No Arabic abstract
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.
Understanding the cosmic ray (CR) ionization rate is crucial in order to simulate the dynamics of, and interpret the chemical species observed in molecular clouds. Calculating the CR ionization rate requires both accurate knowledge of the spectrum of MeV to GeV protons at the edge of the cloud as well as a model for the propagation of CRs into molecular clouds. Some models for the propagation of CRs in molecular clouds assume the CRs to stream freely along magnetic field lines, while in others they propagate diffusively due to resonant scattering off of magnetic disturbances excited by MHD turbulence present in the medium. We discuss the conditions under which CR diffusion can operate in a molecular cloud, calculate the local CR spectrum and ionization rate in both a free-streaming and diffusive propagation model, and highlight the different results from the two models. We also apply these two models to the propagation through the ISM to obtain the spectrum seen by Voyager 1, and show that such a spectrum favors a diffusive propagation model.
Blazars are potential candidates of cosmic-ray acceleration up to ultrahigh energies ($Egtrsim10^{18}$ eV). For an efficient cosmic-ray injection from blazars, $pgamma$ collisions with the extragalactic background light (EBL) and cosmic microwave background (CMB) can produce neutrino spectrum peaks near PeV and EeV energies, respectively. We analyze the contribution of these neutrinos to the diffuse background measured by the IceCube neutrino observatory. The fraction of neutrino luminosity originating from individual redshift ranges is calculated using the distribution of BL Lacs and FSRQs provided in the textit{Fermi}-LAT 4LAC catalog. Furthermore, we use a luminosity dependent density evolution to find the neutrino flux from unresolved blazars. The results obtained in our model indicate that as much as $approx10%$ of the flux upper bound at a few PeV energies can arise from cosmic-ray interactions on EBL. The same interactions will also produce secondary electrons and photons, initiating electromagnetic cascades. The resultant photon spectrum is limited by the isotropic diffuse $gamma$-ray flux measured between 100 MeV and 820 GeV. The latter, together with the observed cosmic-ray flux at $E>10^{16.5}$ eV, can constrain the baryonic loading factor depending on the maximum cosmic-ray acceleration energy.
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.
We present 1D cosmic ray transport models, numerically solving equations of pure advection and diffusion for the electrons and calculating synchrotron emission spectra. We find that for exponential halo magnetic field distributions advection leads to approximately exponential radio continuum intensity profiles, whereas diffusion leads to profiles that can be better approximated by a Gaussian function. Accordingly, the vertical radio spectral profiles for advection are approximately linear, whereas for diffusion they are of `parabolic shape. We compare our models with deep ATCA observations of two edge-on galaxies, NGC 7090 and 7462, at $lambdalambda$ 22 and 6 cm. Our result is that the cosmic ray transport in NGC 7090 is advection dominated with $V=150^{+80}_{-30}~rm km,s^{-1}$, and that the one in NGC 7462 is diffusion dominated with $D=3.0pm 1.0 times 10^{28}E_{rm GeV}^{0.5}~rm cm^2,s^{-1}$. NGC 7090 has both a thin and thick radio disc with respective magnetic field scale heights of $h_{rm B1}=0.8pm 0.1$ kpc and $h_{rm B2}=4.7pm 1.0$ kpc. NGC 7462 has only a thick radio disc with $h_{rm B2}=3.8pm 1.0$ kpc. In both galaxies, the magnetic field scale heights are significantly smaller than what estimates from energy equipartition would suggest. A non-negligible fraction of cosmic ray electrons can escape from NGC 7090, so that this galaxy is not an electron calorimeter.
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.