Characterization of foreground emission on degree angular scales for CMB B-mode observations: Thermal dust and synchrotron signal from Planck and WMAP data

We quantify the contamination from polarized diffuse Galactic synchrotron and thermal dust emissions to the B modes of the cosmic microwave background (CMB) anisotropies on the degree angular scale, using data from the Planck and Wilkinson Microwave Anisotropy Probe (WMAP) satellites. We compute power spectra of foreground polarized emissions in 352 circular sky patches located at Galactic latitude | b | > 20\ub0, each of which covers about 1.5% of the sky. We make use of the spectral properties derived from Planck and WMAP data to extrapolate, in frequency, the amplitude of synchrotron and thermal dust B-mode spectra in the multipole bin centered at \u2113 43 80. In this way we estimate the amplitude and frequency of the foreground minimum for each analyzed region. We detect both dust and synchrotron signal on degree angular scales and at a 3\u3c3 confidence level in 28 regions. Here the minimum of the foreground emission is found at frequencies between 60 and 100 GHz with an amplitude expressed in terms of the equivalent tensor-to-scalar ratio, rFG,min, between 3c0.06 and 3c1. Some of these regions are located at high Galactic latitudes in areas close to the ones that are being observed by suborbital experiments. In all the other sky patches where synchrotron or dust B modes are not detectable with the required confidence, we put upper limits on the minimum foreground contamination and find values of rFG,min between 3c0.05 and 3c1.5 in the frequency range 60-90 GHz. Our results indicate that, with the current sensitivity at low frequency, it is not possible to exclude the presence of synchrotron contamination to CMB cosmological B modes at the level requested to measure a gravitational waves signal with r 43 0.01 at frequency 72 100 GHz anywhere. Therefore, more accurate data are essential in order to better characterize the synchrotron polarized component and, eventually, to remove its contamination to CMB signal through foreground cleaning. \ua9 2016 ESO

A 3D model for carbon monoxide molecular line emission as a potential cosmic microwave background polarization contaminant

We present a model for simulating Carbon Monoxide (CO) rotational line emission in molecular clouds, taking account of their 3D spatial distribution in galaxies with different geometrical properties. The model implemented is based on recent results in the literature and has been designed for performing Monte-Carlo simulations of this emission. We compare the simulations produced with this model and calibrate them, both on the map level and on the power spectrum level, using the second release of data from the Planck satellite for the Galactic plane, where the signal-to-noise ratio is highest. We use the calibrated model to extrapolate the CO power spectrum at low Galactic latitudes where no high sensitivity observations are available yet. We then forecast the level of unresolved polarized emission from CO molecular clouds which could contaminate the power spectrum of Cosmic Microwave Background (CMB) polarization B-modes away from the Galactic plane. Assuming realistic levels of the polarization fraction, we show that the level of contamination is equivalent to a cosmological signal with r 720.02. The Monte-Carlo MOlecular Line Emission (MCMole3D) Python package, which implements this model, is being made publicly available

The Classical Harmonic Vibrations of the Atomic Centers of Mass with Micro Amplitudes and Low Frequencies Monitored by the Entanglement between the Two Two-level Atoms in a Single mode Cavity

We study the entanglement dynamics of the two two-level atoms coupling with a single-mode polarized cavity field after incorporating the atomic centers of mass classical harmonic vibrations with micro amplitudes and low frequencies. We propose a quantitative vibrant factor to modify the concurrence of the two atoms states. When the vibrant frequencies are very low, we obtain that: (i) the factor depends on the relative vibrant displacements and the initial phases rather than the absolute amplitudes, and reduces the concurrence to three orders of magnitude; (ii) the concurrence increases with the increase of the initial phases; (iii) the frequency of the harmonic vibration can be obtained by measuring the maximal value of the concurrence during a small time. These results indicate that even the extremely weak classical harmonic vibrations can be monitored by the entanglement of quantum states.Comment: 10 pages, 3 figure

BICEP2 II: Experiment and Three-Year Data Set

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 to 5 degrees ($\ell$=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 $\mu$K sqrt(s). The full data set reached Stokes Q and U map depths of 87.2 nK in square-degree pixels (5.2 $\mu$K arcmin) over an effective area of 384 square degrees within a 1000 square degree 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.Comment: 30 pages, 24 figure

BICEP2 / Keck Array V: Measurements of B-mode Polarization at Degree Angular Scales and 150 GHz by the Keck Array

The Keck Array is a system of cosmic microwave background (CMB) polarimeters, each similar to the BICEP2 experiment. In this paper we report results from the 2012 and 2013 observing seasons, during which the Keck Array consisted of five receivers all operating in the same (150 GHz) frequency band and observing field as BICEP2. We again find an excess of B-mode power over the lensed-$\Lambda$CDM expectation of $> 5 \sigma$ in the range $30 < \ell < 150$ and confirm that this is not due to systematics using jackknife tests and simulations based on detailed calibration measurements. In map difference and spectral difference tests these new data are shown to be consistent with BICEP2. Finally, we combine the maps from the two experiments to produce final Q and U maps which have a depth of 57 nK deg (3.4 $\mu$K arcmin) over an effective area of 400 deg$^2$ for an equivalent survey weight of 250,000 $\mu$K$^{-2}$. The final BB band powers have noise uncertainty a factor of 2.3 times better than the previous results, and a significance of detection of excess power of $> 6\sigma$.Comment: 13 pages, 9 figure

BICEP2 / Keck Array VIII: Measurement of gravitational lensing from large-scale B-mode polarization

We present measurements of polarization lensing using the 150 GHz maps which include all data taken by the BICEP2 & Keck Array CMB polarization experiments up to and including the 2014 observing season (BK14). Despite their modest angular resolution ($\sim 0.5^\circ$), the excellent sensitivity ($\sim 3\mu$K-arcmin) of these maps makes it possible to directly reconstruct the lensing potential using only information at larger angular scales ($\ell\leq 700$). From the auto-spectrum of the reconstructed potential we measure an amplitude of the spectrum to be $A^{\phi\phi}_{\rm L}=1.15\pm 0.36$ (Planck $\Lambda$CDM prediction corresponds to $A^{\phi\phi}_{\rm L}=1$), 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 $A^{\phi\phi}_{\rm L}=1.13\pm 0.20$. These direct measurements of $A^{\phi\phi}_{\rm L}$ are consistent with the $\Lambda$CDM cosmology, and with that derived from the previously reported BK14 B-mode auto-spectrum ($A^{\rm BB}_{\rm L}=1.20\pm 0.17$). 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.Comment: 12 pages, 8 figure

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency is much smaller than the particle's orbital one. We make neither a priori assumptions about the direction of the wavevector nor on the orbital geometry of the planet. We find that, while the semi-major axis is left unaffected, the eccentricity, the inclination, the longitude of the ascending node, the longitude of pericenter and the mean anomaly undergo non-vanishing long-term changes. They are not secular trends because of the slow modulation introduced by the tidal matrix coefficients and by the orbital elements themselves. They could be useful to indepenedently constrain the ultra-low frequency waves which may have been indirectly detected in the BICEP2 experiment. Our calculation holds, in general, for any gravitationally bound two-body system whose characteristic frequency is much larger than the frequency of the external wave. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.Comment: LaTex2e, 24 pages, no figures, no tables. Changes suggested by the referees include