Supernova remnants (SNRs) are considered as being the sources of galactic cosmic rays. In order to understand the origin, acceleration, and composition of these cosmic rays, detailed knowledge of the physical conditions in the local interstellar medi
um is needed. The shock interaction of SNRs with molecular clouds that gives rise to strong molecular emission in the far-IR and sub-mm wavelength regimes can be used as a highly valuable tracer of these conditions. The application of MHD shock models in the interpretation of the resulting line emission can yield information on the energetic and chemical impact of supernova remnants. We have mapped two regions in the supernova remnant W44 with the APEX telescope in ${}^{12}$CO (3-2), (4-3), (6-5), (7-6) and ${}^{13}$CO (3-2). The extraction of integrated intensities on five different positions, corresponding to local maxima of CO emission, allows to compare these intensities to the outputs of a grid of models, which combine an MHD shock code with a radiative transfer module based on the large velocity gradient approximation. We find that the observed CO line emission is compatible with non-stationary shocks and a pre-shock density of $10^4$ cm${}^{-3}$. Our models furthermore allow to constrain shock ages, velocities, the pre-shock magnetic field strength components perpendicular to the line-of-sight, and the full ladder of CO transitions. Finally, our analysis can be used to estimate the contribution of such SNRs to, e.g. the galactic energy balance and the momentum-injection into the surrounding interstellar medium.
