ABSTRACT
Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in ...cosmic ray transport. The transition from a ballistic to a diffusive-propagation regime is presented in direct numerical calculations of diffusion coefficients for homogeneous magnetic field lines subject to turbulent perturbations. Simulation results are compared with theoretical derivations of the parallel diffusion coefficient’s dependences on the energy and the fluctuation amplitudes in the limit of weak turbulence. The present study shows that the widely used extrapolation of the energy scaling for the parallel diffusion coefficient to high turbulence levels predicted by quasi-linear theory does not provide a universally accurate description in the resonant-scattering regime. It is highlighted here that the numerically calculated diffusion coefficients can be polluted for low energies due to missing resonant interaction possibilities of the particles with the turbulence. Five reduced-rigidity regimes are established, which are separated by analytical boundaries derived in this work. Consequently, a proper description of cosmic ray propagation can only be achieved by using a turbulence-level-dependent diffusion coefficient and can contribute to solving the Galactic cosmic ray gradient problem.
ABSTRACT We present a systematic study of non-thermal electron-proton plasma and its emission processes in starburst galaxies in order to explain the correlation between the luminosity in the radio ...band and the recently observed gamma luminosity. In doing so, a steady state description of the cosmic-ray (CR) electrons and protons within the spatially homogeneous starburst is considered where continuous momentum losses are included as well as catastrophic losses due to diffusion and advection. The primary source of the relativistic CRs, e.g., supernova remnants, provides a quasi-neutral plasma with a power-law spectrum in momentum where we account for rigidity-dependent differences between the electron and proton spectrum. We examine the resulting leptonic and hadronic radiation processes by synchrotron radiation, inverse Compton scattering, Bremsstrahlung, and hadronic pion production. Finally, the observations of NGC 253, M82, NGC 4945, and NGC 1068 in the radio and gamma-ray bands as well as the observed supernova rate are used to constrain a best-fit model. In the case of NGC 253, M82, and NGC 4945 our model is able to accurately describe the data, showing that: (i) supernovae are the dominant particle accelerators for NGC 253, M82, and NGC 4945, but not for NGC 1068; (ii) all considered starburst galaxies are poor proton calorimeters in which for NGC 253 the escape is predominantly driven by the galactic wind, whereas the diffusive escape dominates in NGC 4945 and M82 (at energies >1 TeV); and (iii) secondary electrons from hadronic pion production are important to model the radio flux, but the associated neutrino flux is below the current observation limit.
Context.
Cosmic-ray propagation is strongly dependent on the large-scale configuration of the Galactic magnetic field. In particular, the Galactic center region provides highly interesting cosmic-ray ...data from gamma-ray maps and it is clear that a large fraction of the cosmic rays detected at Earth originate in this region of the Galaxy. Yet because of confusion from line-of-sight integration, the magnetic field structure in the Galactic center is not well known and no large-scale magnetic field model exists at present.
Aims.
In this paper, we develop a magnetic field model, derived from observational data on the diffuse gas, nonthermal radio filaments, and molecular clouds.
Methods.
We derive an analytical description of the magnetic field structure in the central molecular zone by combining observational data with the theoretical modeling of the basic properties of magnetic fields.
Results.
We provide a first description of the large-scale magnetic field in the Galactic center region. We present first test simulations of cosmic-ray propagation and the impact of the magnetic field structure on the cosmic-ray distribution in the three dimensions.
Conclusions.
Our magnetic field model is able to describe the main features of polarization maps; it is particularly important to note that they are significantly better than standard global Galactic magnetic field models. It can also be used to model cosmic-ray propagation in the Galactic center region more accurately.
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Abstract The very high energy (VHE) emission of the central molecular zone (CMZ) is rarely modeled in 3D. Most approaches describe the morphology in 1D or simplify the diffusion to the isotropic ...case. In this work, we show the impact of a realistic 3D magnetic field configuration and gas distribution on the VHE γ -ray distribution of the CMZ. We solve the 3D cosmic-ray transport equation with an anisotropic diffusion tensor using the approach of stochastic differential equations as implemented in the CRPropa framework. We test two different source distributions for five different anisotropies of the diffusion tensor, covering the range of effectively fieldline-parallel diffusion to isotropic diffusion. Within the tested magnetic field configuration, the anisotropy of the diffusion tensor is close to the isotropic case, and three point sources within the CMZ are favored. Future missions such as the upcoming CTA will reveal more small-scale structures that are not yet included in the model. Therefore, a more detailed 3D gas distribution and magnetic field structure will be needed.
Cosmic-ray transport in astrophysical environments is often dominated by the diffusion of particles in a magnetic field composed of both a turbulent and a mean component. This process, which is ...two-fold turbulent mixing in that the particle motion is stochastic with respect to the field lines, needs to be understood in order to properly model cosmic-ray signatures. One of the most important aspects in the modeling of cosmic-ray diffusion is that fully resonant scattering, the most effective such process, is only possible if the wave spectrum covers the entire range of propagation angles. By taking the wave spectrum boundaries into account, we quantify cosmic-ray diffusion parallel and perpendicular to the guide field direction at turbulence levels above 5% of the total magnetic field. We apply our results of the parallel and perpendicular diffusion coefficient to the Milky Way. We show that simple purely diffusive transport is in conflict with observations of the inner Galaxy, but that just by taking a Galactic wind into account, data can be matched in the central 5 kpc zone. Further comparison shows that the outer Galaxy at
>
5
kpc, on the other hand, should be dominated by perpendicular diffusion, likely changing to parallel diffusion at the outermost radii of the Milky Way.
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 the case of discretely defined ...magnetic fields, typically given on a homogeneous grid structure. However, the interpolation method influences the magnetic field properties and, therefore, also the propagation of particles through these fields. To determine the resulting error, we compare three different interpolation routines-trilinear, tricubic, and nearest neighbor interpolation-in the case of isotropic, turbulent magnetic fields. First, we analyze the impact of the different interpolation methods on the root mean square field strength, the divergence, and the spectrum of the turbulent magnetic field. Here, the nearest neighbor interpolation shows some clear benefits compared with the trilinear method; however, that changes significantly if we consider the particle propagation. In principle, a better interpolation method also yields a better description of the particle transport. In the case of field line random walk, it is shown that none of these methods, especially not the nearest neighbor interpolation, is able to yield an accurate description of the diffusion coefficient, exposing the need for a continuous, grid-less turbulent magnetic field. We optimize the performance of an algorithm that generates such a magnetic field by more than an order of magnitude. Further, the necessary number of wave-modes is determined, so that this continuous method supports realistic simulations over a larger energy range without limitations by the available memory.
The recent detection of possible neutrino emission from the blazar TXS 0506+056 was the first high-energy neutrino associated with an astrophysical source, making this special type of active galaxies ...a promising neutrino emitter. The fact that two distinct episodes of neutrino emission were detected with a separation of around 3 yr raises the possibility that emission could be periodic. Periodic emission is expected from supermassive binary black hole systems due to jet precession close to the binary's merger. Here, we show that, if TXS 0506+056 is a binary source, then the next neutrino flare could already have occurred, possibly still hidden in IceCube's not-yet-analyzed data. We derive the binary properties that would lead to the detection of gravitational waves from this system by the Laser Interferometer Space Antenna (LISA) over the next decade. Our results for the first time quantify the timescale of these correlations for the example of TXS 0506+056, connecting the possible neutrino and gravitational-wave signatures of such sources.
ABSTRACT
Understanding the time-scales for diffusive processes and their degree of anisotropy is essential for modelling cosmic ray transport in turbulent magnetic fields. We show that the diffusion ...time-scales are isotropic over a large range of energy and turbulence levels, notwithstanding the high degree of anisotropy exhibited by the components of the diffusion tensor for cases with an ordered magnetic field component. The predictive power of the classical scattering relation as a description for the relation between the parallel and perpendicular diffusion coefficients is discussed and compared to numerical simulations. Very good agreement for a large parameter space is found, transforming classical scattering relation predictions into a computational prescription for the perpendicular component. We discuss and compare these findings, in particular, the time-scales to become diffusive with the time-scales that particles reside in astronomical environments, the so-called escape time-scales. The results show that, especially at high energies, the escape times obtained from diffusion coefficients may exceed the time-scales required for diffusion. In these cases, the escape time cannot be determined by the diffusion coefficients.
Abstract
Motivated by cosmic ray (CR) re-acceleration at a potential Galactic Wind Termination
Shock (GWTS), we present a numerical model for time-dependent Diffusive Shock Acceleration (DSA). We use ...the stochastic differential equation solver (DiffusionSDE) of the cosmic ray
propagation framework CRPropa3.2 with two modifications: An importance sampling module is
introduced to improve statistics at high energies in order to keep the simulation time short. An
adaptive time step is implemented in the DiffusionSDE module. This ensures to efficiently meet
constraints on the time and diffusion step, which is crucial to obtain the correct shock spectra.
The time evolution of the spectrum at a one-dimensional planar shock is verified against the
solution obtained by the grid-based solver VLUGR3 for both energy-independent and energy-dependent
diffusion. We show that the injection of pre-accelerated particles can lead to a broken power law
spectrum in momentum if the incoming spectrum of CRs is harder than the re-accelerated
spectrum. If the injected spectrum is steeper, the shock spectrum dominates at all energies. We
finally apply the developed model to the GWTS by considering a spherically symmetric shock, a
spiral Galactic magnetic field, and anisotropic diffusion. The time-dependent spectrum at the
shock is modeled as a basis for further studies.
Abstract
In astrophysics, the search for sources of the highest-energy cosmic rays continues. For further progress, not only ever better observatories but also ever more realistic numerical ...simulations are needed. We compare different approaches for numerical test simulations of ultra-high-energy cosmic rays in the intergalactic magnetic field and show that all methods provide correct statistical propagation characteristics of the particles in means of their diffusive behaviour. Through convergence tests, we show that the necessary requirements for the methods differ and ultimately reveal significant differences in the required simulation time.
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