Expected constraints on the Galactic magnetic field using PLANCK data

We explore in this paper the ability to constrain the Galactic magnetic field intensity and spatial distribution with the incoming data from the Planck satellite experiment. We perform realistic simulations of the Planck observations at the polarized frequency bands from 30 to 353 GHz for two all-sky surveys as expected for the nominal mission. These simulations include CMB, synchrotron and thermal dust Galactic emissions and instrumental noise. (Note that systematic effects are not considered in this paper). For the synchrotron and thermal dust Galactic emissions we use a coherent 3D model of the Galaxy describing its mater density and the magnetic field direction and intensity. We first simulate the synchrotron and dust emissions at 408 MHz and 545 GHz, respectively, and then we extrapolate them to the Planck frequency bands. We perform a likelihood analysis to compare the simulated data to a set of models obtained by varying the pitch angle of the regular magnetic field spatial distribution, the relative amplitude of the turbulent magnetic field, the radial scale of the electron and dust grain distributions, and the extrapolation spectral indices for the synchrotron and thermal dust emissions. We are able to set tight constraints on all the parameters considered. We have also found that the observed spatial variations of the synchrotron and thermal dust spectral indices should not affect our ability to recover the other parameters of the model. From this, we conclude that the Planck satellite experiment can precisely measure the main properties of the Galactic magnetic field. An accurate reconstruction of the matter distribution would require on the one hand an improved modelling of the ISM and on the other hand to use extra data sets like rotation measurements of pulsars.