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Oppermann, Niels (2013): Signal inference in Galactic astrophysics. Dissertation, LMU München: Fakultät für Physik



In this thesis we present a combination of methodological work with very wide focus and some specific astrophysical applications. We advance the knowledge on the Galactic interstellar medium by studying new ways of inferring select properties related to its magnetic field. We derive the statistical tools needed in a rigorous way from probabilistic considerations. One quantity describing the statistical properties of magnetic fields is their helicity. We apply a recently developed technique to detect magnetic helicity from astronomical observations to data from the Milky Way. No indications of helicity are found. Using a series of simulations in the Galactic setting, we are able to show that the technique fails to detect helicity in cases in which the underlying electron density varies too strongly. Thus, we are able to conclude that either this is the case in the Milky Way or the Galactic magnetic field is non-helical. We further develop a technique, needed among other things to enable the correct application of the helicity test, to reconstruct continuous signals from noisy data for which the noise level is unknown. To do this, we make use of the statistical correlation structure of the signal which we reconstruct from the same data set in a self-consistent way. Fluctuations in the data that are inconsistent with this correlation structure are then assigned to the data's error budget. The development of this technique is partly motivated by the goal of creating an all-sky map of the Galactic contribution to the astronomical Faraday rotation effect, which probes both the Galactic magnetic field and the density of free thermal electrons. Since the quantity that is observed is the Faraday rotation of a radio source, influenced by all magnetic fields between the source and the observer, extragalactic contributions need to be filtered out. We use the technique for reconstructions in the presence of an uncertain degree of noisiness to assign the extragalactic contributions - as well as some other observational effects - to the error budget of the data and thus single out the Galactic contribution. The resulting map is the most detailed and precise map of its kind and the only one in which the extragalactic contributions have been filtered out. Finally, we develop a method to reconstruct log-normal signal fields, i.e. strictly positive signal fields for which the strengths of the fluctuations vary over several orders of magnitude. This is done with a view to reconstructions of emission maps due to different processes in the Galactic interstellar medium.