational waves and, by extension, the inflationary paradigm.

Objectives and Methodology

The research aims to disentangle the $B$-mode signal into components originating from gravitational lensing, galactic dust, and potentially, primordial gravitational waves. BICEP2/Keck's data, focused on a small patch of sky and characterized by low noise at 150 GHz, is contrasted with Planck's broader but relatively noisier coverage at multiple frequencies (30 GHz to 353 GHz). This multi-frequency analysis facilitates spectral discrimination of the $B$-mode signal based on its spectral energy distribution (SED).

The analysis uses cross-correlation of $B$-mode polarization across frequencies, a more reliable measure than auto-correlation due to its robustness against systematic errors. The paper also incorporates models of interstellar dust, leveraging Planck's observations at high frequencies to constrain the amplitude of dust contamination in BICEP2/Keck's signal. The dust model assumes a power-law spatial spectrum and a modified black body SED, with polarization properties parameterized by the dust spectral index $\beta_d$.

Key Findings

• $B$-Mode Signal Detection: The cross-correlation between BICEP2/Keck and Planck data at 150 GHz and 353 GHz indicates a significant $B$-mode signal, a substantial portion of which correlates with the Planck high-frequency dust maps. BICEP2/Keck data confirms these observations, affirming the presence of a dust component but also constraints on any primordial gravitational wave signal.
• Tensor-to-Scalar Ratio ($r$) Limits: The analysis results in an upper limit of $r_{0.05} < 0.12$ at a 95% confidence level, with a peak likelihood at $r \approx 0.05$. This is consistent with Planck's large-scale anisotropy constraints when transformed to the same angular scales used by BICEP2.
• Impact of Dust: The likelihood analysis robustly detects the presence of dust in the $B$-mode polarization. The combination of BICEP2/Keck with Planck's data allows the team to gauge the dust's frequency-dependent behavior, substantially improving the separation of dust from a potential inflationary $B$-mode signal.
• Negligible Synchrotron Contribution: Adding lower-frequency data to the analysis places tight constraints on synchrotron emission as a source of the observed $B$-mode signal.

Implications and Future Work

The results validate the importance of cross-correlating ground-based, deep-field observations with satellite data to separate cosmological signals from foreground contaminants. They emphasize that while interstellar dust contributes to the observed $B$-mode power, the constrained upper limit on $r$ maintains the viability of inflationary theories that predict low levels of primordial gravitational waves.

This joint analysis approach sets a precedent for future studies, with next-generation CMB experiments continuing to refine these constraints. Ground-based observatories must aim for simultaneous multi-frequency observations, as demonstrated by extension plans for the Keck Array utilizing multiple frequency bands including 95 GHz to further constrain $r$ and better quantify the dust contribution. Future efforts, particularly from space missions designed for polarization sensitivity and resolution, will be crucial to distinguish between the contributions of lensing, dust, and any primordial signal in the pursuit of the inflationary signature.