Search

Precision measurements of cosmic microwave background (CMB) polarization require extreme control of instrumental systematics. In a companion paper we have presented cosmological constraints from observations with the BICEP2 and Keck Array experiments up to and including the 2015 observing season (BK15), resulting in the deepest CMB polarization maps to date and a statistical sensitivity to the tensor-to-scalar ratio of $\sigma(r) = 0.020$. In this work we characterize the beams and constrain potential systematic contamination from main beam shape mismatch at the three BK15 frequencies (95, 150, and 220 GHz). Far-field maps of 7,360 distinct beam patterns taken from 2010-2015 are used to measure differential beam parameters and predict the contribution of temperature-to-polarization leakage to the BK15 B-mode maps. In the multifrequency, multicomponent likelihood analysis that uses BK15, Planck, and WMAP maps to separate sky components, we find that adding this predicted leakage to simulations induces a bias of $\Delta r = 0.0027 \pm 0.0019$. Future results using higher-quality beam maps and improved techniques to detect such leakage in CMB data will substantially reduce this uncertainty, enabling the levels of systematics control needed for BICEP Array and other experiments that plan to definitively probe large-field inflation., Comment: 18 pages, 9 figures, 4 tables. Minor correction to Figure 2 and caption

We present results from an analysis of all data taken by the BICEP2/Keck CMB polarization experiments up to and including the 2015 observing season. This includes the first Keck Array observations at 220 GHz and additional observations at 95 & 150 GHz. The $Q/U$ maps reach depths of 5.2, 2.9 and 26 $\mu$K$_{cmb}$ arcmin at 95, 150 and 220 GHz respectively over an effective area of $\approx 400$ square degrees. The 220 GHz maps achieve a signal-to-noise on polarized dust emission approximately equal to that of Planck at 353 GHz. We take auto- and cross-spectra between these maps and publicly available WMAP and Planck maps at frequencies from 23 to 353 GHz. We evaluate the joint likelihood of the spectra versus a multicomponent model of lensed-$\Lambda$CDM+$r$+dust+synchrotron+noise. The foreground model has seven parameters, and we impose priors on some of these using external information from Planck and WMAP derived from larger regions of sky. The model is shown to be an adequate description of the data at the current noise levels. The likelihood analysis yields the constraint $r_{0.05}<0.07$ at 95% confidence, which tightens to $r_{0.05}<0.06$ in conjunction with Planck temperature measurements and other data. The lensing signal is detected at $8.8 \sigma$ significance. Running maximum likelihood search on simulations we obtain unbiased results and find that $\sigma(r)=0.020$. These are the strongest constraints to date on primordial gravitational waves., Comment: 23 pages, 23 figures, as accepted by PRL, data and figures available for download at http://bicepkeck.org/

We present the strongest constraints to date on anisotropies of cosmic microwave background (CMB) polarization rotation derived from 150 GHz data taken by the BICEP2/Keck Array CMB experiments up to and including the 2014 observing season (BK14). The definition of the polarization angle in BK14 maps has gone through self-calibration in which the overall angle is adjusted to minimize the observed TB and EB power spectra. After this procedure, the QU maps lose sensitivity to a uniform polarization rotation but are still sensitive to anisotropies of polarization rotation. This analysis places constraints on the anisotropies of polarization rotation, which could be generated by CMB photons interacting with axionlike pseudoscalar fields or Faraday rotation induced by primordial magnetic fields. The sensitivity of BK14 maps ($\sim 3\mu$K-arcmin) makes it possible to reconstruct anisotropies of the polarization rotation angle and measure their angular power spectrum much more precisely than previous attempts. Our data are found to be consistent with no polarization rotation anisotropies, improving the upper bound on the amplitude of the rotation angle spectrum by roughly an order of magnitude compared to the previous best constraints. Our results lead to an order of magnitude better constraint on the coupling constant of the Chern-Simons electromagnetic term $g_{a\gamma}\leq 7.2\times 10^{-2}/H_I$ (95% confidence) than the constraint derived from the B-mode spectrum, where $H_I$ is the inflationary Hubble scale. This constraint leads to a limit on the decay constant of $10^{-6}\lesssim f_a/M_{\rm pl}$ at mass range of $10^{-33}< m_a< 10^{-28}$ eV for $r=0.01$, assuming $g_{a\gamma}\sim\alpha/(2\pi f_a)$ with $\alpha$ denoting the fine structure constant. The upper bound on the amplitude of the primordial magnetic fields is 30nG (95% confidence) from the polarization rotation anisotropies., Comment: 6 pages, 2 figures

A linear polarization field on the sphere can be uniquely decomposed into an E-mode and a B-mode component. These two components are analytically defined in terms of spin-2 spherical harmonics. Maps that contain filtered modes on a partial sky can also be decomposed into E-mode and B-mode components. However, the lack of full sky information prevents orthogonally separating these components using spherical harmonics. In this paper, we present a technique for decomposing an incomplete map into E and B-mode components using E and B eigenmodes of the pixel covariance in the observed map. This method is found to orthogonally define E and B in the presence of both partial sky coverage and spatial filtering. This method has been applied to the BICEP2 and the Keck Array maps and results in reducing E to B leakage from LCDM E-modes to a level corresponding to a tensor-to-scalar ratio of $r<1\times10^{-4}$., Comment: 21 pages, 23 figures, minor updates to reflect accepted version

We present results from an analysis of all data taken by the BICEP2 & Keck Array CMB polarization experiments up to and including the 2014 observing season. This includes the first Keck Array observations at 95 GHz. The maps reach a depth of 50 nK deg in Stokes $Q$ and $U$ in the 150 GHz band and 127 nK deg in the 95 GHz band. We take auto- and cross-spectra between these maps and publicly available maps from WMAP and Planck at frequencies from 23 GHz to 353 GHz. An excess over lensed-LCDM is detected at modest significance in the 95x150 $BB$ spectrum, and is consistent with the dust contribution expected from our previous work. No significant evidence for synchrotron emission is found in spectra such as 23x95, or for correlation between the dust and synchrotron sky patterns in spectra such as 23x353. We take the likelihood of all the spectra for a multi-component model including lensed-LCDM, dust, synchrotron and a possible contribution from inflationary gravitational waves (as parametrized by the tensor-to-scalar ratio $r$), using priors on the frequency spectral behaviors of dust and synchrotron emission from previous analyses of WMAP and Planck data in other regions of the sky. This analysis yields an upper limit $r_{0.05}<0.09$ at 95% confidence, which is robust to variations explored in analysis and priors. Combining these $B$-mode results with the (more model-dependent) constraints from Planck analysis of CMB temperature plus BAO and other data, yields a combined limit $r_{0.05}<0.07$ at 95% confidence. These are the strongest constraints to date on inflationary gravitational waves., Comment: 17 pages, 18 figures, minor updates to reflect accepted version, data and figures available for download at http://bicepkeck.org/