We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior, data likelih
ood, and numerical inverse extra-regularization schemes are derived and classified. The Bayesian methodology presented in this paper tries to unify and extend the following methods: Wiener-filtering, Tikhonov regularization, Ridge regression, Maximum Entropy, and inverse regularization techniques. The inverse techniques considered here are the asymptotic regularization, the Jacobi, Steepest Descent, Newton-Raphson, Landweber-Fridman, and both linear and non-linear Krylov methods based on Fletcher-Reeves, Polak-Ribiere, and Hestenes-Stiefel Conjugate Gradients. The structures of the up-to-date highest-performing algorithms are presented, based on an operator scheme, which permits one to exploit the power of fast Fourier transforms. Using such an implementation of the generalized Wiener-filter in the novel ARGO-software package, the different numerical schemes are benchmarked with 1-, 2-, and 3-dimensional problems including structured white and Poissonian noise, data windowing and blurring effects. A novel numerical Krylov scheme is shown to be superior in terms of performance and fidelity. These fast inverse methods ultimately will enable the application of sampling techniques to explore complex joint posterior distributions. We outline how the space of the dark-matter density field, the peculiar velocity field, and the power spectrum can jointly be investigated by a Gibbs-sampling process. Such a method can be applied for the redshift distortions correction of the observed galaxies and for time-reversal reconstructions of the initial density field.
Most cool core clusters of galaxies possess active galactic nuclei (AGN) in their centers. These AGN inflate buoyant bubbles containing non-thermal radio emitting particles. If such bubbles efficiently confine cosmic rays (CR) then this could explain
``radio ghosts seen far from cluster centers. We simulate the diffusion of cosmic rays from buoyant bubbles inflated by AGN. Our simulations include the effects of the anisotropic particle diffusion introduced by magnetic fields. Our models are consistent with the X-ray morphology of AGN bubbles, with disruption being suppressed by the magnetic draping effect. We conclude that for such magnetic field topologies, a substantial fraction of cosmic rays can be confined inside the bubbles on buoyant rise timescales even when the parallel diffusivity coefficient is very large. For isotropic diffusion at a comparable level, cosmic rays would leak out of the bubbles too rapidly to be consistent with radio observations. Thus, the long confinement times associated with the magnetic suppression of CR diffusion can explain the presence of radio ghosts. We show that the partial escape of cosmic rays is mostly confined to the wake of the rising bubbles, and speculate that this effect could: (1) account for the excitation of the H$alpha$ filaments trailing behind the bubbles in the Perseus cluster, (2) inject entropy into the metal enriched material being lifted by the bubbles and, thus, help to displace it permanently from the cluster center and (3) produce observable $gamma$-rays via the interaction of the diffusing cosmic rays with the thermal intracluster medium (ICM).
