Galactic Magnetic Field Reconstruction I. Constraints from polarized diffuse emission: Methodology and simulations
The polarized Galactic synchrotron and thermal dust emission constitutes a major tool for the study of the Galactic Magnetic Field (GMF), and to constrain its amplitude and geometry for the regular and turbulent components. In this paper, we review the modeling of the polarized Galactic emission of interest and present our strategy to best exploit the currently existing data sets. Then, we investigate a Markov Chain Monte Carlo (MCMC) method to constrain the model parameter space through maximum-likelihood analysis. Relying on simulations, for a well-known model of the large-scale non-turbulent GMF, we provide MCMC constraints from the polarized thermal dust emission for two sets of input models of different degree of complexity, proving that the GMF geometrical structure can be self-consistently reconstructed from the dust polarized emission. We discuss limitations and caveats of the methodology and we identify sources of systematic errors in the model reconstructions. We also demonstrate that our methodology can be used to constrain the regular GMF geometry independently of the accuracy of the reconstruction of the Galactic dust grain distribution. Finally, we use the results of this analysis to demonstrate the coherence of the approach via the accuracy to which we can reconstruct Galactic synchrotron emission.