Signal inference in Galactic astrophysics

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.