Spatial variations in the spectral index of polarized synchrotron emission in the 9 yr WMAP sky maps

We estimate the spectral index, beta, of polarized synchrotron emission as observed in the 9 yr WMAP sky maps using two methods, linear regression ("T-T plot") and maximum likelihood. We partition the sky into 24 disjoint sky regions, and evaluate the spectral index for all polarization angles between 0 deg and 85 deg in steps of 5. Averaging over polarization angles, we derive a mean spectral index of beta_all-sky=-2.99+-0.01 in the frequency range of 23-33 GHz. We find that the synchrotron spectral index steepens by 0.14 from low to high Galactic latitudes, in agreement with previous studies, with mean spectral indices of beta_plane=-2.98+-0.01 and beta_high-lat=-3.12+-0.04. In addition, we find a significant longitudinal variation along the Galactic plane with a steeper spectral index toward the Galactic center and anticenter than toward the Galactic spiral arms. This can be well modeled by an offset sinusoidal, beta(l)=-2.85+0.17sin(2l-90). Finally, we study synchrotron emission in the BICEP2 field, in an attempt to understand whether the claimed detection of large-scale B-mode polarization could be explained in terms of synchrotron contamination. Adopting a spectral index of beta=-3.12, typical for high Galactic latitudes, we find that the most likely bias corresponds to about 2% of the reported signal (r=0.003). The flattest index allowed by the data in this region is beta=-2.5, and under the assumption of a straight power-law frequency spectrum, we find that synchrotron emission can account for at most 20% of the reported BICEP2 signal.Comment: 11 pages, 9 figures, updated to match version published in Ap

Sensitivity and foreground modelling for large-scale CMB B-mode polarization satellite missions

The measurement of the large-scale B-mode polarization in the cosmic microwave background (CMB) is a fundamental goal of future CMB experiments. However, because of unprecedented sensitivity, future CMB experiments will be much more sensitive to any imperfect modelling of the Galactic foreground polarization in the reconstruction of the primordial B-mode signal. We compare the sensitivity to B-modes of different concepts of CMB satellite missions (LiteBIRD, COrE, COrE+, PRISM, EPIC, PIXIE) in the presence of Galactic foregrounds. In particular, we quantify the impact on the tensor-to-scalar parameter of incorrect foreground modelling in the component separation process. Using Bayesian fitting and Gibbs sampling, we perform the separation of the CMB and Galactic foreground B-modes. The recovered CMB B-mode power spectrum is used to compute the likelihood distribution of the tensor-to-scalar ratio. We focus the analysis to the very large angular scales that can be probed only by CMB space missions, i.e. the Reionization bump, where primordial B-modes dominate over spurious B-modes induced by gravitational lensing. We find that fitting a single modified blackbody component for thermal dust where the "real" sky consists of two dust components strongly bias the estimation of the tensor-to-scalar ratio by more than 5{\sigma} for the most sensitive experiments. Neglecting in the parametric model the curvature of the synchrotron spectral index may bias the estimated tensor-to-scalar ratio by more than 1{\sigma}. For sensitive CMB experiments, omitting in the foreground modelling a 1% polarized spinning dust component may induce a non-negligible bias in the estimated tensor-to-scalar ratio.Comment: 20 pages, 8 figures, 6 tables. Updated to match version accepted by MNRA

Electromagnetic Casimir energy with extra dimensions

We calculate the energy-momentum tensor due to electromagnetic vacuum fluctuations between two parallel hyperplanes in more than four dimensions, considering both metallic and MIT boundary conditions. Using the axial gauge, the problem can be mapped upon the corresponding problem with a massless, scalar field satisfying respectively Dirichlet or Neumann boundary conditions. The pressure between the plates is constant while the energy density is found to diverge at the boundaries when there are extra dimensions. This can be related to the fact that Maxwell theory is then no longer conformally invariant. A similar behavior is known for the scalar field where a constant energy density consistent with the pressure can be obtained by improving the energy-momentum tensor with the Huggins term. This is not possible for the Maxwell field. However, the change in the energy-momentum tensor with distance between boundaries is finite in all cases.Comment: 16 pages, typos corrected, published versio

The Effect of Asymmetric Beams in the Wilkinson Microwave Anisotropy Probe Experiment

We generate simulations of the cosmic microwave background (CMB) temperature field as observed by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, taking into account the detailed shape of the asymmetric beams and scanning strategy of the experiment, and use these to re-estimate the WMAP beam transfer functions. This method avoids the need of artificially symmetrizing the beams, as done in the baseline WMAP approach, and instead measures the total convolution effect by direct simulation. We find only small differences with respect to the nominal transfer functions, typically less than 1% everywhere, and less than 0.5% at ℓ < 400. The net effect on the CMB power spectrum is less than 0.6%. The effect on all considered cosmological parameters is negligible. For instance, we find that the spectral index of scalar perturbations after taking into account the beam asymmetries is n_s = 0.964 ± 0.014, corresponding to a negative shift of –0.1σ compared to the previously released WMAP results. Our CMB sky simulations are made publicly available and can be used for general studies of asymmetric beam effects in the WMAP data

Optimized Large-Scale CMB Likelihood And Quadratic Maximum Likelihood Power Spectrum Estimation

We revisit the problem of exact CMB likelihood and power spectrum estimation with the goal of minimizing computational cost through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al.\ (1997), and here we develop it into a fully working computational framework for large-scale polarization analysis, adopting \WMAP\ as a worked example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked \WMAP\ sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8\% at $\ell\le32$, and a maximum shift in the mean values of a joint distribution of an amplitude--tilt model of 0.006$\sigma$. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation that requires less than 3 GB of memory and 2 CPU minutes per iteration for $\ell \le 32$, rendering low-$\ell$ QML CMB power spectrum analysis fully tractable on a standard laptop.Comment: 13 pages, 13 figures, accepted by ApJ