Context. Indirect observations of the cosmic-ray electron (CRE) distribution via synchrotron emission is crucial for deepening the understanding of the CRE transport in the interstellar medium, and in investigating the role of galactic outflows. Aims. In this paper, we quantify the contribution of diffusion-and advection-dominated transport of CREs in the galaxy M51 considering relevant energy loss processes. Methods. We used recent measurement from M51 that allow for the derivation of the diffusion coefficient, the star formation rate, and the magnetic field strength. With this input, we solved the 3D transport equation numerically including the spatial dependence as provided by the measurements, using the open-source transport framework CRPropa (v3.1). We included 3D transport (diffusion and advection), and the relevant loss processes. Results. We find that the data can be described well with the parameters from recent measurements. For the best fit, it is required that the wind velocity, following from the observed star formation rate, must be decreased by a factor of 5. We find a model in which the inner galaxy is dominated by advective escape and the outer galaxy is composed by both diffusion and advection. Conclusions. Three-dimensional modelling of cosmic-ray transport in the face-on galaxy M51 allows for conclusions about the strength of the outflow of such galaxies by quantifying the need for a wind in the description of the cosmic-ray signatures. This opens up the possibility of investigating galactic winds in face-on galaxies in general.

Context. The details of cosmic-ray transport have a strong impact on galaxy evolution. The peak of the cosmic-ray energy distribution is observable in the radio continuum using the electrons as proxy. Aims. We aim to measure the distance that the cosmic-ray electrons (CREs) are transported during their lifetime in the nearby galaxy M 51 across one order of magnitude in cosmic-ray energy (approximately 1–10 GeV). To this end, we use new ultra-low frequency observations from the LOw Frequency ARay (LOFAR) at 54 MHz and ancillary data between 144 and 8350 MHz. Methods. As the CREs originate from supernova remnants, the radio maps are smoothed in comparison to the distribution of the star formation. By convolving the map of the star formation rate (SFR) surface density with a Gaussian kernel, we can linearise the radio–SFR relation. The best-fitting convolution kernel is then our estimate of the CRE transport length. Results. 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 = √4Dtsyn, where D is the isotropic diffusion coefficient and tsyn 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)×1028 cm2 s−1. With D ∝ E0.001 ± 0.185, the diffusion coefficient is independent of the CRE energy E in the range considered. Conclusions. Our results suggest that the transport of GeV-cosmic ray electrons in the star-forming discs of galaxies is governed by energy-independent diffusion.

Context. Indirect observations of the cosmic-ray electron (CRE) distribution via synchrotron emission is crucial for deepening the understanding of the CRE transport in the interstellar medium, and in investigating the role of galactic outflows. Aims. In this paper, we quantify the contribution of diffusion and advection dominated transport of cosmic-ray electrons in the galaxy M51 considering relevant energy loss processes. Methods. We use recent measurement from M51 that allow for the derivation of the diffusion coefficient, the star formation rate, and the magnetic field strength. With this input, we solve the 3D transport equation numerically including the spatial dependence as provided by the measurements, using the open-source transport framework CRPropa (v3.1). We include three-dimensional transport (diffusion and advection), and the relevant loss processes. Results. We find that the data can be described well with the parameters from recent measurements. For the best fit, it is required that the wind velocity, following from the observed star formation rate, must be decreased by a factor of 5. We find that a model in which the inner galaxy is dominated by advective escape and the outer galaxy by diffusive one fits the data well. Conclusions. Three-dimensional modeling of cosmic-ray transport in the face-on galaxy M51 allows for conclusions about the strength of the outflow of such galaxies by quantifying the need for a wind in the description of the cosmic-ray signatures. This opens up the possibility of investigating galactic winds in face-on galaxies in general.