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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 ΛCDM E-modes to a level corresponding to a tensor-to-scalar ratio of, Astronomy

We present results from an analysis of all data taken by the BICEP2 and Keck Array cosmic microwave background (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 to 353 GHz. An excess over lensed ΛCDM is detected at modest significance in the 95 × 150 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 23 × 95, or for correlation between the dust and synchrotron sky patterns in spectra such as 23 × 353. We take the likelihood of all the spectra for a multicomponent model including lensed ΛCDM, 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 r0.05 < 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 baryon acoustic oscillations and other data yields a combined limit r0.05 < 0.07 at 95% confidence. These are the strongest constraints to date on inflationary gravitational waves., Astronomy, Physics

We present measurements of polarization lensing using the 150 GHz maps, which include all data taken by the BICEP2 and Keck Array Cosmic Microwave Background polarization experiments up to and including the 2014 observing season (BK14). Despite their modest angular resolution ($\sim 0\buildrel{\circ}\over{.} 5$), the excellent sensitivity (~3μK-arcmin) of these maps makes it possible to directly reconstruct the lensing potential using only information at larger angular scales (${\ell }\leqslant 700$). From the auto-spectrum of the reconstructed potential, we measure an amplitude of the spectrum to be ${A}_{{\rm{L}}}^{\phi \phi }=1.15\pm 0.36$ (Planck ΛCDM prediction corresponds to ${A}_{{\rm{L}}}^{\phi \phi }=1$) and reject the no-lensing hypothesis at $5.8\sigma $, which is the highest significance achieved to date using an EB lensing estimator. Taking the cross-spectrum of the reconstructed potential with the Planck 2015 lensing map yields ${A}_{{\rm{L}}}^{\phi \phi }=1.13\pm 0.20$. These direct measurements of ${A}_{{\rm{L}}}^{\phi \phi }$ are consistent with the ΛCDM cosmology and with that derived from the previously reported BK14 B-mode auto-spectrum (${A}_{{\rm{L}}}^{\mathrm{BB}}=1.20\pm 0.17$). We perform a series of null tests and consistency checks to show that these results are robust against systematics and are insensitive to analysis choices. These results unambiguously demonstrate that the B modes previously reported by BICEP/Keck at intermediate angular scales ($150\lesssim {\ell }\lesssim 350$) are dominated by gravitational lensing. The good agreement between the lensing amplitudes obtained from the lensing reconstruction and B-mode spectrum starts to place constraints on any alternative cosmological sources of B modes at these angular scales., Astronomy, Physics

bicep2 and the Keck Array are polarization-sensitive microwave telescopes that observe the cosmic microwave background (CMB) from the South Pole at degree angular scales in search of a signature of inflation imprinted as B-mode polarization in the CMB. bicep2 was deployed in late 2009, observed for three years until the end of 2012 at 150 GHz with 512 antenna-coupled transition edge sensor bolometers, and has reported a detection of B-mode polarization on degree angular scales. The Keck Array was first deployed in late 2010 and will observe through 2016 with five receivers at several frequencies (95, 150, and 220 GHz). bicep2 and the Keck Array share a common optical design and employ the field-proven bicep1 strategy of using small-aperture, cold, on-axis refractive optics, providing excellent control of systematics while maintaining a large field of view. This design allows for full characterization of far-field optical performance using microwave sources on the ground. Here we describe the optical design of both instruments and report a full characterization of the optical performance and beams of bicep2 and the Keck Array at 150 GHz., Astronomy

In a companion paper, we have reported a >5σ detection of degree scale B-mode polarization at 150 GHz by the Bicep2 experiment. Here we provide a detailed study of potential instrumental systematic contamination to that measurement. We focus extensively on spurious polarization that can potentially arise from beam imperfections. We present a heuristic classification of beam imperfections according to their symmetries and uniformities, and discuss how resulting contamination adds or cancels in maps that combine observations made at multiple orientations of the telescope about its boresight axis. We introduce a technique, which we call "deprojection," for filtering the leading order beam-induced contamination from time-ordered data, and show that it reduces power in Bicep2's actual and null-test BB spectra consistent with predictions using high signal-to-noise beam shape measurements. We detail the simulation pipeline that we use to directly simulate instrumental systematics and the calibration data used as input to that pipeline. Finally, we present the constraints on BB contamination from individual sources of potential systematics. We find that systematics contribute BB power that is a factor of ~10× below Bicep2's three-year statistical uncertainty, and negligible compared to the observed BB signal. The contribution to the best-fit tensor/scalar ratio is at a level equivalent to r = (3–6) × 10−3., Astronomy

We have developed antenna-coupled transition-edge sensor (TES) bolometers for a wide range of cosmic microwave background (CMB) polarimetry experiments, including BICEP2, Keck Array, and the balloon borne SPIDER. These detectors have reached maturity and this paper reports on their design principles, overall performance, and key challenges associated with design and production. Our detector arrays repeatedly produce spectral bands with 20%-30% bandwidth at 95, 150, or 220~GHz. The integrated antenna arrays synthesize symmetric co-aligned beams with controlled side-lobe levels. Cross-polarized response on boresight is typically ~0.5%, consistent with cross-talk in our multiplexed readout system. End-to-end optical efficiencies in our cameras are routinely 35% or higher, with per detector sensitivities of NET~300 uKrts. Thanks to the scalability of this design, we have deployed 2560 detectors as 1280 matched pairs in Keck Array with a combined instantaneous sensitivity of ~9 uKrts, as measured directly from CMB maps in the 2013 season. Similar arrays have recently flown in the SPIDER instrument, and development of this technology is ongoing., Astronomy

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 deg2 patch of sky centered on RA 0h, Dec. −57.5deg. 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 μK deg in Q and U at 143 GHz). We detect 150×353 cross-correlation in B-modes at high significance. We fit the single- and cross-frequency power spectra at frequencies ≥150 GHz to a lensed-ΛCDM 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 r0.05<0.12 at 95% confidence. Marginalizing over dust and r, lensing B-modes are detected at 7.0σ significance., Astronomy

We report on the design and performance of the BICEP2 instrument and on its three-year data set. BICEP2 was designed to measure the polarization of the cosmic microwave background (CMB) on angular scales of 1°-5°(l = 40-200), near the expected peak of the B-mode polarization signature of primordial gravitational waves from cosmic inflation. Measuring B-modes requires dramatic improvements in sensitivity combined with exquisite control of systematics. The BICEP2 telescope observed from the South Pole with a 26 cm aperture and cold, on-axis, refractive optics. BICEP2 also adopted a new detector design in which beam-defining slot antenna arrays couple to transition-edge sensor (TES) bolometers, all fabricated on a common substrate. The antenna-coupled TES detectors supported scalable fabrication and multiplexed readout that allowed BICEP2 to achieve a high detector count of 500 bolometers at 150 GHz, giving unprecedented sensitivity to B-modes at degree angular scales. After optimization of detector and readout parameters, BICEP2 achieved an instrument noise-equivalent temperature of 15.8 μ {K}\sqrt{{s}}. The full data set reached Stokes Q and U map depths of 87.2 nK in square-degree pixels (5.'2 μK) over an effective area of 384 deg2 within a 1000 deg2 field. These are the deepest CMB polarization maps at degree angular scales to date. The power spectrum analysis presented in a companion paper has resulted in a significant detection of B-mode polarization at degree scales., Astronomy