microwave frequencies, we rely on an $H_\alpha$-template provided by @2003ApJS..146..407F. Modeling of the free-free emission component on the basis of an $H_alpha$-template is feasible because both emission processes depend on the emission measure $\int n_e^2{\mathrm{d}}l$, where $n_e$ is the number density of electrons. This template is a composite of three $H_\alpha$-surveys and is because of its high resolution (on average $6\farcm0$ FWHM) particularly well suited for CMB foreground modelling. The morphology of the free-free map is very complex and the emission reaches out to intermediate Galactic latitude.

For relating $H_\alpha$-fluxes $A_{H_\alpha}$ given in units of Rayleighs to the free-free signal’s antenna temperature $T_\mathrm{free-free}$ measured in Kelvin, @1998PASA...15..111V gives the formula: $$\frac{T_\mathrm{free-free}(\umu\mathrm{K})}{A_{H_\alpha}(R)} \simeq 
14.0\left(\frac{T_p}{10^4~\mathrm{K}}\right)^{0.317}\cdot 10^{290~\mathrm{K}\cdot T_p^{-1}}\cdot 
g_\mathrm{ff}\cdot\left(\frac{\nu}{10\mbox{ GHz}}\right)^{-2}\mbox{.}$$ $T_p$ denotes the plasma temperature and is set to $10^4~\mathrm{K}$ in this work. An approximation for the Gaunt factor $g_\mathrm{ff}$ valid for microwave frequencies in the range $\nu_p\ll\nu\ll k_B T/h$ ($\nu_p$ is the plasma frequency) is given by [@2003ApJS..146..407F]: $$g_\mathrm{ff} = \frac{\sqrt{3}}{\pi}
\left[\ln\left(\frac{(2 k_B T_p)^{3/2}}{\pi e^2 \nu\sqrt{m_e}}\right)-\frac{5}{2}\gamma_E\right]\mbox{,}$$ where $e$ and $m_e$ denote electron charge and mass (in Gaussian units) and $\gamma_E\simeq0.57721$ is the Euler constant. The contribution of fractionally ionised helium to the free-free emissivity as well as the absorption by interstellar dust 