Modelling the Galactic Magnetic Field on the Plane in 2D
  We present a method for parametric modelling of the physical components of
the Galaxy's magnetised interstellar medium, simulating the observables, and
mapping out the likelihood space using a Markov Chain Monte-Carlo analysis. We
then demonstrate it using total and polarised synchrotron emission data as well
as rotation measures of extragalactic sources. With these three datasets, we
define and study three components of the magnetic field: the large-scale
coherent field, the small-scale isotropic random field, and the ordered field.
In this first paper, we use only data along the Galactic plane and test a
simple 2D logarithmic spiral model for the magnetic field that includes a
compression and a shearing of the random component giving rise to an ordered
component. We demonstrate with simulations that the method can indeed constrain
multiple parameters yielding measures of, for example, the ratios of the
magnetic field components. Though subject to uncertainties in thermal and
cosmic ray electron densities and depending on our particular model
parametrisation, our preliminary analysis shows that the coherent component is
a small fraction of the total magnetic field and that an ordered component
comparable in strength to the isotropic random component is required to explain
the polarisation fraction of synchrotron emission. We outline further work to
extend this type of analysis to study the magnetic spiral arm structure, the
details of the turbulence as well as the 3D structure of the magnetic field.
