Search

We estimate collapse rates of axion stars in our galaxy based on the axion minicluster mass function of the Milky Way dark matter halo. We consider axion-like particles with different temperature evolution of the axion mass, including the QCD axion with $m_a=50\,\mu$eV. Combining estimates for the present-day axion star mass function from our previous work with the axion star accretion model predicted by self-similar growth, we can infer the expected number of bosenovae occurring within the Milky Way. Our estimates suggest that for an observation time of $t_\mathrm{obs}=1\,$yr, the majority of the up to $\sim 10^{13}$ bosenovae per galaxy occur in the densest miniclusters with initial overdensity parameter $\Phi\lesssim 10^4$. We discuss the detectability of such recurring axion bursts within our galactic vicinity and find that, for models with derivative couplings including axion-fermion interactions, potential broadband axion DM experiments can probe a large range of ALP masses $m_a\lesssim 10^{-6}\,$eV and with moderate improvements even the QCD axion case. For axions with non-derivative-type interactions like the axion-photon coupling, our analysis suggests that optimistic predictions with order-one dark matter abundance of axion stars $f_\star \sim 1$ can be probed by dedicated burst searches.

Axion-like particles, which we call axions, can compose the missing dark matter and may form substructures such as miniclusters and axion stars. We obtain the mass distributions of axion stars derived from their host miniclusters in our galaxy and find a significant number of axion stars reaching the decay mass, the critical mass set by the axion-photon coupling. Axion stars that have reached the decay mass can accrete surrounding axions either via or directly from their host miniclusters, subsequently converting them into radio photons through parametric resonance. We demonstrate that this accretion provides observable signals by proposing two scenarios: 1) external accretion of background dark matter occurring via miniclusters, and 2) internal accretion of isolated systems occurring directly from the minicluster onto its core. The emitted radio photons are nearly monochromatic with energies around the half of the axion mass. The radio-line signal emanating from such axion stars provides a distinctive opportunity searching for axions, overcoming the widespread radio backgrounds. We estimate the expected radio-line flux density to constrain the axion-photon coupling $g_{a\gamma\gamma}$ at each axion mass and find that the resultant line flux density is strong enough to be observed in radio telescopes such as LOFAR, FAST, ALMA, and upcoming SKA. We can constrain the axion-photon coupling down to $g_{a\gamma\gamma} \simeq 10^{-12} - 10^{-11}\,{\rm GeV}^{-1}$, reaching even $10^{-13}\,{\rm GeV}^{-1}$ depending on the accretion models of axion stars, over an axion mass range of $m_a\simeq 10^{-7} - 10^{-2}\,{\rm eV}$. From a different perspective, this radio-line signal could be a strong hint of an axion at the corresponding mass and also of axion stars within our galaxy., Comment: 34 pages, 7 figures, 2 tables

A quantitative analysis of model uncertainties for calculations of the maximum depth of proton-initiated extensive air showers (EAS) has been performed. Staying within the standard physics picture and using the conventional approach to the treatment of high energy interactions, we found that present uncertainties on the energy dependence of the inelastic cross section, the rate of diffraction, and the inelasticity of hadronic collisions allow one to increase the predicted average EAS maximum depth by about 10 g/cm$^2$. Invoking more exotic assumptions regarding a potentially significant modification of the parton hadronization procedure by hypothetical collective effects, we were able to change drastically the predicted energy dependence of the inelasticity of proton-air interactions and to increase thereby the predicted EAS maximum depth by up to $\simeq 30$ g/cm$^2$. However, those latter modifications are disfavored by the data of the LHCf experiment, regarding forward neutron production in proton-proton collisions at the Large Hadron Collider, and by measurements of the muon production depth by the Pierre Auger Observatory., Comment: Accepted for PRD

The end state of binary-neutron-star (BNS) mergers can manifest conditions to produce high-energy neutrinos. Inspired by the event GW170817, detected in gravitational waves and in optical/infrared emission, we investigate a scenario in which cosmic-ray (CR) particles are accelerated, in a population of BNS mergers, in the energy range from the knee to the ankle. By taking into account the measured thermal and non-thermal energy density of the photon fields in the source environment as a function of the time after the merger, we model the CR interactions and the consequent neutrino production. We propagate the escaped CR and neutrino fluxes through the extragalactic space and compare the expected diffuse fluxes to the experimental data and current limits. Depending on the accelerated CR mass composition and on the contribution of this possible source class to the sub-ankle CR flux, we provide indications on the rate of BNS merger events and the amount of baryons present in the source site., Comment: 33 pages and 25 figures

The propagation of very-high-energy gamma-rays (VHEGRs) in the extragalactic space offers the opportunity to study astrophysical phenomena not reproducible in laboratories. In particular, the deviation from predictions of the observed photon flux from distant sources at the GeV energy scale still represents an open problem. Commonly, this deviation is interpreted as the result of the deflection out of the line of sight of the source of the cascade-produced charged leptons by weak magnetic fields present in the intergalactic medium (IGM). However, plasma instabilities could have an effect on the energy- and momentum-distribution of the secondary electrons and positrons, modifying the development of electromagnetic cascades. In this work, we study the influence of plasma instabilities on the energy spectrum of electromagnetic cascades through a parametric study, performed with the Monte Carlo code CRPropa. We parameterize plasma instabilities with an energy loss length normalisation $\lambda_0$ and a power law index $\alpha$ of its electron/positron energy dependence. We simulate photon spectra at Earth for different blazar scenarios and find that plasma instabilities can reproduce the suppression in the GeV-photon flux of real astrophysical sources, such as 1ES 0229+200, when the energy loss length of electrons/positrons at 1.0 TeV is $\lambda_0 \simeq 100\,\text{kpc}$ and $\alpha\simeq0$. The energy fraction lost by the secondary electron pairs due to the instability is estimated to be about $1\%$ over the typical interaction length of Inverse Compton scattering for these parameter values., Comment: 12 pages, 14 figures

We apply current analytical knowledge on the characteristic mass and linear evolution of miniclusters down to redshift $z=0$ to the hypothetical minicluster distribution of the Milky Way. Using the mass-radius relation and a core-halo relation for stable soliton solutions composed of axion-like particles (ALPs), we connect the galactic minicluster mass distribution to that of their ALP star cores. We consider different temperature evolutions of the ALP field with masses in the range $10^{-12}\,\mathrm{eV} \leq m_a \leq 10^{-3}\,$eV and infer the abundance and properties of QCD axion- and ALP stars in our galaxy. We re-evaluate detection prospects for collisions of neutron stars with both ALP stars and miniclusters as well as relativistic ALP bursts, so-called Bosenovae. Our analysis shows that the collision rates between miniclusters and neutron stars can become as large as $\sim 10^5\,$yr$^{-1}$ galaxy$^{-1}$, but that the fraction of encounters that can lead to resonance between ALP mass and magnetosphere plasma frequency is generally well below $\sim 1\,$yr$^{-1}$ galaxy$^{-1}$, depending on the ALP model. We confirm previous results that merger rates of ALP stars are extremely small $< 10^{-12}\,$yr$^{-1}$ galaxy$^{-1}$, while their host miniclusters can merge much more frequently, up to $\sim 10^3\,$yr$^{-1}$ galaxy$^{-1}$ for the QCD axion. We find that Bosenovae and parametric resonance are much more likely to lead to observable signatures than neutron star encounters. We also suggest that a combination of accretion and parametric resonance can lead to observable radio lines for a wide range of ALP masses $m_a$ and photon-couplings $g_{a\gamma\gamma}$., Comment: 30 pages, 20 figures

Motivated by the excess of the muon content of cosmic ray induced extensive air showers (EAS), relative to EAS modeling, observed by the Pierre Auger Observatory, and by the tension between Auger data and air shower simulations on the maximal muon production depth $X^{\mu}_{\max}$, we investigate the possibility to modify the corresponding EAS simulation results, within the Standard Model of particle physics. We start by specifying the kinematic range for secondary hadron production, which is of relevance for such predictions. We further investigate the impact on the predicted EAS muon number and on $X^{\mu}_{\max}$ of various modifications of the treatment of hadronic interactions, in the framework of the QGSJET-III model, in particular the model calibration to accelerator data, the amount of the "glue" in the pion, and the energy dependence of the pion exchange process. None of the considered modifications of the model allowed us to enhance the EAS muon content by more than 10\%. On the other hand, for the maximal muon production depth, some of the studied modifications of particle production give rise up to $\sim 10$ g/cm$^2$ larger $X^{\mu}_{\max}$ values, which increases the difference with Auger observations., Comment: Version accepted for Astroparticle Physics

Flavor-dependent neutrino transport is described by a well-known kinetic equation for occupation-number matrices in flavor space. However, as an overlooked theoretical problem, we show that in the inhomogeneous case, neutrino-neutrino refractive energy is not conserved. We derive the missing gradient terms in the fast flavor limit (vanishing neutrino masses), and prove that the missing refractive energy is traded with the huge reservoir of neutrino kinetic energy through gradients of the weak interaction potential. Even small changes of the kinetic energy accommodate the refractive energy gained or lost. Flavor evolution alone is negligibly affected by the new terms., Comment: Small changes to the text, version published on Physical Review Letters; 5 pages, 1 figures, plus Supplemental Material

The paradigm-changing possibility of collective neutrino-antineutrino oscillations was recently advanced in analogy to collective flavor oscillations. However, the amplitude for the backward scattering process $\nu_{\mathbf{p}_1}\overline\nu_{\mathbf{p}_2}\to\nu_{\mathbf{p}_2}\overline\nu_{\mathbf{p}_1}$ is helicity-suppressed and vanishes for massless neutrinos, implying that there is no off-diagonal refractive index between $\nu$ and $\overline\nu$ of a single flavor of massless neutrinos. For a nonvanishing mass, collective helicity oscillations are possible, representing de-facto $\nu$--$\overline\nu$ oscillations in the Majorana case. However, such phenomena are suppressed by the smallness of neutrino masses as discussed in the previous literature., Comment: 3 pages, 2 figures, with appendices

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

Missing cascades from TeV blazar beams indicate that collective plasma effects may play a significant role in their energy loss. It is possible to mimic the evolution of such highly energetic pair beams in laboratory experiments using modern accelerators. The fate of the beam is governed by two different processes, energy loss through the unstable mode and energetic broadening of the pair beam through diffusion in momentum space. We chalk out this evolution using a Fokker-Planck approach in which the drift and the diffusion terms respectively describe these phenomena in a compact form. We present particle-in-cell simulations to trace the complete evolution of the unstable beam-plasma system for a generic narrow Gaussian pair beam for which the growth rate is reactive. We show that the instability leads to an energetic broadening of the pair beam, slowing down the instability growth in the linear phase, in line with the analytical and numerical solutions of the Fokker-Planck equation. Whereas in a laboratory experiment the change in the momentum distribution is an easily measured observable as a feedback of the instability, the consequence of diffusive broadening in an astrophysical scenario can be translated to an increase in the opening angle of the pair beam., Comment: 20 pages, 10 figures

The prompt contribution to the atmospheric neutrino flux is analyzed. It is demonstrated that the corresponding theoretical uncertainties related to perturbative treatment of charm production, notably, the ones stemming from the low and high $x$ behavior of parton distribution functions, can be conveniently studied at the level of charm quark production. Additionally, we discuss the non-perturbative contribution to the prompt neutrino flux, related to the intrinsic charm content of the proton, and analyze its main features., Comment: v2: accepted version

Experimental observations of extensive air showers have revealed an excess of the muon content with respect to their theoretical simulations, which we refer to as the muon puzzle. This muon puzzle hampers a precise determination of the ultra-high-energy cosmic ray mass composition. We investigate the potential of producing states of dense quark-gluon matter (which we call fireballs) to resolve the muon puzzle as quantified with data from the Pierre Auger Observatory on the depth of the shower maximum and the number of muons at ground. Adopting a phenomenological fireball model, we find that the inelasticity enhancement associated with the formation of a plasma state is in tension with data on the electromagnetic longitudinal shower development. Instead, we restrict the fireball model to only enhance the strangeness produced in Standard Model hadronic interactions, and dub this model the strangeball model. With an analytic approach based on the Heitler-Matthews model we then find explicit sets of strangeball parameters that resolve the muon puzzle. Constraints from data on shower-to-shower fluctuations of the muon number require strangeness enhancements already at energies accessible to current-generation collider experiments. At Tevatron and LHC energies we estimate 40% of the interactions to produce strangeballs, corresponding to a 5-9% increase of the average fraction of energy retained in the hadronic cascade compared to predictions from current hadronic interaction models. A comparison with relevant measurements of the LHCf and LHCb detectors does not directly exclude this scenario, though the obtained tension with LHCb suggests a stringent test at 14 TeV., Comment: This is the Accepted Manuscript version of an article accepted for publication in Journal of Cosmology and Astroparticle Physics. Neither SISSA Medialab Srl nor IOP Publishing Ltd is responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at DOI 10.1088/1475-7516/2023/02/017. 29 pages, 13 figures, 3 tables

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

Compilation of the six contributions to the ICRC conference 2021 by the CORSIKA 8 Collaboration. The status of the project is illustrated. In particular, the secondary hadron as well as the electromagnetic cascades are being validated individually, and current results are reviewed. A novel framework for radio emission simulations is presented, which is designed given the modular nature of CORSIKA 8 to support, both, the CoREAS as well as the ZHS formalism. At the same time, first Cherenkov emission calculations are shown which are based on CORSIKA 8 coupled with a GPU Cherenkov emission code. Finally, a new powerful feature of CORSIKA 8 is illustrated, where the entire genealogy of air shower particles can be studied in all details., Comment: ICRC 2021 conference, 6 proceedings, 51 pages

We investigate toy models for spatial and temporal instabilities in collective neutrino oscillations induced by neutrino self-interactions, with special emphasis on inhomogeneous systems with densities following a profile. Simulations are based on a mathematica program that solves the Liouville equation with or without vacuum terms, refractive terms from a background medium, and neutrino-neutrino forward scattering, in one space dimension and in time. A discrete number of momentum modes are characterized by the neutrino velocity projection on the spatial direction. We also consider the effects of charged current interaction source terms and neutral current scattering contributions. We find that refractive effects from the medium, in particular for density distributions with a profile, and neutral current non-forward scattering off the background medium can strongly influence fast collective flavor transformations. Specifically we find that if both are present, fast flavor conversions can be strongly suppressed or at least delayed., Comment: 20 pages, 10 figures consisting of 37 pdf files in total; additional references and small updates

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)

Neutrinos from a supernova (SN) might undergo fast flavor conversions near the collapsed stellar core. We perform a detailed study of this intriguing possibility, analyzing time-dependent state-of-the-art 3D SN models of 9 and 20 Msun. Both models were computed with multi-D three-flavor neutrino transport based on a two-moment solver, and both exhibit the presence of the lepton-number emission self-sustained asymmetry (LESA). The transport solution does not provide the angular distributions of the neutrino fluxes, which are crucial to track the fast flavor instability. To overcome this limitation, we use a recently proposed approach based on the angular moments of the energy-integrated electron lepton-number distribution. With this method we find the possibility of fast neutrino flavor instability at radii <~20 km, which is well interior to the neutrinosphere. Our results confirm recent observations in a 2D SN model and in 2D/3D models with fixed matter background, which were computed with Boltzmann neutrino transport. However, the flavor unstable locations are not isolated points as discussed previously, but thin skins surrounding volumes where electron antineutrinos are more abundant than electron neutrinos. These volumes grow with time and appear first in the convective layer of the proto-neutron star (PNS), where a decreasing electron fraction (Ye) and high temperatures favor the occurrence of regions with negative neutrino chemical potential. Since Ye remains higher in the LESA dipole direction, where convective lepton-number transport out from the nonconvective PNS core slows down the deleptonization, flavor unstable conditions become more widespread in the opposite hemisphere. This interesting phenomenon deserves further investigation, since its impact on SN modeling and possible consequences for SN dynamics and neutrino observations are presently unclear. (abridged), Comment: 21 pages, 13 figures; more detailed explanations added due to referee comments; accepted by PRD

Dark matter axion condensates may experience stimulated decays into photon pairs. This effect has been often interpreted as a parametric resonance of photons from the axion-photon coupling, leading to an exponential growth of the photon occupation number in a narrow instability band. Most of the previous literature does not consider the possible evolution of the axion field due to the photon growth. We revisit this effect presenting a mean field solution of the axion-photon kinetic equations, in terms of number of photons and pair correlations. We study the limit of no axion depletion, recovering the known instability. Moreover, we extend the results including a possible depletion of the axion field. In this case we find that the axion condensate exhibits the behaviour of an inverted pendulum. We discuss the relevance of these effects for two different cases: an homogeneous axion field at recombination and a localized axion clump and discuss constraints that could result from the induced photon background., Comment: 15 pages, 3 pdf figures. v2: 17 pages, 3 figures. Discussion enlarged. Added Appendix on axion instability in the expanding Universe. Matches the version accepted on PRD

Dwarf galaxies are dark matter-dominated and therefore promising targets for the search for weakly interacting massive particles (WIMPs), which are well-known candidates for dark matter. Annihilation of WIMPs produce ultra-relativistic cosmic-ray electrons and positrons that emit synchrotron radiation in the presence of magnetic fields. For typical magnetic field strengths (few $\mu $G) and $\mathcal O$(GeV--TeV) WIMP masses, this emission peaks at hundreds of MHz. Here, we use the non-detection of 150-MHz radio continuum emission from the dwarf spheroidal galaxy Canes Venatici I with the LOw-Frequency ARray (LOFAR) to derive constraints on the annihilation cross section of WIMPs into primary electron-positron and other fundamental particle-antiparticle pairs. Our main underlying assumption is that the transport of the cosmic rays can be described by the diffusion approximation, thus requiring a non-zero magnetic field strength with small-scale structure. In particular, by adopting magnetic field strengths of $\mathcal O(1\,\mu$G) and diffusion coefficients $\sim 10^{27}~\rm cm^2\,s^{-1}$, we obtain limits that are comparable with those set by \emph{Fermi} Large Area Telescope using gamma-ray observations of this particular galaxy. Assuming s-wave annihilation and WIMPs making up 100 per cent of the DM density, our benchmark limits exclude several thermal WIMP realisations in the $[2,20]$-GeV mass range. We caution, however, that our limits for the cross section are subject to enormous uncertainties which we also quantitatively assess. In particular, variations on the propagation parameters or on the DM halo can shift our limits up by several orders of magnitude (in the pessimistic scenario)., Comment: 11 pages, 12 figures. Matches published version

We investigate the possible parametric growth of photon amplitudes in a background of axion-like particle (ALP) dark matter. The observed extragalactic background radiation limits the allowed enhancement effect. We derive the resulting constraints on the axion-photon coupling constant $g_{a\gamma}$ from Galactic ALP condensates as well as over-densities. If ALP condensates of size $R$ exist in our Galaxy, a scan for extremely narrow unresolved spectral lines with frequency $\nu$ can constrain the axion-photon coupling at ALP mass $m_a=4\pi\nu$ to $g_{a\gamma}\lesssim2\times10^{-14}(10\,{\rm kpc}/R)\,{\rm GeV}^{-1}$. Radio to optical background data yield constraints at this level within observed wavebands or ALP mass windows over a broad range $0.08\, \mu \text{eV} \lesssim m_a \lesssim 8 \text{ eV}$. These condensate constraints on $g_{a\gamma}$ probe down to the QCD axion band for $m_a \gtrsim$ 10 $\mu$eV., Comment: 6+7 pages, 2 figures, 3 tables, Comments welcome!

We review open questions and prospects for progress in ultrahigh-energy cosmic ray (UHECR) research, based on a series of discussions that took place during the `The High-Energy Universe: Gamma-Ray, Neutrino, and Cosmic-ray Astronomy' MIAPP workshop in 2018. Specifically, we overview open questions on the origin of the bulk of UHECRs, the UHECR mass composition, the origin of the end of the cosmic-ray spectrum, the transition from Galactic to extragalactic cosmic rays, the effect of magnetic fields on the trajectories of UHECRs, anisotropy expectations for specific astrophysical scenarios, hadronic interactions, and prospects for discovering neutral particles as well as new physics at ultrahigh energies. We also briefly present upcoming and proposed UHECR experiments and discuss their projected science reach., Comment: 47 pages, 17 figures, Review to appear in "Frontiers in Astronomy and Space Science" special issue, "Multi-Messenger Astrophysics: New Windows to the Universe"

Axion-like particles are dark matter candidates motivated by the Peccei-Quinn mechanism and also occur in effective field theories where their masses and photon couplings are independent. We estimate the dispersion of circularly polarized photons in a background of oscillating axion-like particles (ALPs) with the standard $g_{a\gamma}\,a\,F_{\mu\nu}\tilde F^{\mu\nu}/4$ coupling to photons. This leads to birefringence or rotation of linear polarization by ALP dark matter. Cosmic microwave background (CMB) birefringence limits $\Delta \alpha \lesssim (1.0)^\circ$ enable us to constrain the axion-photon coupling $g_{a\gamma} \lesssim 10^{-17}-10^{-12}\,{\rm GeV}^{-1}$, for ultra-light ALP masses $m_a \sim 10^{-27} - 10^{-24}$ eV. This improves upon previous axion-photon coupling limits by up to four orders of magnitude. Future CMB observations could tighten limits by another one to two orders., Comment: 6+2 pages, 1 figure, 1 table; substantially revised version, overall conclusions essentially unchanged

Fast flavor conversions of supernova neutrinos, possible near the neutrinosphere, depends on an interesting interplay of collisions and neutrino oscillations. Contrary to naive expectations, the rate of self-induced neutrino oscillations, due to neutrino-neutrino forward scattering, comfortably exceeds the rate of collisions even deep inside the supernova core. Consistently accounting for collisions and oscillations, we present the first calculations to show that collisions can create the conditions for fast flavor conversions of neutrinos, but oscillations can continue without significant damping thereafter. This may have interesting consequences for supernova explosions and the nature of its associated neutrino emission., Comment: 7 pages, 5 figures

We study the evolution of magnetohydrodynamic turbulence taking into account the chiral anomaly effect. This chiral magnetohydrodynamic description of the plasma is expected to be relevant for temperatures comparable to the electroweak scale, and therefore for the evolution of magnetic fields in the early Universe and young neutron stars. We focus on the case of freely decaying chiral magnetohydrodynamic turbulence and discuss the dissipation of ideal MHD invariants. Using the variational approach we discuss the minimum energy configurations of magnetic field and velocity. As in the case of the standard magnetohydrodynamic turbulence, we find that the natural relaxation state is given by a force-free field, $\nabla \times \mathbf{B} \propto \mathbf{B}$. However, the precise form of this configuration is now determined by parameters describing the chiral anomaly effect, leading to some important differences when compared to the non-chiral turbulence. Using this result we argue that the evolution of velocity and magnetic field will tend to effectively decouple during the transition to this minimal energy state., Comment: 14 pages, 0 figures

Neutrino production, absorption, transport, and flavor evolution in astrophysical environments is described by a kinetic equation $D\varrho=-i[{\sf H},\varrho]+{\cal C}[\varrho]$. Its basic elements are generalized occupation numbers $\varrho$, matrices in flavor space, that depend on time $t$, space $\bf x$, and momentum $\bf p$. The commutator expression encodes flavor conversion in terms of a matrix $\sf H$ of oscillation frequencies, whereas ${\cal C}[\varrho]$ represents source and sink terms as well as collisions. The Liouville operator on the left hand side involves linear derivatives in $t$, $\bf x$ and $\bf p$. The simplified expression $D=\partial_t+\hat{\bf p}\cdot{\partial}_{\bf x}$ for ultra-relativistic neutrinos was recently questioned in that flavor-dependent velocities should appear instead of the unit vector $\hat{\bf p}$. Moreover, a new damping term was postulated as a result. We here derive the full flavor-dependent velocity structure of the Liouville term although it appears to cause only higher-order corrections. Moreover, we argue that on the scale of the neutrino oscillation length, the kinetic equation can be seen as a first-order wave equation.

We calculate the gravitational wave spectrum produced by magneto-hydrodynamic turbulence in a first order phase transitions. We focus in particular on the role of decorrelation of incompressible (solenoidal) homogeneous isotropic turbulence, which is dominated by the sweeping effect. The sweeping effect describes that turbulent decorrelation is primarily due to the small scale eddies being swept with by large scale eddies in a stochastic manner. This effect reduces the gravitational wave signal produced by incompressible MHD turbulence by around an order of magnitude compared to previous studies. Additionally, we find a more complicated dependence for the spectral shape of the gravitational wave spectrum on the energy density sourced by solenoidal modes (magnetic and kinetic). The high frequency tail follows either a $k^{-5/3}$ or a $k^{-8/3}$ power law for large and small solenoidal turbulence density parameter, respectively. Further, magnetic helicity tends to increase the gravitational wave energy at low frequencies. Moreover, we show how solenoidal modes might impact the gravitational wave spectrum from dilatational modes e.g. sound waves. We find that solenoidal modes greatly affect the shape of the gravitational wave spectrum due to the sweeping effect on the dilatational modes. For a high velocity flow, one expects a $k^{-2}$ high frequency tail, due to sweeping. In contrast, for a low velocity flow and a sound wave dominated flow, we expect a $k^{-3}$ high frequency tail. If neither of these limiting cases is realized, the gravitational wave spectrum may be a broken power law with index between -2 and -3, extending up to the frequency at which the source is damped by viscous dissipation., Comment: 28 pages, 6 figures, submitted to CQG, minor mistakes corrected, minor improvements added, figures 2,4,5 and 6 have been slightly revised, major revision of figure 3, appendix added

This work presents a scenario of ultra-high energy cosmic ray source distribution where a nearby source is solely responsible for the anisotropies in arrival directions of cosmic rays while the rest of the sources contribute only isotropically. An analytical approach focused on large-scale anisotropies, which are influenced by deflections in a Kolmogorov-type turbulent magnetic field, is employed to provide more general results. When the recent Pierre Auger Observatory angular power spectrum above 8 EeV is used the restricted model gives, under the assumption of the small angle approximation, a solution where the RMS deflection with respect to the line of sight is $\alpha_{\rm rms} = \left(50^{+11}_{-10}\right)^\circ$, while the relative flux from the single source $\eta=0.03\pm 0.01$. Furthermore, the solution can be translated into constraints on the source distance, luminosity, and extra-galactic magnetic field strength. For Centaurus A and the Virgo cluster the required relation between the coherence length and the RMS magnetic field strength is obtained: a coherence length of $~\sim 100\,\mathrm{kpc}$ would imply the RMS field strength around $1\,\mathrm{nG}$ for iron dominated and above $10\,\mathrm{nG}$ for proton dominated composition. We also performed trajectory simulations with our publicly available code CRPropa to show that our analytical model can serve as a good approximation as long as the deflections in cosmic magnetic fields can be described as a random walk. The simulations showed that generally structured fields tend to suppress large-scale anisotropies, especially the dipole, compared to anisotropies at smaller scales described by higher multipoles., Comment: 27 pages, 15 figures

We compute the fluxes of radio photons from conversion of axion-like particle dark matter in cosmic magnetic fields. We find that for axion-like particle masses around $10^{-6}\,$eV and effective coupling constants to photons $g_{a\gamma}\gtrsim10^{-13}\,{\rm GeV}^{-1}$ strongly magnetized nearby stellar winds may give detectable line-like radio photon signals, although predicted fluxes are highly uncertain due to the poorly known structure of the magnetic fields. Nevertheless, it may be worth while to conduct a dedicated search in the direction of such sources. When combined with a possible future laboratory detection of axion-like dark matter such observations may in turn provide information on the small scale magnetic field structure in such objects., Comment: 9 revtex pages, comments welcome

With the publicly available astrophysical simulation framework for propagating extraterrestrial UHE particles, CRPropa 3, it is now possible to study realistic UHECR source scenarios including deflections in Galactic and extragalactic magnetic fields in an efficient way. Here we discuss three recent studies that have already been done in that direction. The first one investigates what can be expected in the case of maximum allowed intergalactic magnetic fields. Here is shown that, even if voids contain strong magnetic fields, deflections of protons with energies $\gtrsim 60 \; \text{EeV}$ from nearby sources might be small enough to allow for UHECR astronomy. The second study looks into several scenarios with a smaller magnetization focusing on large-scale anisotropies. Here is shown that the local source distribution can have a more significant effect on the large-scale anisotropy than the EGMF model. A significant dipole component could, for instance, be explained by a dominant source within 5 Mpc distance. The third study looks into whether UHECRs can come from local radio galaxies. If this is the case it is difficult to reproduce the observed low level of anisotropy. Therefore is concluded that the magnetic field strength in voids in the EGMF model used here is too low and/or there are additional sources of UHECRs that were not taken into account in these simulations., Comment: UHECR2016 conference proceeding

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

We study the propagation of ultra-high-energy cosmic rays in the magnetised cosmic web. We focus on the particular case of highly magnetised voids ($B \sim \text{nG}$), using the upper bounds from the Planck satellite. The cosmic web was obtained from purely magnetohydrodynamical cosmological simulations of structure formation considering different power spectra for the seed magnetic field in order to account for theoretical uncertainties. We investigate the impact of these uncertainties on the propagation of cosmic rays, showing that they can affect the measured spectrum and composition by up to $\simeq 80\%$ and $\simeq 5\%$, respectivelly. In our scenarios, even if magnetic fields in voids are strong, deflections of 50 EeV protons from sources closer than $\sim\;$50 Mpc are less than $15^\circ$ in approximately 10-50% of the sky, depending on the distribution of sources and magnetic power spectrum. Therefore, UHECR astronomy might be possible in a significant portion of the sky depending on the primordial magnetic power spectrum, provided that protons constitute a sizeable fraction of the observed UHECR flux., Comment: 12 pages, 10 figures

Cosmic rays (CRs) govern the energetics of present-day galaxies and might have also played a pivotal role during the Epoch of Reionization. In particular, energy deposition by low-energy ($E \lesssim 10$ MeV) CRs accelerated by the first supernovae, might have heated and ionized the neutral intergalactic medium (IGM) well before ($z \approx 20$) it was reionized, significantly adding to the similar effect by X-rays or dark matter annihilations. Using a simple, but physically motivated reionization model, and a thorough implementation of CR energy losses, we show that CRs contribute negligibly to IGM ionization, but heat it substantially, raising its temperature by $\Delta T=10-200$ K by $z=10$, depending on the CR injection spectrum. Whether this IGM pre-heating is uniform or clustered around the first galaxies depends on CR diffusion, in turn governed by the efficiency of self-confinement due to plasma streaming instabilities that we discuss in detail. This aspect is crucial to interpret future HI 21 cm observations which can be used to gain unique information on the strength and structure of early intergalactic magnetic fields, and the efficiency of CR acceleration by the first supernovae., Comment: 10 pages, 7 figures

In this work the influence of the chiral anomaly effect on the evolution of magnetohydrodynamic turbulence was studied. We argue that in the early universe, before the electroweak symmetry breaking, and for temperatures high enough such that the electron mass can be ignored, the description of a charged plasma in general needs to take into account the interplay between turbulence and the anomaly effects. It was demonstrated that this generalization can have important consequences on the evolution of turbulence, leading to the creation of maximally-helical fields from initially non-helical ones. Therefore, chiral effects can strongly support turbulent inverse cascade, and lead to a slower decrease of the magnetic field with time, and also to a faster growth of the correlation length, when compared to the evolution predicted by the standard magnetohydrodynamical description. Using the weak anomaly approximation, and treating the anomaly contributions to magnetic energy and helicity as a small perturbation, we derive the specific solutions for the inverse cascade regime that demonstrate how chiral effects support the inverse cascade., Comment: 12 pages, 4 figures

We use the CRPropa code to simulate the propagation of ultra high energy cosmic rays (with energy $\geq 10^{18} \rm eV$ and pure proton composition) through extragalactic magnetic fields that have been simulated with the cosmological ENZO code.We test both primordial and astrophysical magnetogenesis scenarios in order to investigate the impact of different magnetic field strengths in clusters, filaments and voids on the deflection of cosmic rays propagating across cosmological distances. We also study the effect of different source distributions of cosmic rays around simulated Milky-Way like observers. Our analysis shows that the arrival spectra and anisotropy of events are rather insensitive to the distribution of extragalactic magnetic fields, while they are more affected by the clustering of sources within a $\sim 50$ Mpc distance to observers. Finally, we find that in order to reproduce the observed degree of isotropy of cosmic rays at $\sim $ EeV energies, the average magnetic fields in cosmic voids must be $\sim 0.1 \rm \ nG$, providing limits on the strength of primordial seed fields., Comment: 13 pages, 20 figures

We determine the effect of intergalactic magnetic fields on the distribution of high energy gamma rays by performing three-dimensional Monte Carlo simulations of the development of gamma-ray-induced electromagnetic cascades in the magnetized intergalactic medium. We employ the so-called 'Large Sphere Observer' method to efficiently simulate blazar gamma ray halos. We study magnetic fields with a Batchelor spectrum and with maximal left- and right-handed helicities. We also consider the case of sources whose jets are tilted with respect to the line of sight. We verify the formation of extended gamma ray halos around the source direction, and observe spiral-like patterns if the magnetic field is helical. We apply the $Q$-statistics to the simulated halos to extract their spiral nature and also propose an alternative method, the $S$-statistics. Both methods provide a quantative way to infer the helicity of the intervening magnetic fields from the morphology of individual blazar halos for magnetic field strengths $B \gtrsim 10^{-15}\,{\rm G}$ and magnetic coherence lengths $L_{\rm c} \gtrsim 100\,{\rm Mpc}$. We show that the $S$-statistics has a better performance than the $Q$-statistics when assessing magnetic helicity from the simulated halos., Comment: 14 pages, 7 figures

One of the key predictions of the WIMP paradigm for Dark Matter (DM) is that DM particles can annihilate into charged particles. These annihilations will proceed in e.g. Galactic subhalos such as dwarf Galaxies or, as recently pointed out, high velocity clouds such as the "Smith Cloud". In this note, we focus on the radio emission associated with DM annihilations into electrons and positrons occurring in the Smith Cloud. The phenomenology of this emission is discussed in quite some detail. We argue that the uncertainties in the propagation can be captured by the typical diffusion-loss length parameter (Syrovatskii variable) but that the angle-integrated radio fluxes are independent of the propagation. We conclude that if the Smith Cloud is indeed dominated by DM, radio signals from DM annihilation stand out amongst other messengers. Furthermore, low frequencies such as the ones observed by e.g. the Low Frequency Array (LOFAR) and the next-generation Square Kilometre Array (SKA) are optimal for searches for DM in the Smith Cloud. As a practical application, we set conservative constraints on dark matter annihilation cross section using data of continuum radio emission from the Galaxy at 22 MHz and at 1.4 GHz. Stronger constraints could be reached by background subtraction, exploiting the profile and frequency dependence of the putative DM signal. We set stronger but tentative limits using the median noise in brightness temperature from the Green Bank Telescope and the LOFAR sensitivities., Comment: 23 pages, 17 figures. Extended discussion on how the limits/forecasts are obtained. Matches published version

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory., Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary files

We present the simulation framework CRPropa version 3 designed for efficient development of astrophysical predictions for ultra-high energy particles. Users can assemble modules of the most relevant propagation effects in galactic and extragalactic space, include their own physics modules with new features, and receive on output primary and secondary cosmic messengers including nuclei, neutrinos and photons. In extension to the propagation physics contained in a previous CRPropa version, the new version facilitates high-performance computing and comprises new physical features such as an interface for galactic propagation using lensing techniques, an improved photonuclear interaction calculation, and propagation in time dependent environments to take into account cosmic evolution effects in anisotropy studies and variable sources. First applications using highlighted features are presented as well., Comment: 23 pages, 9 figures, 2 tables, version accepted for publication in JCAP

We analyse solutions of the MHD equations around the electroweak transition taking into account the effects of the chiral anomaly. It is shown that a transition that is not of the first order has direct consequences on the evolution of the asymmetry between left- and right-handed leptons. Assuming an initial chiral asymmetry in the symmetric phase at temperatures higher than the transition temperature, as well as the existence of magnetic fields, it is demonstrated that the asymmetry typically grows with time, until it undergoes a fast decrease at the transition, and then eventually gets damped at lower temperatures in the broken phase. We argue that it is unlikely to have any significant magnetic field amplification as a consequence of the electroweak transition in the Standard model, even when the chiral anomaly is introduced. The presence of a chiral asymmetry between left- and right-handed charge carriers naturally leads to the creation of helical magnetic fields from non-helical fields and this can have consequences on their subsequent evolution., Comment: 21 pages, 7 figures; matches published version

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal., Comment: Replaced with published version. Added journal reference and DOI

We investigate the evolution of the chiral magnetic instability in a protoneutron star and compute the resulting magnetic power and helicity spectra. The instability may act during the early cooling phase of the hot protoneutron star after supernova core collapse, where it can contribute to the buildup of magnetic fields of strength up to the order of $10^{14}$ G. The maximal field strengths generated by this instability, however, depend considerably on the temperature of the protoneutron star, on density fluctuations and turbulence spectrum of the medium. At the end of the hot cooling phase the magnetic field tends to be concentrated around the submillimeter to cm scale, where it is subject to slow resistive damping., Comment: 18 pages, 10 figures; Accepted for publication in JCAP

The majority of the matter in the universe is still unidentified and under investigation by both direct and indirect means. Many experiments searching for the recoil of dark-matter particles off target nuclei in underground laboratories have established increasingly strong constraints on the mass and scattering cross sections of weakly interacting particles, and some have even seen hints at a possible signal. Other experiments search for a possible mixing of photons with light scalar or pseudo-scalar particles that could also constitute dark matter. Furthermore, annihilation or decay of dark matter can contribute to charged cosmic rays, photons at all energies, and neutrinos. Many existing and future ground-based and satellite experiments are sensitive to such signals. Finally, data from the Large Hadron Collider at CERN are scrutinized for missing energy as a signature of new weakly interacting particles that may be related to dark matter. In this review article we summarize the status of the field with an emphasis on the complementarity between direct detection in dedicated laboratory experiments, indirect detection in the cosmic radiation, and searches at particle accelerators., Comment: 74 pages, 27 figures, to be published in "Progress in Particle and Nuclear Physics" 2015

We study photon-ALP conversion by resonance effects in the magnetized plasma of galaxy clusters and compare the predicted distortion of the cosmic microwave background spectrum in the direction of such objects to measurements of the thermal Sunyaev-Zeldovich effect. Using galaxy cluster models based on current knowledge, we obtain upper limits on the photon-ALP coupling constant $g$ of $\lesssim \mathcal{O}(10^{-11}$ GeV$^{-1}$). The constraints apply to the mass range of $2\cdot 10^{-14}$ eV $ \lesssim m_\text{ALP} \lesssim 3\cdot 10^{-12}$ eV in which resonant photon-ALP conversions can occur. These limits are slightly stronger than current limits, and furthermore provide an independent constraint. We find that a next generation PRISM-like experiment would allow limits down to $g \approx \mathcal{O} (10^{-14}$ GeV$^{-1})$, two orders of magnitude stronger than the currently strongest limits in this mass range., Comment: 18 pages, 5 figures; version published in JCAP

Neutrinos in the cosmic ray flux with energies near 1 EeV and above are detectable with the Surface Detector array of the Pierre Auger Observatory. We report here on searches through Auger data from 1 January 2004 until 20 June 2013. No neutrino candidates were found, yielding a limit to the diffuse flux of ultra-high energy neutrinos that challenges the Waxman-Bahcall bound predictions. Neutrino identification is attempted using the broad time-structure of the signals expected in the SD stations, and is efficiently done for neutrinos of all flavors interacting in the atmosphere at large zenith angles, as well as for "Earth-skimming" neutrino interactions in the case of tau neutrinos. In this paper the searches for downward-going neutrinos in the zenith angle bins $60^\circ-75^\circ$ and $75^\circ-90^\circ$ as well as for upward-going neutrinos, are combined to give a single limit. The $90\%$ C.L. single-flavor limit to the diffuse flux of ultra-high energy neutrinos with an $E^{-2}$ spectrum in the energy range $1.0 \times 10^{17}$ eV - $2.5 \times 10^{19}$ eV is $E_\nu^2 dN_\nu/dE_\nu < 6.4 \times 10^{-9}~ {\rm GeV~ cm^{-2}~ s^{-1}~ sr^{-1}}$., Comment: Replaced with published version. Added journal reference and DOI

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV., Comment: Replaced with published version. Added journal reference and DOI

The propagation of ultra-high energy cosmic rays in extragalactic magnetic fields can be diffusive, depending on the strength and properties of the fields. In some cases the propagation time of the particles can be comparable to the age of the universe, causing a suppression in the flux measured on Earth. In this work we use magnetic field distributions from cosmological simulations to assess the existence of a magnetic horizon at energies around 10$^{18}$ eV., Comment: 4 pages, 2 figures. Proceedings of the Particles and Nuclei International Conference (PANIC 2014)

Solving the question of the origin of ultra-high energy cosmic rays (UHECRs) requires the development of detailed simulation tools in order to interpret the experimental data and draw conclusions on the UHECR universe. CRPropa is a public Monte Carlo code for the galactic and extragalactic propagation of cosmic ray nuclei above $\sim 10^{17}$ eV, as well as their photon and neutrino secondaries. In this contribution the new algorithms and features of CRPropa 3, the next major release, are presented. CRPropa 3 introduces time-dependent scenarios to include cosmic evolution in the presence of cosmic ray deflections in magnetic fields. The usage of high resolution magnetic fields is facilitated by shared memory parallelism, modulated fields and fields with heterogeneous resolution. Galactic propagation is enabled through the implementation of galactic magnetic field models, as well as an efficient forward propagation technique through transformation matrices. To make use of the large Python ecosystem in astrophysics CRPropa 3 can be steered and extended in Python., Comment: 16th International workshop on Advanced Computing and Analysis Techniques in physics research (ACAT 2014) proceedings, 6 pages, 6 figures

We investigate the possibility that the recently detected TeV-PeV neutrino events by IceCube can originate from extragalactic ultra-high-energy cosmic ray interactions with the cosmic microwave background or the UV/optical/IR background. This is done by simulating the propagation of the cosmic rays from their sources to the observer, including the production and propagation of secondary neutrinos and gamma rays. For this purpose we use the publicly available simulation package CRPropa 2.0. We find that in all the scenarios considered here the simulated neutrino flux level remains at least one order of magnitude below the flux level indicated by the IceCube events, thus showing it is difficult to interpret the IceCube events in terms of a cosmogenic neutrino flux., Comment: Rencontres de Moriond EW 2014 proceedings

Ultra-high energy cosmic rays can propagate diffusively in cosmic magnetic fields. When their propagation time is comparable to the age of the universe, a suppression in the flux relative to the case in the absence of magnetic fields will occur. In this work we find an approximate parametrization for this suppression for energies below $\sim$ Z EeV using several magnetic field distributions obtained from cosmological simulations of the magnetized cosmic web. We assume that the magnetic fields have a Kolmogorov power spectrum with the field strengths distributed according to these simulations. We show that, if magnetic fields are coupled to the matter distribution, low field strengths will fill most of the volume, making the suppression milder compared to the case of a constant magnetic field with strength equal to the mean value of this distribution. We also derive upper limits for this suppression to occur for some models of extragalactic magnetic fields, as a function of the coherence length of these fields., Comment: 20 pages, 7 figures