usage with [[*Planck*]{}]{} by (see Fig. \[figure\_synchromap\]). The average angular resolution of this survey is $0\fdg85$ (FWHM).

Recent observations with WMAP [@2003ApJS..148...97B] indicate that the spectral slope of the synchrotron emission changes dramatically from $\gamma = -0.75$ at frequencies below 22 GHz to $\gamma = -1.25$ above 22 GHz. Theoretically, this may be explained by a momentum-dependent diffusion coefficient for cosmic ray electrons. In order to take account of this spectral steepening, the amplitudes $A_\mathrm{synchro}$ are multiplied with a prefactor in order to obtain the synchrotron fluxes at $\nu=22~\mathrm{GHz}$. This value is then extrapolated to [[*Planck*]{}’s ]{}observing frequencies with a spectral index of $\gamma = -1.25$: The amplitudes $A_\mathrm{synchro}$ of the input map are given in units of MJy/sr, and for the flux $S_\mathrm{synchro}(\nu)$ one thus obtains: $$S_\mathrm{synchro}(\nu) = 
\sqrt{\frac{22~\mathrm{GHz}}{408~\mathrm{MHz}}}\cdot A_\mathrm{synchro}\cdot
\left(\frac{\nu}{408~\mathrm{MHz}}\right)^{-1.25}\mbox{.}$$

Here, the fact that the synchrotron spectral index shows significant variations across the Milky Way due to varying magnetic field strength is ignored. Instead, a spatially constant spectral behaviour is assumed.

Galactic free-free emission {#foreground_freefree}
---------------------------

The Galactic ionised plasma produces free-free emission, which is an important source of contamination in CMB observations, as recently confirmed by @2003ApJS..148...97B in WMAP observations. Aiming at modelling the free-free emission at 