To better understand the origin and properties of cosmological magnetic fields, a detailed knowledge of magnetic fields in the large-scale structure of the Universe (galaxy clusters, filaments) is crucial. We propose a new statistical approach to stu
dy magnetic fields on large scales with the rotation measure grid data that will be obtained with the new generation of radio interferometers.
The extraction of foreground and CMB maps from multi-frequency observations relies mostly on the different frequency behavior of the different components. Existing Bayesian methods additionally make use of a Gaussian prior for the CMB whose correlati
on structure is described by an unknown angular power spectrum. We argue for the natural extension of this by using non-trivial priors also for the foreground components. Focusing on diffuse Galactic foregrounds, we propose a log-normal model including unknown spatial correlations within each component and cross-correlations between the different foreground components. We present case studies at low resolution that demonstrate the superior performance of this model when compared to an analysis with flat priors for all components.
(abridged) Observations of Faraday rotation for extragalactic sources probe magnetic fields both inside and outside the Milky Way. Building on our earlier estimate of the Galactic contribution, we set out to estimate the extragalactic contributions.
We discuss the problems involved; in particular, we point out that taking the difference between the observed values and the Galactic foreground reconstruction is not a good estimate for the extragalactic contributions. We point out a degeneracy between the contributions to the observed values due to extragalactic magnetic fields and observational noise and comment on the dangers of over-interpreting an estimate without taking into account its uncertainty information. To overcome these difficulties, we develop an extended reconstruction algorithm based on the assumption that the observational uncertainties are accurately described for a subset of the data, which can overcome the degeneracy with the extragalactic contributions. We present a probabilistic derivation of the algorithm and demonstrate its performance using a simulation, yielding a high quality reconstruction of the Galactic Faraday rotation foreground, a precise estimate of the typical extragalactic contribution, and a well-defined probabilistic description of the extragalactic contribution for each data point. We then apply this reconstruction technique to a catalog of Faraday rotation observations. We vary our assumptions about the data, showing that the dispersion of extragalactic contributions to observed Faraday depths is most likely lower than 7 rad/m^2, in agreement with earlier results, and that the extragalactic contribution to an individual data point is poorly constrained by the data in most cases.
We develop a method to infer log-normal random fields from measurement data affected by Gaussian noise. The log-normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders of magnitud
e. We use the formalism of minimum Gibbs free energy to derive an algorithm that uses the signals correlation structure to regularize the reconstruction. The correlation structure, described by the signals power spectrum, is thereby reconstructed from the same data set. We show that the minimization of the Gibbs free energy, corresponding to a Gaussian approximation to the posterior marginalized over the power spectrum, is equivalent to the empirical Bayes ansatz, in which the power spectrum is fixed to its maximum a posteriori value. We further introduce a prior for the power spectrum that enforces spectral smoothness. The appropriateness of this prior in different scenarios is discussed and its effects on the reconstructions results are demonstrated. We validate the performance of our reconstruction algorithm in a series of one- and two-dimensional test cases with varying degrees of non-linearity and different noise levels.
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle of minimum
Gibbs free energy which was previously used to derive a signal reconstruction algorithm handling uncertainties in the signal covariance. We extend this algorithm to simultaneously uncertain noise and signal covariances using the same principles in the derivation. The resulting equations are general enough to be applied in many different contexts. We demonstrate the performance of the algorithm by applying it to specific example situations and compare it to algorithms not allowing for uncertainties in the noise covariance. The results show that the method we suggest performs very well under a variety of circumstances and is indeed qualitatively superior to the other methods in cases where uncertainty in the noise covariance is present.
