A CMB Gibbs sampler for localized secondary anisotropies

As well as primary fluctuations, CMB temperature maps contain a wealth of additional information in the form of secondary anisotropies. Secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev-Zeldovich (SZ) effects due to galaxy clusters, are difficult to unambiguously disentangle from foreground contamination and the primary CMB however. We develop a Bayesian formalism for rigorously characterising anisotropies that are localised on the sky, taking the TSZ and KSZ effects as an example. Using a Gibbs sampling scheme, we are able to efficiently sample from the joint posterior distribution for a multi-component model of the sky with many thousands of correlated physical parameters. The posterior can then be exactly marginalised to estimate properties of the secondary anisotropies, fully taking into account degeneracies with the other signals in the CMB map. We show that this method is computationally tractable using a simple implementation based on the existing Commander component separation code, and also discuss how other types of secondary anisotropy can be accommodated within our framework.

A multi-level solver for Gaussian constrained CMB realizations

We present a multi-level solver for drawing constrained Gaussian realizations or finding the maximum likelihood estimate of the CMB sky, given noisy sky maps with partial sky coverage. The method converges substantially faster than existing Conjugate Gradient (CG) methods for the same problem. For instance, for the 143 GHz Planck frequency channel, only 3 multi-level W-cycles result in an absolute error smaller than 1 microKelvin in any pixel. Using 16 CPU cores, this translates to a computational expense of 6 minutes wall time per realization, plus 8 minutes wall time for a power spectrum-dependent precomputation. Each additional W-cycle reduces the error by more than an order of magnitude, at an additional computational cost of 2 minutes. For comparison, we have never been able to achieve similar absolute convergence with conventional CG methods for this high signal-to-noise data set, even after thousands of CG iterations and employing expensive preconditioners. The solver is part of the Commander 2 code, which is available with an open source license at http://commander.bitbucket.org/.