M51 total intensity image at 333MHz

While much modelling has been carried out on the CRE distribution and propagation of the Milky Way, little has been done on normal external star-forming galaxies. Recent spectral data from a new generation of radio telescopes enable us to find more robust estimations of the CRE propagation To model the synchrotron spectral index of M51 using the diffusion energy-loss equation and to compare the model results with the observed spectral index determined from recent low-frequency observations with LOFAR.

We solve the time-dependent diffusion energy-loss equation for CREs in M51. This is the first time that this model for CRE propagation has been solved for a realistic distribution of CRE sources, which we derive from the observed star formation rate, in an external galaxy. The radial variation of the synchrotron spectral index and scale-length produced by the model are compared to recent LOFAR and older VLA observational data and also to new observations of M51 at 325MHz obtained with the GMRT.