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Register a new userInterpolation of turbulent magnetic fields and its consequences on diffusive cosmic ray propagation
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Numerical simulations of the propagation of charged particles through magnetic fields solving the equation of motion often leads to the usage of an interpolation in case of discretely defined magnetic fields, typically given on a homogeneous grid structure. However, the interpolation method influences the magnetic field properties on the scales of the grid spacing and the choice of interpolation routine can therefore change the result. At the same time, it provides an impact, i.e. error, on the spatial particle distribution. We compare three different interpolation routines -- trilinear, tricubic and nearest neighbor interpolation -- in the case of turbulent magnetic fields and show that there is no benefit in using trilinear interpolation. We show that in comparison, the nearest neighbor interpolation provides the best performance, i.e. requires least CPU time and results in the smallest error. In addition, we optimize the performance of an algorithm that generates a continuous grid-less turbulent magnetic field by more than an order of magnitude. This continuous method becomes practicable for the simulation of large particle numbers and its accuracy is only limited by the used number of wave-modes. We show that by using more than 100 wave-modes the diffusive behavior of the spatial particle distribution in form of the diffusion coefficient is determined with an error less than a few percentage.
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The detection of a PeV high-energy neutrino of astrophysical origin, observed by the IceCube Collaboration and correlated with a 3$sigma$ significance with Fermi measurements to the gamma-ray blazar TXS 0506+056, further stimulated the discussion on the production channels of high-energy particles in blazars. Many models also consider a hadronic component that would not only contribute to the emission of electromagnetic radiation in blazars but also lead to the production of secondary high-energy neutrinos and gamma-rays. Relativistic and compact plasma structures, so-called plasmoids, have been discussed in such flares to be moving along the jet axis. The frequently used assumption in such models that diffusive transport can describe particles in jet plasmoids is investigated in the present contribution. While the transport in the stationary scenario is diffusive for most of the parameter space, a flaring scenario is always accompanied by a non-diffusive phase in the beginning. In this paper, we present those conditions that determine the time scale to reach the diffusion phase as a function of the model parameters in the jet. We show that the type of the charged-particle transport, diffusive or ballistic, has a large influence on many observables, including the spectral energy distribution of blazars.
(Abridged) Recent results from the Pierre Auger Observatory (PAO) indicate that the composition of ultra-high-energy cosmic rays (UHECRs) with energies above $10^{19}$ eV may be dominated by heavy nuclei. An important question is whether the distribution of arrival directions for such UHECR nuclei can exhibit observable anisotropy or positional correlations with their astrophysical source objects despite the expected strong deflections by intervening magnetic fields. For this purpose, we have simulated the propagation of UHECR nuclei including models for both the extragalactic magnetic field and the Galactic magnetic field. Assuming that only iron nuclei are injected steadily from sources with equal luminosity and spatially distributed according to the observed large scale structure in the local Universe, at the number of events published by the PAO so far, the arrival distribution of UHECRs would be consistent with no auto-correlation at 95% confidence if the mean number density of UHECR sources $n_s >~ 10^{-6}$ Mpc$^{-3}$, and consistent with no cross-correlation with sources within 95% errors for $n_s >~ 10^{-5}$ Mpc$^{-3}$. On the other hand, with 1000 events above $5.5 times 10^{19}$ eV in the whole sky, next generation experiments can reveal auto-correlation with more than 99% probability even for $n_s <~ 10^{-3}$ Mpc$^{-3}$, and cross-correlation with sources with more than 99% probability for $n_s <~ 10^{-4}$ Mpc$^{-3}$. In addition, we find that the contribution of Centaurus A is required to reproduce the currently observed UHECR excess in the Centaurus region. Secondary protons generated by photodisintegration of primary heavy nuclei during propagation play a crucial role in all cases, and the resulting anisotropy at small angular scales should provide a strong hint of the source location if the maximum energies of the heavy nuclei are sufficiently high.
We review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker-Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of magneto-hydrodynamic (MHD) equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming well as adiabatic compression and several radiative loss mechanisms. We discuss applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium.
The masses of clusters of galaxies estimated by gravitational lensing exceed in many cases the mass estimates based on hydrostatic equilibrium. This may suggest the existence of nonthermal pressure. We ask if radio galaxies can heat and support the cluster gas with injected cosmic ray protons and magnetic field densities, which are permitted by Faraday rotation and gamma ray observations of clusters of galaxies. We conclude that they are powerful enough to do this within a cluster radius of roughly 1 Mpc. If present, nonthermal pressures could lead to a revised estimate of the ratio of baryonic mass to total mass, and the apparent baryonic overdensity in clusters would disappear. In consequence, $Omega_{rm cold}$, the clumping part of the cosmological density $Omega_{o}$, would be larger than $0.4,h_{50}^{-1/2}$.
Cosmic ray (CR) currents through magnetised plasma drive strong instabilities producing amplification of the magnetic field. This amplification helps explain the CR energy spectrum as well as observations of supernova remnants and radio galaxy hot spots. Using magnetohydrodynamic (MHD) simulations, we study the behaviour of the non-resonant hybrid (NRH) instability (also known as the Bell instability) in the case of CR currents perpendicular and parallel to the initial magnetic field. We demonstrate that extending simulations of the perpendicular case to 3D reveals a different character to the turbulence from that observed in 2D. Despite these differences, in 3D the perpendicular NRH instability still grows exponentially far into the non-linear regime with a similar growth rate to both the 2D perpendicular and 3D parallel situations. We introduce some simple analytical models to elucidate the physical behaviour, using them to demonstrate that the transition to the non-linear regime is governed by the growth of thermal pressure inside dense filaments at the edges of the expanding loops. We discuss our results in the context of supernova remnants and jets in radio galaxies. Our work shows that the NRH instability can amplify magnetic fields to many times their initial value in parallel and perpendicular shocks.
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