Modelling the Galactic Magnetic Field on the Plane in 2D

We present a Markov chain Monte-Carlo (MCMC) method for modelling the Galactic magnetic field using total and polarised synchrotron emission data as well as rotation measures of extragalactic sources. With these three datasets, we study the three components of the magnetic field: the large-scale regular 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 parameters such as the ratios of the magnetic field components. Finally, we apply the methods to the data and find that they are well fitted by a model where the magnetic field energy density has regular, random, and ordered components in roughly the ratios 10, 50, and 40 per cent, respectively, at the peak along magnetic arms. We outline further work to extend this type of analysis to study the details of the turbulence as well as the vertical profile of the magnetic field.