Joint Bayesian component separation and CMB power spectrum estimation

We describe and implement an exact, flexible, and computationally efficient algorithm for joint component separation and CMB power spectrum estimation, building on a Gibbs sampling framework. Two essential new features are 1) conditional sampling of foreground spectral parameters, and 2) joint sampling of all amplitude-type degrees of freedom (e.g., CMB, foreground pixel amplitudes, and global template amplitudes) given spectral parameters. Given a parametric model of the foreground signals, we estimate efficiently and accurately the exact joint foreground-CMB posterior distribution, and therefore all marginal distributions such as the CMB power spectrum or foreground spectral index posteriors. The main limitation of the current implementation is the requirement of identical beam responses at all frequencies, which restricts the analysis to the lowest resolution of a given experiment. We outline a future generalization to multi-resolution observations. To verify the method, we analyse simple models and compare the results to analytical predictions. We then analyze a realistic simulation with properties similar to the 3-yr WMAP data, downgraded to a common resolution of 3 degree FWHM. The results from the actual 3-yr WMAP temperature analysis are presented in a companion Letter.Comment: 23 pages, 16 figures; version accepted for publication in ApJ -- only minor changes, all clarifications. More information about the WMAP3 analysis available at http://www.astro.uio.no/~hke under the Research ta

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how are they modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a perfect agreement with numerical simulations.Comment: 7 pages, 8 figures. To be published in Physical Review

Cosmology with the largest galaxy cluster surveys: Going beyond Fisher matrix forecasts

We make the first detailed MCMC likelihood study of cosmological constraints that are expected from some of the largest, ongoing and proposed, cluster surveys in different wave-bands and compare the estimates to the prevalent Fisher matrix forecasts. Mock catalogs of cluster counts expected from the surveys -- eROSITA, WFXT, RCS2, DES and Planck, along with a mock dataset of follow-up mass calibrations are analyzed for this purpose. A fair agreement between MCMC and Fisher results is found only in the case of minimal models. However, for many cases, the marginalized constraints obtained from Fisher and MCMC methods can differ by factors of 30-100%. The discrepancy can be alarmingly large for a time dependent dark energy equation of state, w(a); the Fisher methods are seen to under-estimate the constraints by as much as a factor of 4--5. Typically, Fisher estimates become more and more inappropriate as we move away from LCDM, to a constant-w dark energy to varying-w dark energy cosmologies. Fisher analysis, also, predicts incorrect parameter degeneracies. From the point of mass-calibration uncertainties, a high value of unknown scatter about the mean mass-observable relation, and its redshift dependence, is seen to have large degeneracies with the cosmological parameters sigma_8 and w(a) and can degrade the cosmological constraints considerably. We find that the addition of mass-calibrated cluster datasets can improve dark energy and sigma_8 constraints by factors of 2--3 from what can be obtained compared to CMB+SNe+BAO only. Since, details of future cluster surveys are still being planned, we emphasize that optimal survey design must be done using MCMC analysis rather than Fisher forecasting. [abridged]Comment: 26 pages, 13 figures, 7 tables, accepted for publication in JCA

Cosmic Shear from Galaxy Spins

We discuss the origin of galactic angular momentum, and the statistics of the present day spin distribution. It is expected that the galaxy spin axes are correlated with the intermediate principal axis of the gravitational shear tensor. This allows one to reconstruct the shear field and thereby the full gravitational potential from the observed galaxy spin fields. We use the direction of the angular momentum vector without any information of its magnitude, which requires a measurement of the position angle and inclination on the sky of each disk galaxy. We present the maximum likelihood shear inversion procedure, which involves a constrained linear minimization. The theory is tested against numerical simulations. We find the correlation strength of nonlinear structures with the initial shear field, and show that accurate large scale density reconstructions are possible at the expected noise level.Comment: Accepted by the ApJL, revised discussion, minor changes, LaTex file, 8 pages, 1 ps figur