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

¹ Hamburger Sternwarte, University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
e-mail: volker.heesen@hs.uni-hamburg.de
² Thüringer Landessternwarte, Sternwarte 5, 07778 Tautenburg, Germany
³ Max-Planck Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
⁴ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute, 44780 Bochum, Germany
⁵ School of Astronomy, Institute for Research in Fundamental Sciences, 19395-5531 Tehran, Iran
⁶ Theoretical Physics IV: Plasma-Astroparticle Physics, Faculty for Physics & Astronomy, Ruhr-Universität Bochum, 44780 Bochum, Germany

Received: 15 October 2022
Accepted: 10 December 2022

Abstract

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 l_CRE = √4Dt_syn, where D is the isotropic diffusion coefficient and t_syn 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 ∝ E^{0.001 ± 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.