M51 observed with LOFAR at 54MHz

The best-fitting convolution kernel is then our estimate of the CRE transport length. We find that the CRE transport length increases at low frequencies, as expected since the CRE have longer lifetimes. The CRE transport length is lCRE = QSRT(4Dtsyn), where D is the isotropic diffusion coefficient and rsyn is the CRE lifetime as given by synchrotron and inverse Compton losses.

We find that the data can be well fitted by diffusion, where D=(2.14+/-0.13)x10^28^cm^2^/s. With D{prop.to}E^0.001+/-0.185^, the diffusion coefficient is independent of the CRE energy E in the range considered. Our results suggest that the transport of GeV-cosmic ray electrons in the star-forming discs of galaxies is governed by energy-independent diffusion.