Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter this turbulence are typically 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 affect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semianalytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any astrophysical system of interest that is under the influence of weak magnetic turbulence. Here, we adopt that the assigned magnetic turbulence is constrained to a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump—which has long been established for some special cases—is a universal feature of stochastic acceleration that emerges around the momentum χ _eq where acceleration and continuous loss are in equilibrium if the particle’s residence time in the system is sufficient at χ _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 reexamine the interactions of ultra-high-energy cosmic rays (UHECRs) with photons from the cosmic microwave background (CMB) under a changed, locally nonlinear temperature–redshift relation T ( z ). This changed temperature–redshift relation has recently been suggested by the postulate of subjecting thermalized and isotropic photon gases such as the CMB to an SU(2) rather than a U(1) gauge group. This modification of ΛCDM is called SU(2) _CMB , and some cosmological parameters obtained by SU(2) _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) _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 × 10 ^18 eV) for hard injection spectra and without considering the effects of magnetic fields. The reduction in CMB photon density also favors a decreased cosmic ray source evolution than the best fit using ΛCDM. In consequence, it seems that SU(2) _CMB favors sources that evolve like the star formation rate, such as starburst galaxies and gamma-ray bursts, over active galactic nuclei 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.

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 χ_ eq where acceleration and continuous loss are in equilibrium if the particle's residence time in the system is sufficient at χ_ 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 present a comprehensive multi-messenger study of NGC 1068, the prototype Seyfert II galaxy recently associated with high-energy IceCube neutrinos. Various aspects of the source, including its nuclear activity, jet, outflow, and starburst region, are analyzed in detail using a multi-wavelength approach and relevant luminosities are derived. We then explore its gamma-ray and neutrino emissions and investigate potential mechanisms underlying these phenomena and their relations with the different astrophysical components to try to understand which one is responsible for the IceCube neutrinos. By first using simple order-of-magnitude arguments and then applying specific theoretical models, we infer that only the region close to the accretion disc around the supermassive black hole has both the right density of X-ray photons needed to provide the targets for protons to sustain neutrino production and of optical/infrared photons required to absorb the associated but unobserved gamma rays. We conclude by highlighting ongoing efforts to constrain a possible broad connection between neutrinos and active galactic nuclei, as well as future synergies between astronomical and neutrino facilities.

NGC 1068 is a nearby, widely studied Seyfert II galaxy presenting radio, infrared, X-ray, and γ-ray emission, along with strong evidence for high-energy neutrino emission. Recently, the evidence for neutrino emission was explained in a multimessenger model, whereby the neutrinos originate from the corona of the active galactic nucleus. In this environment, γ-rays are strongly absorbed, so that an additional contribution is necessary, for instance, from the circumnuclear starburst ring. In this work, we discuss whether the radio jet can be an alternative source of the γ-rays between about 0.1 and 100 GeV, as observed by Fermi-LAT. In particular, we include both leptonic and hadronic processes, namely, accounting for inverse Compton emission and signatures from pp as well as pγ interactions. In order to constrain our calculations, we used VLBA and ALMA observations of the radio knot structures, which are spatially resolved at different distances from the supermassive black hole. Our results show that the best leptonic scenario for the prediction of the Fermi-LAT data is provided by the radio knot closest to the central engine. For that to be the case, a magnetic field strength of ∼1 mG is needed as well as a strong spectral softening of the relativistic electron distribution at (1 − 10) GeV. However, we show that neither such a weak magnetic field strength, nor such a strong softening is expected for that knot. A possible explanation for the ∼10 GeV γ-rays could potentially be provided by hadronic pion production in case of a gas density ≳104 cm−3. Nonetheless, this process is not found to contribute significantly to the low-energy end of the Fermi-LAT range. We conclude that the emission sites in the jet are not sufficient to explain the γ-rays across the whole Fermi-LAT energy band.

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 is motivated 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 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 star burst 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 tightly-knit with the actual temperature redshift relation of the CMB.

The existing discrepancies between the observation of local and extraction of global cosmological parameters motivate an extension of the $\Lambda$CDM cosmological model. A proposed extension called SU(2)$_\rm{CMB}$ describes cosmic microwave background (CMB) photons with an SU(2) instead of a U(1) gauge group. This mitigates some of these tensions, for example $H_0, \Omega_m, \sigma_8$, pushes the recombination epoch to higher redshifts, and thereby effectively reduces CMB photon densities. In this work, we study the impact of the SU(2) modified CMB evolution on the propagation of ultra-high energy cosmic rays (UHECRs) and their related fluxes of cosmogenic photons and neutrinos. The measured and predicted fluxes are the basis used to constrain source properties and rely on the $\Lambda$CDM CMB evolution. Thus, a modification of the past CMB densities impacts these flux predictions and possibly the constraints on the sources. In particular, we show an increased proton flux below the ankle ($10^{18.5}\,$eV), and slightly increased cosmogenic neutrino fluxes in comparison to $\Lambda$CDM.

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.

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 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. It has been shown that such hard spectra can be the result of the finite life-time of UHECR sources, if only a few individual sources dominate the UHECR flux at the highest energies. In this work we investigate the requirements on their CR power and life-time dependent on the characteristics of a purely turbulent, extragalactic magnetic field (EGMF). Without accounting for the anisotropy data, we are able to draw some robust constraints on the contribution of the brightest local radio galaxies, if the initial source spectrum at the acceleration side is soft, i.e. with a spectral index $\alpha\gtrsim 2$, as expected from conventional shock-acceleration theory. Moreover, we show that a local source could provide a dominant UHECR contribution which agrees with the mass composition at energies $E\gtrsim 40$ EeV data only in the case of a strong EGMF.

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.

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.

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 and AGN corona to describe the multi-messenger data.

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.

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.

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.

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.

The nonthermal 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. 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 cosmic ray 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. We present a brief outlook to the potential consequences of our results for the understanding of the composition around the second knee or the cosmic ray spectrum, or for the viability of explaining ultra-high energy cosmic rays with a dominant contribution by radio galaxies.

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.

Abstract The Neutrino Mass Ordering (NMO) remains one of the outstanding questions in the field of neutrino physics. One strategy to measure the NMO is to observe matter effects in the oscillation pattern of atmospheric neutrinos above $$\sim 1\,\mathrm {GeV}$$ ∼1GeV , as proposed for several next-generation neutrino experiments. Moreover, the existing IceCube DeepCore detector can already explore this type of measurement. We present the development and application of two independent analyses to search for the signature of the NMO with three years of DeepCore data. These analyses include a full treatment of systematic uncertainties and a statistically-rigorous method to determine the significance for the NMO from a fit to the data. Both analyses show that the dataset is fully compatible with both mass orderings. For the more sensitive analysis, we observe a preference for normal ordering with a p-value of $$p_\mathrm {IO} = 15.3\%$$ pIO=15.3% and $$\mathrm {CL}_\mathrm {s}=53.3\%$$ CLs=53.3% for the inverted ordering hypothesis, while the experimental results from both analyses are consistent within their uncertainties. Since the result is independent of the value of $$\delta _\mathrm {CP}$$ δCP and obtained from energies $$E_\nu \gtrsim 5\,\mathrm {GeV}$$ Eν≳5GeV , it is complementary to recent results from long-baseline experiments. These analyses set the groundwork for the future of this measurement with more capable detectors, such as the IceCube Upgrade and the proposed PINGU detector.