10,635 research outputs found
Mosaicking with cosmic microwave background interferometers
Measurements of cosmic microwave background (CMB) anisotropies by
interferometers offer several advantages over single-dish observations. The
formalism for analyzing interferometer CMB data is well developed in the
flat-sky approximation, valid for small fields of view. As the area of sky is
increased to obtain finer spectral resolution, this approximation needs to be
relaxed. We extend the formalism for CMB interferometry, including both
temperature and polarization, to mosaics of observations covering arbitrarily
large areas of the sky, with each individual pointing lying within the flat-sky
approximation. We present a method for computing the correlation between
visibilities with arbitrary pointing centers and baselines and illustrate the
effects of sky curvature on the l-space resolution that can be obtained from a
mosaic.Comment: 9 pages; submitted to Ap
Systematic Errors in Cosmic Microwave Background Interferometry
Cosmic microwave background (CMB) polarization observations will require
superb control of systematic errors in order to achieve their full scientific
potential, particularly in the case of attempts to detect the B modes that may
provide a window on inflation. Interferometry may be a promising way to achieve
these goals. This paper presents a formalism for characterizing the effects of
a variety of systematic errors on interferometric CMB polarization
observations, with particular emphasis on estimates of the B-mode power
spectrum. The most severe errors are those that couple the temperature
anisotropy signal to polarization; such errors include cross-talk within
detectors, misalignment of polarizers, and cross-polarization. In a B mode
experiment, the next most serious category of errors are those that mix E and B
modes, such as gain fluctuations, pointing errors, and beam shape errors. The
paper also indicates which sources of error may cause circular polarization
(e.g., from foregrounds) to contaminate the cosmologically interesting linear
polarization channels, and conversely whether monitoring of the circular
polarization channels may yield useful information about the errors themselves.
For all the sources of error considered, estimates of the level of control that
will be required for both E and B mode experiments are provided. Both
experiments that interfere linear polarizations and those that interfere
circular polarizations are considered. The fact that circular experiments
simultaneously measure both linear polarization Stokes parameters in each
baseline mitigates some sources of error.Comment: 19 pages, 9 figures, submitted to Phys. Rev.
Markov chain Monte Carlo analysis of Bianchi VII_h models
We have extended the analysis of Jaffe et al. to a complete Markov chain
Monte Carlo (MCMC) study of the Bianchi type models including a
dark energy density, using 1-year and 3-year Wilkinson Microwave Anisotropy
Probe (WMAP) cosmic microwave background (CMB) data. Since we perform the
analysis in a Bayesian framework our entire inference is contained in the
multidimensional posterior distribution from which we can extract marginalised
parameter constraints and the comparative Bayesian evidence. Treating the
left-handed Bianchi CMB anisotropy as a template centred upon the `cold-spot'
in the southern hemisphere, the parameter estimates derived for the total
energy density, `tightness' and vorticity from 3-year data are found to be:
, , with orientation ). This template is preferred by a factor of roughly
unity in log-evidence over a concordance cosmology alone. A Bianchi type
template is supported by the data only if its position on the sky is heavily
restricted. The low total energy density of the preferred template, implies a
geometry that is incompatible with cosmologies inferred from recent CMB
observations. Jaffe et al. found that extending the Bianchi model to include a
term in creates a degeneracy in the plane. We explore this region fully by MCMC and find that the
degenerate likelihood contours do not intersect areas of parameter space that 1
or 3 year WMAP data would prefer at any significance above . Thus we
can confirm that a physical Bianchi model is not responsible for
this signature.Comment: 8 pages, 10 figures, significant update to include more accurate
results and conclusions to match version accepted by MNRA
Fast directional continuous spherical wavelet transform algorithms
We describe the construction of a spherical wavelet analysis through the
inverse stereographic projection of the Euclidean planar wavelet framework,
introduced originally by Antoine and Vandergheynst and developed further by
Wiaux et al. Fast algorithms for performing the directional continuous wavelet
analysis on the unit sphere are presented. The fast directional algorithm,
based on the fast spherical convolution algorithm developed by Wandelt and
Gorski, provides a saving of O(sqrt(Npix)) over a direct quadrature
implementation for Npix pixels on the sphere, and allows one to perform a
directional spherical wavelet analysis of a 10^6 pixel map on a personal
computer.Comment: 10 pages, 3 figures, replaced to match version accepted by IEEE
Trans. Sig. Pro
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