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

TL;DR

This study measures how cosmic-ray electrons travel in galaxy M 51 using LOFAR radio observations, revealing that their diffusion is energy-independent across 1-10 GeV, which impacts understanding of galaxy evolution.

Contribution

First direct measurement of cosmic-ray electron transport length in M 51 at ultra-low frequencies, demonstrating energy-independent diffusion in galaxy disks.

Findings

CRE transport length increases at lower frequencies

Diffusion coefficient D ≈ 2.14 x 10^28 cm^2/s is energy-independent

Transport governed by energy-independent diffusion

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 measure the length that the cosmic-ray electrons (CRE) 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 the CRE 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 $l_{\rm CRE} = \sqrt{4Dt_{\rm syn}}$, where $D$ is the isotropic diffusion coefficient and $t_{\rm syn}$ is the CRE lifetime as given by synchrotron and inverse Compton losses. We find that the data can be well fitted by diffusion, where $D=(2.14\pm 0.13) \times 10^{28}~\rm cm^2\,s^{-1}$. With $D\propto E^{0.001\pm 0.185}$, 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.