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Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter these turbulence get on average accelerated according to the so-called second-order Fermi process. However, in most astrophysical environments there are additional competing processes, such as different kinds of first-order energy changes and particle escape, that effect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semi-analytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any arbitrary astrophysical system of interest. Here, we adopt that the assigned magnetic turbulence is constrained on a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump -- that has for some special cases long been established -- is a universal feature of stochastic acceleration that emerges around the momentum $\chi_{\rm eq}$ where acceleration and continuous loss are in equilibrium if the particle's residence time in the system is sufficient at $\chi_{\rm eq}$. In general, the impact of continuous and catastrophic momentum changes plays a crucial role in the shape of the steady-state momentum distribution of the accelerated particles, where simplified unbroken power-law approximations are often not adequate.

We re-examine the interactions of ultra-high energy cosmic rays (UHECRs) with photons from the cosmic microwave background (CMB) under a changed, locally non-linear temperature redshift relation $T(z)$. This changed temperature redshift relation has recently been suggested by the postulate of subjecting thermalised and isotropic photon gases such as the CMB to an SU(2) rather than a U(1) gauge group. This modification of $\Lambda$CDM is called SU(2)$_{\rm CMB}$, and some cosmological parameters obtained by SU(2)$_{\rm CMB}$ seem to be in better agreement with local measurements of the same quantities, in particular $H_0$ and S$_8$. In this work, we apply the reduced CMB photon density under SU(2)$_{\rm CMB}$ to the propagation of UHECRs. This leads to a higher UHECR flux just below the ankle in the cosmic ray spectrum and slightly more cosmogenic neutrinos under otherwise equal conditions for emission and propagation. Most prominently, the proton flux is significantly increased below the ankle ($5\times10^{18}$ eV) for hard injection spectra and without considering the effects of magnetic fields. The reduction in CMB photon density also favours a decreased cosmic ray source evolution than the best fit using $\Lambda$CDM. In consequence, it seems that SU(2)$_{\rm CMB}$ favours sources that evolve as the star formation rate (SFR), like starburst galaxies (SBG) and gamma-ray bursts (GRB), over active galactic nuclei (AGNs) as origins of UHECRs. We conclude that the question about the nature of primary sources of UHECRs is directly affected by the assumed temperature redshift relation of the CMB., Comment: 8 pages, 10 figures

CRPropa is a Monte Carlo framework for simulating the propagation of (ultra-) high-energy particles in the Universe, including cosmic rays, gamma rays, electrons, and neutrinos. It covers energies from ZeV down to GeV for gamma rays and electrons, and TeV for cosmic rays and neutrinos, supporting various astrophysical environments such as the surroundings of astrophysical sources, galactic, and extragalactic environments. The newest version, CRPropa 3.2, represents a significant leap forward towards a universal multi-messenger framework, opening up the possibility for many more astrophysical applications. This includes extensions to simulate cosmic-ray acceleration and particle interactions within astrophysical source environments, a full Monte Carlo treatment of electromagnetic cascades, improved ensemble-averaged Galactic propagation, significant performance improvements for cosmic-ray tracking through magnetic fields, and a user-friendly implementation of custom photon fields, among many more enhancements. This contribution will give an overview of the new features and present several applications to cosmic-ray and gamma-ray propagation., Comment: PoS 444 (38th ICRC) (2023) 1471

The observational data on ultrahigh energy cosmic rays (UHECR), in particular their mass composition, show strong indications for extremely hard spectra of individual mass groups of CR nuclei at Earth. In this work, we show that such hard spectra can be the result of the finite life-time of UHECR sources, if a few individual sources dominate the UHECR flux at the highest energies. In this case, time delays induced by deflections in the turbulent extragalactic magnetic field as well as from the diffusive or advective escape from the source environment can suppress low-energy CRs, leading to a steepening of the observed spectrum. Considering radio galaxies as the main source of UHECRs, we discuss the necessary conditions that few individual sources dominate over the total contribution from the bulk of sources that have been active in the past. We provide two proof-of-principle scenarios showing that for a turbulent extragalactic magnetic field with a strength $B$ and a coherence length $l_{\rm coh}$, the life-time of a source at a distance $d_{\rm src}$ should satisfy ${t_{\rm act} \sim \left( B/1\,\text{nG} \right)^2\,\left( d_{\rm src}/10\,\text{Mpc} \right)^2\,\left( l_{\rm coh}/1\,\text{Mpc} \right)\,\text{Myr}}$ to obtain the necessary hardening of the CR spectrum at Earth.

The landscape of high- and ultra-high-energy astrophysics has changed in the last decade, largely due to the inflow of data collected by large-scale cosmic-ray, gamma-ray, and neutrino observatories. At the dawn of the multimessenger era, the interpretation of these observations within a consistent framework is important to elucidate the open questions in this field. CRPropa 3.2 is a Monte Carlo code for simulating the propagation of high-energy particles in the Universe. This version represents a major leap forward, significantly expanding the simulation framework and opening up the possibility for many more astrophysical applications. This includes, among others: efficient simulation of high-energy particles in diffusion-dominated domains, self-consistent and fast modelling of electromagnetic cascades with an extended set of channels for photon production, and studies of cosmic-ray diffusion tensors based on updated coherent and turbulent magnetic-field models. Furthermore, several technical updates and improvements are introduced with the new version, such as: enhanced interpolation, targeted emission of sources, and a new propagation algorithm (Boris push). The detailed description of all novel features is accompanied by a discussion and a selected number of example applications., Comment: 32 pages, 9 figures

Multi-wavelength observations indicate that some starburst galaxies show a dominant non-thermal contribution from their central region. These active galactic nuclei (AGN)-starburst composites are of special interest, as both phenomena on their own are potential sources of highly-energetic cosmic rays and associated gamma-ray and neutrino emission. In this work, a homogeneous, steady-state two-zone multi-messenger model of the non-thermal emission from the AGN corona as well as the circumnuclear starburst region is developed and subsequently applied to the case of NGC 1068, which has recently shown some first indications of high-energy neutrino emission. Here, we show that the entire spectrum of multi-messenger data - from radio to gamma-rays including the neutrino constraint - can be described very well if both, starburst and AGN corona, are taken into account. Using only a single emission region is not sufficient.

Radio galaxies are promising candidates as the sources of ultrahigh energy cosmic rays (UHECRs). In this work, we examine if the stringent constraints imposed by the dipole and quadropole anisotropies as well as the UHECR spectrum and composition allow that radio galaxies are the dominant extragalactic cosmic ray sources. In order to calculate the UHECR flux emitted by individual radio galaxies, we constrain their properties using information from the radio-CR correlation and a dynamical evolution model. In addition to the UHECR flux from individual, local sources, we include the diffuse flux emitted by the bulk of non-local radio galaxies based on their radio luminosity distribution. Analyzing the source parameters within a range around their expected properties, we finally determine the configurations of local sources describing well the UHECR spectrum, composition and large-scale anisotropies. We obtain a good description of all data even in the case that we include only a small number of local sources. In particular, we find that scenarios where few sources like Fornax A and Virgo A dominate the flux above the ankle, while low-luminosity radio galaxies contribute an isotropic background dominating below the ankle, provide a good fit to the data.

Recent multi-wavelength observations indicate that some starburst galaxies show a dominant nonthermal contribution from its central region. These active galactic nuclei (AGN)-starburst composites are of special interest, as both phenomena on their own are potential sources of the high-energetic cosmic rays and their accompanied gamma-ray and neutrino emission. Here, we will focus on NGC 1068, which is known since several years from its atypical radio-gamma-ray correlation. Recently this source has also shown strong indications of high energy neutrino emission. A first semi-analytical, two-component multi-messenger model is presented that already gives some constraints on the AGN-starburst composite characteristics of NGC 1068 and exposes the need to include both starburst \emph{and} AGN corona to describe the multi-messenger data.

The non-thermal source abundances of elements play a crucial role in the understanding of cosmic ray phenomena from a few GeV up to several tens of EeV. In this work a first systematic approach is presented that describes the change of the abundances from the thermal to the non-thermal state via non-linear diffusive shock acceleration by a temporally evolving shock. Hereby, not only time-dependent ionization states of elements contained in the ambient gas are considered, but also elements condensed on solid, charged dust grains, which not only can be injected into the acceleration process as well, but are from our findings even the dominant injection channel for most heavy elements. This generic parametrized model is then applied to the case of particle acceleration by supernova remnants in various ISM phases as well as Wolf-Rayet (WR) wind environments. We show that the overall low to medium energy cosmic ray distribution by WR explosions yield a significantly harder, which makes this contribution quite promising in order to explain the spectral hardening of the flux of certain elements, such as helium, observed by AMS-02 and other experiments at rigidities of about 1 TV, which would also be an important test for the potential role of WR-progenitor supernovae as the sources of Galactic cosmic rays around the second knee.

The AMS-02 experiment has reported precise measurements of energy spectra of several cosmic-ray species in the range of ~(0.5-2000) GeV/n. An intriguing finding is the differences in the spectral shape between the different species. Protons exhibit the steepest spectrum of all the species, and helium, carbon, oxygen and iron spectra are found to be harder than that of neon, magnesium and silicon. These observations are difficult to explain as diffusive shock acceleration, the currently most plausible theory for cosmic particle acceleration at high energies, expects independence of the spectral index from mass and charge of the accelerated particle. Moreover, propagation in the Galaxy has been shown to not being able to compensate for this discrepancy. In this work, we present an explanation based on two-component model for the origin of cosmic rays in the Galaxy -- the first component originating from regular supernova remnants in the interstellar medium and the second component from Wolf-Rayet supernovae. Using recent results on cosmic-ray injection enhancement at supernova shocks in the uniform interstellar medium and in the wind environment of Wolf-Rayet stars, we show that the combination of the two components may explain most of the behavior observed by the AMS-02 experiment., Comment: 8 pages, ICRC 2021, PoS template

The landscape of high- and ultra-high-energy astrophysics has changed in the last decade, in large part owing to the inflow of high-quality data collected by present cosmic-ray, gamma-ray, and neutrino observatories. At the dawn of the multimessenger era, the interpretation of these observations within a consistent framework is important to elucidate the open questions in this field. CRPropa 3.2 is a Monte Carlo code for simulating the propagation of high-energy particles in the Universe. This new version represents a step further towards a more complete simulation framework for multimessenger studies. Some of the new developments include: cosmic-ray acceleration, support for particle interactions within astrophysical sources, full Monte Carlo treatment of electromagnetic cascades, improved ensemble-averaged Galactic propagation, and a number of technical enhancements. Here we present some of these novel features and some applications to gamma- and cosmic-ray propagation., Comment: 8 pages, 4 figures; Proceedings of the 37th International Cosmic Ray Conference (ICRC2021)

The nonthermal source abundances of elements play a crucial role in the understanding of cosmic ray (CR) phenomena from a few GeV up to several tens of EeV. We present a first systematic approach to describe the change of the abundances from the thermal to the nonthermal state via diffusive shock acceleration by a temporally evolving shock. We consider hereby not only ionization states of elements contained in the ambient gas, which we allow to be time dependent due to shock heating, but also elements condensed on solid, charged dust grains which can be injected into the acceleration process as well. Our generic parametrized model is then applied to the case of particle acceleration by supernova remnants in various ISM phases, for which we use state-of-the-art computation packages to calculate the ionization states of all elements. The resulting predictions for low energy cosmic ray (LECR) source abundances are compared with the data obtained by various experiments. We obtain excellent agreement for shocks in warm ionized ISM environments, which include HII regions, if dust grains are injected into the diffusive shock acceleration process with a much higher efficiency than ions. Less dependence of the fit quality is found on the mass-to-charge ratio of ions. For neutral environments, assuming that there are shocks in the weakly ionized component, and for the hot ionized medium we obtain generally inferior fits, but except for the cold neutral medium we do not exclude them as subdominant sites of Galactic CR production. The key challenge is found to be putting the LECR abundance of pure gas phase elements like neon and the (semi-)volatile elements phosphorus, sulfur and chlorine into the right balance with silicon, calcium and elements of the iron group. Finally, a brief outlook to the potential consequences for the understanding of the CR composition at higher energies is presented.

A consequence of Liouville's theorem indicates that the recently observed large scale anisotropy in the arrival direction of Ultra-High-Energy Cosmic Rays (UHECRs) cannot be produced by the Galactic magnetic field, thus this anisotropy already needs to be present outside our Galaxy. But in this case, the observed energy spectrum and composition of UHECRs differs from the one outside of the Milky Way, due to the suppression or the amplification of the UHECR flux from certain directions by the Galactic magnetic field. In this work, we investigate this effect for the case of a dipole and a quadrupole anisotropy, respectively, for the widely-used JF12 magnetic field model. We investigate boundaries on the maximal amplitude of the observed anisotropy and the maximal charge number of UHECRs. Furthermore, the flux modification is discussed in the light of the Auger data on the recent dipole and also the chemical composition. We find that this modification effect yields a modification of the observed flux of up to $\sim 10\%$ for the investigated magnetic field model and the observed dipole, in particular for a heavy chemical composition of UHECRs as suggested by the 'EPOS-LHC' model.

Many attempts have been made to provide catalogs of potential sources of ultra-high energy cosmic ray (UHECR) particles based on various astronomical tracers, such as observed radio or gamma-ray emission. A closer look reveals, however, that they all suffer from significant bias and selection effects. We present here a demo-version of a catalog for one often-discussed UHECR source class, radio galaxies (or radio-loud AGN), which is based on a complete theoretical description of jet-energetics, particle acceleration physics, relativistic beaming effects and nuclear composition, parametrized by a comprehensible set of adjustable physical quantities. In addition to the bright radio galaxies Centaurus A, Virgo A, Fornax A and Cygnus A discussed in previous work, we find several sources with blazar-like properties that can contribute on a similar level if relativistic beaming effects are considered. We present a simple method to test the basic properties of the catalog for any choice of parameters (without the need to run expensive simulations), and find that in the canonical case the anisotropy signals expected from radio galaxies promise to be in good agreement with current observational findings. In particular, radio galaxies can reproduce almost exactly the direction of the dipole above 8 EeV detected by the Pierre Auger Observatory if we assume that extragalactic magnetic fields are strong (>1nG) only in structures, but very weak in voids. We plan to provide a completed and improved version of this catalog in electronic form, to be used in more detailed UHECR propagation simulations. For immediate applications, we suggest a complete set of 16 strong UHECR sources which can contribute to UHECR anisotropy on the level which can be currently probed by experiment, and note that 6 of them have not been considered in any previous studies., Comment: 8 pages, 2 figures, paper presented at the 36th International Cosmic Ray Conference (ICRC2019), July 24th - August 1st, Madison, WI, USA; updated and final version

The extended jet structures of radio galaxies (RGs) represent an ideal acceleration site for High Energy Cosmic Rays (HECRs) and a recent model showed that the HECR data can be explained by these sources, if the arrival directions of HECRs at energies $\lesssim 8\,\text{EeV}$ from a certain RG, Cygnus A, are isotropized. First, this work introduces the inverted simulation setup in order to probe the isotropy assumption. Here, different extragalactic magnetic field models are compared showing that either a magnetic field of primordial origin that yields a high field strength in the large scale structures of the Universe is needed, or a significant contribution by a multitude of isotropically distributed sources. Secondly, the HECRs contribution by the bulk of RGs of different Fanaroff-Riley (FR) type is determined. Here, the most recent FR-type dependent radio-to-CR correlations $Q_{\rm cr}\propto L_{\rm radio}^{\beta_L}$ are used, and the impact of the slope $\beta_L$ on the HECRs is analyzed in detail. Finally, it is carved out that FR-II RGs provide a promising spectral behavior at the hardening part of the CR flux, between about $3\,\text{EeV}$ and $30\,\text{EeV}$, but most likely not enough CR power. At these energies, FR-I RGs can only provide an appropriate flux in the case of a high acceleration efficiency and $\beta_L\gtrsim 0.9$, otherwise these sources rather contribute below $3\,\text{EeV}$. Further, the required acceleration efficiency for a significant HECR contribution is exposed dependent on $\beta_L$ and the CR spectrum at the acceleration site.

A detailed investigation of radio galaxies has recently stressed these sources as the possible origin of the cosmic rays observed above $3\,\text{EeV}$. Here, the relevance of this model at energies below $3\,\text{EeV}$ is investigated. So, it is shown that the average contribution of radio galaxies can accurately explain the observed CR flux between the second knee and the ankle in the case of a strong source evolution. However, the model cannot provide the increasing heaviness and variance at energies $\lesssim 1\,\text{EeV}$ of the observed chemical composition. In addition, it is exposed that the resulting variance of the chemical composition at Earth shows also at higher energies a clear disagreement with the observations, indicating that the compositional contributions by Centaurus A and Cygnus A need to be less different., Comment: arXiv admin note: text overlap with arXiv:1812.09473

Radio galaxies are intensively discussed as the sources of cosmic rays observed above about 3 EeV, called ultra-high-energy cosmic rays (UHECRs). Here, the key issues from a recent investigation are summed up, where the individual characteristics of radio galaxies, as well as the impact by the extragalactic magnetic-field structures up to a distance of 120 Mpc has been taken into account. It is shown that the average contribution of radio galaxies taken over a very large volume cannot explain the observed features of UHECRs measured at Earth. However, we obtain excellent agreement with the spectrum, composition, and arrival-direction distribution of UHECRs measured by the Pierre Auger Observatory, if we assume that most UHECRs observed arise from only two sources: The ultra-luminous radio galaxy Cygnus A, providing a mostly light composition of nuclear species dominating up to about 60 EeV, and the nearest radio galaxy Centaurus A, providing a heavy composition dominating above 60 EeV. Here we have to assume that extragalactic magnetic fields out to 250 Mpc, which we did not include in the simulation, are able to isotropize the UHECR events at about 8 EeV arriving from Cygnus A.

The abundance of accelerators and the ambient conditions make Cygnus X a natural laboratory for studying the life cycle of cosmic-rays (CRs). This naturally makes the Cygnus X complex a highly interesting source in neutrino astronomy, in particular concerning a possible detection with the IceCube Neutrino Observatory, which has a good view of the northern hemisphere. In this paper, we model the multiwavelength spectrum of the Cygnus, for the first time using a broad data set from radio, MeV (COMPTEL), GeV (Fermi), TeV (Argo) and 10s of TeV (Milagro) energies. The modeling is performed assuming a leptohadronic model. We solve the steady-state transport equation for leptons and hadrons injected homogeneously in the region and test the role of diffusive transport and energy loss by radiation and interaction. The result shows that diffusion loss plays a significant role in Cygnus X and always exceeds the advection loss as well as almost all other loss processes. The best-fit parameters we find are a magnetic field of $B=8.9\times10^{-6}$ G, a target density of $N_t=19.4$ cm$^{-3}$, a cosmic ray spectral index of $\alpha=2.37$ and neutral gas distribution over a depth of 116 pc. We find that the fit describes the data up to TeV energies well, while the Milagro data are underestimated. This transport model with a broad multiwavelength fit provides a neutrino flux which approaches the sensitivity of IceCube at very high energies ($>$ 50 TeV). In the future, the flux sensitivity of IceCube will be improved. With this rather pessimistic model, leaving out the influence of possible strong, high-energy point sources, we already expect the flux in the Cygnus X region to suffice for IceCube to measure a significant neutrino flux in the next decade., Comment: 49 pages, 31 figures

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel $\kappa_\parallel$ and perpendicular $\kappa_\perp$ diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process., Comment: Accepted for publication in JCAP, 33 pages, 17 figures

The luminosity ratio of electrons to protons as it is produced in stochastic acceleration processes in cosmic ray sources is an important quantity relevant for several aspects of the modeling of the sources themselves. It is usually assumed to be around 1:100 in the case of Galactic sources, while a value of 1:10 is typically assumed when describing extragalactic sources. It is supported by observations that the average ratios should be close to these values. At this point, however, there is no possibility to investigate how each individual source behaves. When looking at the physics aspects, a 1:100 ratio is well supported in theory when making the following assumptions: (1) the total number of electrons and protons that is accelerated are the same; (2) the spectral index of both populations after acceleration is $a_e=a_p\approx 2.2$. In this paper, we reinvestigate these assumptions. In particular, assumption (2) is not supported by observational data of the sources and PIC simulation yield different spectral indices as well. We present the detailed calculation of the electron-to-proton ratio, dropping the assumption of equal spectral indices. We distinguish between the ratio of luminosities and the ratio of the differential spectral behavior, which becomes necessary for cases where the spectral indices of the two particle populations are not the same. We discuss the possible range of values when allowing for different spectral indices concerning the spectral behavior of electrons and protons. Additionally, it is shown that the minimum energy of the accelerated population can have a large influence on the results., Comment: 30 pages, 12 figures, accepted for publication in Astroparticle Physics (02/24/2017)

Radio galaxies are intensively discussed as the sources of cosmic rays observed above about $3\,{\times}\,10^{18}\,\text{eV}$, called ultra-high energy cosmic rays (UHECRs). We present a first, systematic approach that takes the individual characteristics of these sources into account, as well as the impact of the extragalactic magnetic-field structures up to a distance of 120 Mpc. We use a mixed simulation setup, based on 3D simulations of UHECRs ejected by observed, individual radio galaxies taken out to a distance of 120 Mpc, and on 1D simulations over a continuous source distribution contributing from beyond 120 Mpc. Additionally, we include the ultra-luminous radio galaxy Cygnus A at a distance of about $250\,$Mpc, as its contribution is so strong that it must be considered as an individual point source. The implementation of the UHECR ejection in our simulation setup is based on a detailed consideration of the physics of radio jets and standard first-order Fermi acceleration. We show that the average contribution of radio galaxies taken over a very large volume cannot explain the observed features of UHECRs measured at Earth. However, we obtain excellent agreement with the spectrum, composition, and arrival-direction distribution of UHECRs measured by the Pierre Auger Observatory, if we assume that most UHECRs observed arise from only two sources: The ultra-luminous radio galaxy Cygnus A, providing a mostly light composition of nuclear species dominating up to about $6\,{\times}\,10^{19}\,$eV, and the nearest radio galaxy Centaurus A, providing a heavy composition dominating above $6\,{\times}\,10^{19}\,$eV. Here we have to assume that extragalactic magnetic fields out to 250 Mpc, which we did not include in the simulation, are able to isotropize the UHECR events at about 8 EeV arriving from Cygnus A.

The origin of cosmic rays is one of the long-standing mysteries in physics and astrophysics. Simple arguments suggest that a scenario of supernova remnants (SNRs) in the Milky Way as the dominant sources for the cosmic ray population below the knee could work: in a generic calculation, it can be shown that these objects can provide the energy budget necessary to explain the observed flux of cosmic rays. However, this argument is based on the assumption that all sources behave in the same way, i.e.\ they all have the same energy budget, spectral behavior and maximum energy. In this paper, we investigate if a realistic population of SNRs is capable of producing the cosmic ray flux as it is observed below the knee. We use 21 SNRs that are well-studied from radio wavelengths up to gamma-ray energies. It could be shown previously (Mandelartz & Becker Tjus 2015) that the high-energy bump in the energy spectrum of these 21 sources can be dominated by hadronic emission. Here, gamma-rays are produced via $\pi^{0}-$decays from cosmic ray interactions in molecular clouds near the supernova remnant, which serves as the cosmic ray accelerator. The cosmic ray spectra show a large variety in their energy budget, spectral behavior and maximum energy. These sources are assumed to be representative for the total class of SNRs, where we assume that about 100 - 200 cosmic ray emitting SNRs should be present today. Finally, we use these source spectra to simulate the cosmic ray transport from individual SNRs in the Galaxy with the GALPROP code for cosmic ray propagation. We find that the cosmic ray budget can be matched well for a diffusion coefficient that is close to $D\propto E^{0.3}$. A stronger dependence on the energy, e.g. $E^{0.5}$, would lead to a spectrum at Earth that is too steep when compared to what is detected and the energy budget cannot be matched, in particular toward high energies., Comment: 43 pages, 7 figures

We present a systematic study of the non-thermal electron-proton plasma and its emission processes in starburst galaxies in order to explain the correlation between the luminosity in the radio band and the recently observed gamma luminosity. In doing so, a steady state description of the cosmic ray electrons and protons within the spatially homogeneous starburst is considered where continuous momentum losses are included as well as catastrophic losses due to diffusion and advection. The primary source of the relativistic cosmic rays, e.g. supernova remnants, provides a quasi-neutral plasma with a power law spectrum in momentum where we account for rigidity dependent differences between the electron and proton spectrum. We examine the resulting leptonic and hadronic radiation processes by synchrotron radiation, inverse Compton scattering, Bremsstrahlung and hadronic pion production. Finally, the observations of NGC 253, M82, NGC 4945 and NGC 1068 in the radio and gamma-ray band as well as the observed supernova rate are used to constrain a best-fit model. In the case of NGC 253, M82, NGC 4945 our model is able to accurately describe the data, showing that: (i) Supernovae are the dominant particle accelerators for NGC 253, M82 and NGC 4945, but not in the case of NGC 1068. (ii) All considered starburst galaxies are poor proton calorimeters in which for NGC 253 the escape is predominantly driven by the galactic wind, whereas the diffusive escape dominates in NGC 4945 and M82 (at energies > 1TeV). (iii) Secondary electrons from hadronic pion production are important to model the radio flux, but the associated neutrino flux is below the current observation limit.