Cosmic-ray electron transport in the galaxy M 51

Abstract

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.

Diffusion of cosmic-ray electrons in M 51 observed with LOFAR at 54 MHz

“…While our method is sensitive to smoothing of the Σ SFR map by CRE diffusion, the radio spectral index distribution is more governed by the escape of CRE from the galaxy. Our best-fitting diffusion coefficient of D ≈ 2 × 10 28 cm 2 s −1 is in good agreement with the results of Dörner et al (2023) but lower than the value by Mulcahy et al (2016), who found D ≈ 6 × 10 28 cm 2 s −1 . The difference can be mostly attributed to the fact that Mulcahy et al (2016) modelled CRE escape only via diffusion, whereas Dörner et al (2023) used a combination of diffusion and advection.…”

“…Our best-fitting diffusion coefficient of D ≈ 2 × 10 28 cm 2 s −1 is in good agreement with the results of Dörner et al (2023) but lower than the value by Mulcahy et al (2016), who found D ≈ 6 × 10 28 cm 2 s −1 . The difference can be mostly attributed to the fact that Mulcahy et al (2016) modelled CRE escape only via diffusion, whereas Dörner et al (2023) used a combination of diffusion and advection. Consequently, the diffusion coefficient has to be higher in order to allow for a fast enough CRE escape (Mulcahy et al 2016).…”

“…Albeit clearly in agreement with non-thermal synchrotron emission, it is not in agreement with an aged spectrum (Mulcahy et al 2014). The recent work by Dörner et al (2023) estimated this escape timescale in the 20-300 Myr range, where a positive gradient with a galactocentric radius is found. If we take an average value at a radius of 7 kpc, we would expect an escape timescale of t esc ≈ 50 Myr (Dörner et al 2023, their Fig.…”

“…Our approach of measuring CRE transport by comparing the radio continuum map with the SFR surface density is complementary to the radio spectral index analysis by Mulcahy et al (2016) and Dörner et al (2023). While our method is sensitive to smoothing of the Σ SFR map by CRE diffusion, the radio spectral index distribution is more governed by the escape of CRE from the galaxy.…”

“…Mulcahy et al (2014) used scale lengths at the edge of M 51 in order to measure the diffusion coefficient. A different approach in face-on galaxies is to use the radial radio spectral index distribution and model this with cosmic ray diffusion (Mulcahy et al 2016;Dörner et al 2023). This approach is in particular sensitive to the escape of cosmic rays, as the radio continuum spectrum otherwise becomes too steep.…”