Cosmic Ray Electrons Research Articles

Cosmic-Ray Acceleration and Magnetic Fields in Galaxy Clusters and Beyond: Insights from Radio Observations

The discovery of diffuse radio emission in galaxy clusters proved the existence of energetic cosmic-ray electrons and cosmic magnetic fields on Mpc-scales in the Universe. Furthermore, both magnetic fields and cosmic-ray electrons are predicted to exist beyond galaxy clusters, namely, in the filaments and voids of the cosmic web. Recent detection of diffuse radio emission in intercluster bridges—the region between two merging clusters—strengthens the theory that both cosmic magnetic fields and cosmic-ray electrons exist on these large scales. Radio observations are our most powerful tool to study cosmic magnetic fields and cosmic-ray electrons in the Universe. The recent improvements in radio astronomy, including the exploration of the low-frequency radio sky, have led to the discovery of countless new radio sources, and hence a new understanding of the origin and evolution of cosmic magnetic fields and cosmic-ray electrons. In this contribution, we summarise the newest discoveries in the field. Furthermore, we discuss what these new radio observations teach us about cosmic magnetic fields and cosmic rays in galaxy clusters and beyond.

Prediction of using LHAASO’s cosmic-ray electron measurements to constrain decaying heavy dark matter

Large High Altitude Air Shower Observatory (LHAASO) is an instrument designed for detecting cosmic rays (CRs) and gamma rays at TeV to PeV energies. The decays of heavy dark matter particles in the Galactic halo may produce high-energy electrons that can be detected by LHAASO. The main background for the LHAASO's CR electron measurements is the hadron residuals due to misidentification of the particle species. In this paper, we estimate the LHAASO's electron background using the known all-particle CR spectrum and the hadron rejection efficiency of LHAASO. With the estimated background, we predict the capability of LHAASO to constrain dark matter (DM) decay lifetime at 95% confidence level for various channels. We find that if neglecting systematic uncertainties, the CR electron measurement by LHAASO can improve the current best results by up to one order of magnitude for DM masses between 100--1000 TeV. However, indirect measurements of CR electrons by ground-based experiments suffer from sizable systematic uncertainties. With the systematic uncertainties included in the calculation, the projected constraints will be largely weakened. So, for using the CR electron observation of LHAASO to constrain the DM parameters, the key point is whether the systematic error can be effectively reduced.

Possible Counterpart Signal of the Fermi Bubbles at the Cosmic-Ray Positrons

The inner Galaxy has hosted cosmic-ray burst events, including those responsible for the gamma-ray Fermi bubbles and the eROSITA bubbles in X-rays. In this work, we study the Alpha Magnetic Spectrometer positron fraction and find three features around 12, 21, and 48 GeV, of which the lowest energy has a 1.4–4.9σ significance, depending on astrophysical background assumptions. Using background simulations that explain the cosmic-ray positron fraction, positron flux, and electron plus positron flux by primary and secondary cosmic rays and cosmic rays from local pulsars, we test these spectral features as originating from electron/positron burst events from the inner Galaxy. We find the 12 GeV feature to be explained by an event of age τ ≃ 3–10 Myr, in agreement with the proposed age of the Fermi bubbles. Furthermore, the energy in cosmic-ray electrons and positrons propagating along the Galactic disk and not within the Fermi bubbles volume is estimated to be 1051.5–1057.5 erg, or O(10−4) − O(1) the cosmic-ray energy causing the Fermi bubbles. We advocate that these positron fraction features are the counterpart signals of the Fermi bubbles, or of substructures within them, or of the eROSITA bubbles.

Origin of the diffuse 4–8 keV emission in M 82

We present the first spatially resolved, X-ray spectroscopic study of the 4−8 keV diffuse emission found in the central part of the nearby starburst galaxy M 82 on a few arcsecond scales. The new details that we see allow a number of important conclusions to be drawn on the nature of the hot gas and its origin as well as feedback on the interstellar medium. We use archival data from the Chandra X-ray Observatory with an exposure time of 570 ks. The Fe XXV emission at 6.7 keV, expected from metal-enriched hot gas, is enhanced only in a limited area close to the starburst disc and is weak or almost absent over the rest of the diffuse emission, resulting in spatial variations in equivalent width from < 0.1 keV to 1.9 keV. This shows the presence of non-thermal emission due to inverse Compton scattering of the far-infrared photons by radio emitting cosmic ray electrons. The morphological resemblance between the diffuse X-ray, radio, and far-infrared emission maps support this concept. Our decomposition of the diffuse emission spectrum indicates that ∼70% of the 4−8 keV luminosity originates from the inverse Compton emission. The metal-rich hot gas with a temperature of ≃5 keV makes a minor contribution to the 4−8 keV continuum, but it accounts for the majority of the observed Fe XXV line. This hot gas appears to emerge from the circumnuclear starburst ring and fill the galactic chimneys identified as mid-infrared and radio emission voids. The energetics argument suggests that much of the supernova energy in the starburst site has gone into creating of the chimneys and is transported to the halo. We argue that a hot, rarefied environment produced by strong supernova feedback results in displacing the brightest X-ray and radio supernova remnants which are instead found to reside in giant molecular clouds. We find a faint X-ray source with a radio counterpart, close to the kinematic centre of the galaxy and we carefully examine the possibility that this source is a low-luminosity active galactic nucleus in an advection-dominated accretion flow phase.

Hint for a TeV neutrino emission from the Galactic Ridge with ANTARES

Interactions of cosmic ray protons, atomic nuclei, and electrons in the interstellar medium in the inner part of the Milky Way produce a γ-ray flux from the Galactic Ridge. If the γ-ray emission is dominated by proton and nuclei interactions, a neutrino flux comparable to the γ-ray flux is expected from the same sky region.Data collected by the ANTARES neutrino telescope are used to constrain the neutrino flux from the Galactic Ridge in the 1-100 TeV energy range. Neutrino events reconstructed both as tracks and showers are considered in the analysis and the selection is optimized for the search of an excess in the region |l|<30°, |b|<2°. The expected background in the search region is estimated using an off-zone region with similar sky coverage. Neutrino signal originating from a power-law spectrum with spectral index ranging from Γν=1 to 4 is simulated in both channels. The observed energy distributions are fitted to constrain the neutrino emission from the Ridge.The energy distributions in the signal region are inconsistent with the background expectation at ∼96% confidence level. The mild excess over the background is consistent with a neutrino flux with a power law with a spectral index 2.45−0.34+0.22 and a flux normalization dNνdEν=4.0−2.0+2.7×10−16 GeV−1cm−2s−1sr−1 at 40 TeV reference energy. Such flux is consistent with the expected neutrino signal if the bulk of the observed γ-ray flux from the Galactic Ridge originates from interactions of cosmic ray protons and nuclei with a power-law spectrum extending well into the PeV energy range.

Electron Reacceleration via Ion Cyclotron Waves in the Intracluster Medium

In galaxy clusters, the intracluster medium (ICM) is expected to host a diffuse, long-lived, and invisible population of “fossil” cosmic-ray electrons (CRe) with 1–100 MeV energies. These CRe, if reaccelerated by 100× in energy, can contribute synchrotron luminosity to cluster radio halos, relics, and phoenices. Reacceleration may be aided by CRe scattering upon the ion-Larmor-scale waves that spawn when ICM is compressed, dilated, or sheared. We study CRe scattering and energy gain due to ion cyclotron (IC) waves generated by continuously driven compression in 1D fully kinetic particle-in-cell simulations. We find that pitch-angle scattering of CRe by IC waves induces energy gain via magnetic pumping. In an optimal range of IC-resonant momenta, CRe may gain up to ∼10%–30% of their initial energy in one compression/dilation cycle with magnetic field amplification ∼3–6×, assuming adiabatic decompression without further scattering and averaging over initial pitch angle.

Simulations of Precessing Jets and the Formation of X-shaped Radio Galaxies

Jet precession is sometimes invoked to explain asymmetries in radio galaxy (RG) jets and “X/S/Z-shaped” RGs, caused by the presence of a binary black hole companion to the source active galactic nucleus or by accretion instabilities. We present a series of simulations of RG jet precession to examine how these sources would evolve over time, including a passive distribution of cosmic-ray electrons so we can model radio synchrotron emissions and create synthetic radio maps of the sources. We find that a single source viewed from different angles can result in differing RG morphological classifications, confusing physical implications of these classifications. Additionally, the jet trajectories can become unstable due to their own self-interactions and lead to “reorientation events” that may look like the effects of external dynamics such as shocks, winds, or cold fronts in the medium. Finally, something akin to an “Odd Radio Circle” may be observed in the case of viewing the radio remnant of such a precessing source from a line of sight near the precession axis.

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

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.

Synchrotron emission from virial shocks around stacked OVRO-LWA galaxy clusters

ABSTRACT Galaxy clusters accrete mass through large-scale, strong, structure-formation shocks. Such a virial shock is thought to deposit fractions ξe and ξB of the thermal energy in cosmic-ray electrons (CREs) and magnetic fields, respectively, thus generating a leptonic virial ring. However, the expected synchrotron signal was not convincingly established until now. We stack low-frequency radio data from the OVRO-LWA around the 44 most massive, high latitude, extended MCXC clusters, enhancing the ring sensitivity by rescaling clusters to their characteristic, R500 radii. Both high (73 MHz) and co-added low (36–68 MHz) frequency channels separately indicate a significant (4–5σ) excess peaked at (2.4–2.6)R500, coincident with a previously stacked Fermi γ-ray signal interpreted as inverse-Compton emission from virial-shock CREs. The stacked radio signal is well fit (TS-test: 4–6σ at high frequency, 4–8σ at low frequencies, and 8–10σ joint) by virial-shock synchrotron emission from the more massive clusters, with $\dot{m}\xi _e\xi _B\simeq (1\!-\!4)\times 10^{-4}$, where $\dot{m}\equiv \dot{M}/(MH)$ is the dimensionless accretion rate for a cluster of mass M and a Hubble constant H. The inferred CRE spectral index is flat, p ≃ 2.0 ± 0.2, consistent with acceleration in a strong shock. Assuming equipartition or using $\dot{m}\xi _e\sim 0.6~{{\ \rm per\ cent}}$ inferred from the Fermi signal yields $\xi _B\simeq (2\!-\!9)~{{\ \rm per\ cent}}$, corresponding to B ≃ (0.1–0.3) $\mu$G magnetic fields downstream of typical virial shocks. Preliminary evidence suggests non-spherical shocks, with factor 2–3 elongations.

Azimuthal asymmetry in cosmic-ray boosted dark matter flux

Light halo dark matter (DM) particles up-scattered by high-energy cosmic rays (referred to as CRDM) can be energetic and become detectable at conventional DM and neutrino experiments. We show that the CRDM flux has a novel and detectable morphological feature. Unlike most of the recently proposed boosted DM (BDM) models which predict azimuthally symmetric DM fluxes around the Galactic Center, the CRDM flux breaks the azimuthal symmetry significantly. Using cosmic-ray electron distribution in the whole Galaxy and optimized search region in the sky according to the morphology of the CRDM flux, we derive so far the most stringent constraints on the DM-electron scattering cross section from the Super-Kamiokande (SK) IV data, which improves the previous constraints from the SK-IV full-sky data by more than an order of magnitude. Based on the improved constraints, we predict that the azimuthal symmetry-breaking effect can be observed in the future Hyper-Kamiokande experiment at $\sim 3\sigma$ level.

Observing signals of spectral features in the cosmic-ray positrons and electrons from Milky Way pulsars

The Alpha Magnetic Spectrometer (AMS-02) has provided unprecedented precision measurements of the electron and positron cosmic-ray fluxes and the positron fraction spectrum. At the higher energies, sources as energetic local pulsars, may contribute to both cosmic-ray species. The discreteness of the source population, can result in features both on the positron fraction measurement and in the respective electron and positron spectra. For the latter, those would coincide in energy and would contrast predictions of smooth spectra as from particle dark matter. In this work, using a library of pulsar population models for the local part of the Milky Way, we perform a power-spectrum analysis on the cosmic-ray positron fraction. We also develop a technique to cross-correlate the electron and positron fluxes. We show that both such analyses, can be used to search statistically for the presence of spectral wiggles in the cosmic-ray data. For a significant fraction of our pulsar simulations, those techniques are already sensitive enough to give a signal for the presence of those features above the regular noise, with forthcoming observations making them even more sensitive. Finally, by cross-correlating the AMS-02 electron and positron spectra, we find an intriguing first hint for a positive correlation between them, of the kind expected by a population of local pulsars.

Optimizing Vanadium Redox Reaction in Na3V2(PO4)3 Cathodes for Sodium-Ion Batteries by the Synergistic Effect of Additional Electrons from Heteroatoms.

Na3V2(PO4)3 (NVP) is one of the most potential cathode materials for sodium-ion batteries (SIBs), but its actual electrochemical performance is limited by the defects of large electron and ion transfer resistance. Multicomponent design is considered an effective method to optimize the conductivity of NVP electrodes. Therefore, Cr and Si are added in NVP to form a multielement component of Na3V1.9Cr0.1(PO4)2.9(SiO4)0.1 (NVP-CS). It is confirmed that 3d electrons of Cr are beneficial for improving the conductivity and increasing the average potential by activating V4+/V5+. Theoretical calculations show that the introduction of Si changes the electronic structure of V and O, thus promoting the electrochemical reaction of V3+/V4+ to exert higher capacity. Due to the coordination of the two elements, a lower migration barrier is obtained in NVP-CS. Specifically, NVP-CS retains the advantages of single-doped electrodes very well (capacity retention of 90% after 300 cycles at 1 C and a high capacity of 94.1 mA h g-1 at 5 C, compared to NVP with only 82.6% capacity retention at 1 C and 59.4 mA h g-1 at 5 C). The excellent electrochemical performance results show that NVP can be successfully optimized by the introduction of Cr and Si. This work can provide some inspiration for multicomponent material research of cathode materials.

Introduction to Faraday tomography and its future prospects

Abstract Faraday tomography is a new method of the study of cosmic magnetic fields enabled by broad-band low-frequency radio observations. Using Faraday tomography it is possible to obtain the Faraday dispersion function, which contains information on the line-of-sight distributions of magnetic fields, thermal electron density, and cosmic ray electron density by measuring the polarization spectrum from a source of synchrotron radiation over a wide band. Furthermore, by combining it with two-dimensional imaging, Faraday tomography allows us to explore the three-dimensional structure of polarization sources. Faraday tomography has been active over the last 20 years, since the broad-band observation has become technically feasible, and polarization sources such as interstellar space, supernova remnants, and galaxies have been investigated. However, the Faraday dispersion function is mathematically the Fourier transform of the polarization spectrum. And since the observable band is finite, it is impossible to obtain a complete Faraday dispersion function by performing a Fourier transform. For this purpose, various methods have been developed to accurately estimate the Faraday dispersion function from the observed polarization spectrum. In addition, the Faraday dispersion function does not directly reflect the distribution of magnetic field, thermal electron density, and cosmic ray electron density in the physical space, and its physical interpretation is not straightforward. Despite these two difficult problems, Faraday tomography is attracting much attention because it has great potential as a new method for studying cosmic magnetic fields and magnetized plasmas. In particular, the next-generation radio telescope SKA (Square Kilometre Array) is capable of polarization observation with unprecedented sensitivity and broad bands, and the application of Faraday tomography is expected to make dramatic progress in the field of cosmic magnetic fields. In this review, we explain the basics of Faraday tomography with simple and instructive examples. Representative algorithms to realize Faraday tomography are introduced, and some applications are shown.

Cosmic-Ray Acceleration and Nonthermal Radiation at Accretion Shocks in the Outer Regions of Galaxy Clusters

Cosmology models predict that external accretion shocks form in the outer region of galaxy clusters owing to supersonic gas infall from filaments and voids in the cosmic web. They are characterized by high sonic and Alfvénic Mach numbers, M s ∼ 10–102 and M A ∼ 102–103, and propagate into weakly magnetized plasmas of β ≡ P g /P B ≳ 102. Although strong accretion shocks are expected to be efficient accelerators of cosmic rays (CRs), nonthermal signatures of shock-accelerated CRs around clusters have not been confirmed, and detailed acceleration physics at such shocks has yet to be understood. In this study, we first establish through two-dimensional particle-in-cell simulations that at strong high-β shocks electrons can be pre-energized via stochastic Fermi acceleration owing to the ion Weibel instability in the shock transition region, possibly followed by injection into diffusive shock acceleration. Hence, we propose that the models derived from conventional thermal leakage injection may be employed for the acceleration of electrons and ions at accretion shocks as well. Applying these analytic models to numerical shock zones identified in structure formation simulations, we estimate nonthermal radiation, such as synchrotron and inverse Compton (IC) emission due to CR electrons and π 0-decay γ-rays due to CR protons, around simulated clusters. Our models with injection parameter Q ≈ 3.5–3.8 predict synthetic synchrotron maps, which seem consistent with recent radio observations of the Coma Cluster. However, the detection of nonthermal IC X-rays and γ-rays from accretion shocks would be quite challenging. We suggest that the proposed analytic models may be adopted as generic recipes for CR production at cosmological shocks.

A New Component from the Quiet Sun from Radio to Gamma Rays: Synchrotron Radiation by Galactic Cosmic-Ray Electrons

The quiet Sun, i.e., in its nonflaring state or nonflaring regions, emits thermal radiation from radio to ultraviolet. The quiet Sun also produces nonthermal radiation observed in gamma rays due to interactions of Galactic cosmic rays (GCRs) with the solar atmosphere and photons. We report on a new component: the synchrotron emission by GCR electrons in the solar magnetic field. To the best of our knowledge this is the first time this emission has been theoretically claimed and modeled. We find that the measured GCR electrons with energies from tens of GeV to a few TeV produce synchrotron emission in X-rays, which is a few orders of magnitude lower than current upper limits of the quiet Sun set by RHESSI and FOXSI, with no energy losses included. For a radially decreasing solar magnetic field we find the expected synchrotron intensity to be almost constant in the solar disk, to peak in the close proximity of the Sun, and to quickly drop away from the Sun. We also estimate the synchrotron emission from radio to gamma rays, and we compare it with current observations, especially with LOFAR. While it is negligible from radio to UV compared to the solar thermal radiation, this emission can potentially be observed at high energies with NuSTAR and more promising future FOXSI observations. This could potentially allow for constraining GCR densities and magnetic-field intensities at the Sun. This study provides a more complete description and a possible new way for understanding the quiet Sun and its environment.

Evolution and feedback of AGN jets of different cosmic ray composition

ABSTRACT Jet feedback from active galactic nuclei (AGN) is one of the most promising mechanisms for suppressing cooling flows in cool-core clusters. However, the composition of AGN jets and bubbles remains uncertain; they could be thermally dominated, or dominated by cosmic ray proton (CRp), cosmic ray electron (CRe), or magnetic energy. In this work, we investigate the evolution and feedback effects of CRp and CRe dominated jets by conducting 3D magnetohydrodynamic simulations of AGN jet-inflated bubbles in the intracluster medium using the FLASH code. We present the evolution of their energies, dynamics, and heating, and model their expected cavity-power versus radio-luminosity relation (Pcav–LR). We find that bubbles inflated by CRe dominated jets follow a very similar dynamical evolution to CRp dominated bubbles even though CRe within bubbles suffer significantly stronger synchrotron and inverse-Compton cooling. This is because, as CRe lose their energy, the jet-inflated bubbles quickly become thermally dominated within ∼30 Myr. Their total energy stops decreasing with CR energy and evolves similarly to CRp dominated bubbles. The ability of CRe and CRp dominated bubbles to heat the intracluster medium is also comparable; the cold gas formed via local thermal instabilities is well suppressed in both cases. The CRp and CRe bubbles follow different evolutionary trajectories on the Pcav–LR plane, but the values are broadly consistent with observed ranges for FR-I sources. We also discuss observational techniques that have potential for constraining the composition of AGN jets and bubbles.

Bounds on boosted dark matter from direct detection: The role of energy-dependent cross sections

The recoil threshold of Direct Detection experiments limits the mass range of Dark Matter (DM) particles that can be detected, with most DD experiments being blind to sub-MeV DM particles. However, these light DM particles can be boosted to very high energies via collisions with energetic Cosmic Ray electrons. This allows Dark Matter particles to induce detectable recoil in the target of Direct Detection experiments. We derive constraints on scattering cross section of DM and electron, using XENONnT and Super-Kamiokande data. Vector and scalar mediators are considered, in the heavy and light regimes. We discuss the importance of including energy dependent cross sections (due to specific Lorentz structure of the vertex) in our analysis, and show that the bounds can be significantly different than the results obtained assuming constant energy-independent cross-section, often assumed in the literature for simplicity. Our bounds are also compared with other astrophysical and cosmological constraints.

Revisiting GeV-scale annihilating dark matter with the AMS-02 positron fraction

Antimatter cosmic-rays are used to probe new phenomena in physics, including dark matter annihilation. We use the cosmic-ray positron fraction spectrum by the Alpha Magnetic Spectrometer, to search for such an annihilation signal in the Galaxy. We focus on dark matter with mass between 5 and 120 GeV, producing high-energy electrons and positrons. In these cosmic-ray energies the interplay of multiple astrophysical sources and phenomena, makes this search highly sensitive to the underlying astrophysical background assumptions. We use a vast public library of astrophysical models for the cosmic-ray positron fraction background, to derive robust upper limits on the dark matter's annihilation cross section for a number of annihilation channels. This library accounts for different types of cosmic-ray sources and uncertainties on their distribution in space and time. Also, it accounts for uncertainties on those sources' output, their injected into the interstellar medium cosmic-ray spectra and for uncertainties on cosmic-ray propagation. For any given dark matter particle mass and annihilation channel, upper limits on the annihilation cross section are given by bands that stretch a full order of magnitude in its value. Our work provides weaker limits compared to earlier results, that are however robust to all the relevant astrophysical uncertainties. Between 5 and 15 GeV, we find indications for a possible excess flux of cosmic-ray electrons and positrons. That excess is found for most, but not all of our astrophysical background parameter space, and its significance can vary appreciably. Further scrutiny is necessary to improve the understanding of these lower energy cosmic rays. Finally, we note that even if an excess signal is found in these energies, the current background uncertainties do not allow us to accurately deduce its underlying particle properties.

Life cycle of cosmic-ray electrons in the intracluster medium

We simulate the evolution of relativistic eletrons injected into the medium of a small galaxy cluster by a central radio galaxy, studying how the initial jet power affects the dispersal and the emission properties of radio plasma. By coupling passive tracer particles to adaptive-mesh cosmological magnetohydrodynamic (MHD) simulations, we study how cosmic-ray electrons are dispersed as a function of the input jet power. We also investigate how the latter affects the thermal and non-thermal properties of the intracluster medium, with differences discernible up to about one Gyr after the start of the jet. We evolved the energy spectra of cosmic-ray electrons, subject to energy losses that are dominated by synchrotron and inverse Compton emission as well as energy gains via re-acceleration by shock waves and turbulence. We find that in the absence of major mergers, the amount of re-acceleration experienced by cosmic-ray electrons is not enough to produce long-lived detectable radio emissions. However, for all simulations, the role of re-acceleration processes is crucial to maintaining a significant and volume-filling reservoir of fossil electrons (γ ∼ 103) for at least one Gyr after the first injection by jets. This is important in attempting to establish plausible explanations of recent discoveries of cluster-wide emission and other radio phenomena in galaxy clusters.

Cosmic-ray electron transport in the galaxy M 51

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 M 51 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.