Connecting Synchrotron, Cosmic Rays, and Magnetic Fields in the Plane of the Galaxy

We extend previous work modeling the Galactic magnetic field in the plane using synchrotron emission in total and polarised intensity. In this work, we include a more realistic treatment of the cosmic-ray electrons using the GALPROP propagation code optimized to match the existing high-energy data. This addition reduces the degeneracies in our previous analysis and when combined with an additional observed synchrotron frequency allows us to study the low-energy end of the cosmic-ray electron spectrum in a way that has not previously been done. For a pure diffusion propagation, we find a low-energy injection spectrum slightly harder than generally assumed; for J(E) \propto E^{\alpha}, we find {\alpha} = -1.34 \pm 0.12, implying a very sharp break with the spectrum above a few GeV. This then predicts a synchrotron brightness temperature spectral index, {\beta}, on the Galactic plane that is -2.8 < {\beta} < -2.74 below a few GHz and -2.98 < {\beta} < -2.91 up to 23 GHz. We find that models including cosmic-ray re-acceleration processes appear to be incompatible with the synchrotron data.