Owing to the complexity of turbulent magnetic fields, modelling the diffusion of cosmic rays is challenging. Based on the current understanding of anisotropic magnetohydrodynamic (MHD) turbulence, we use test particles to examine the cosmic rays’ superdiffusion in the direction perpendicular to the mean magnetic field. By changing Alfvén Mach number MA and sonic Mach number MS of compressible MHD simulations, our study covers a wide range of astrophysical conditions including subsonic warm gas phase and supersonic cold molecular gas. We show that freely streaming cosmic rays’ perpendicular displacement increases as 3/2 to the power of the time travelled along local magnetic field lines. This power-law index changes to 3/4 if the parallel propagation is diffusive. We find that the cosmic rays’ parallel mean free path decreases in a power-law relation of $M_\mathrm{ A}^{-2}$ in supersonic turbulence. We investigate the energy fraction of slow, fast, and Alfvénic modes and confirm the dominance of Alfvénic modes in the perpendicular superdiffusion. In particular, the energy fraction of fast mode, which is the main agent for pitch-angle scattering, increases with MA, but is insensitive to MS ≥ 2. Accordingly, our results suggest that the suppressed diffusion in supersonic molecular clouds arises primarily due to the variations of MA instead of MS.
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.
more » « less- Award ID(s):
- 2007323
- NSF-PAR ID:
- 10368106
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 514
- Issue:
- 2
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 2658-2666
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
ABSTRACT -
Abstract 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 $$>5$$ > 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.more » « less
-
more » « less
Abstract We recently extended our Parker-type transport equation for energetic particle interaction with numerous dynamic small-scale magnetic flux ropes (SMFRs) to include perpendicular diffusion in addition to parallel diffusion. We present a new analytical solution to this equation assuming heliocentric spherical geometry with spherical symmetry for all SMFR acceleration mechanisms present in the transport theory. With the goal of identifying the dominant mechanism(s) through which particles are accelerated by SMFRs, a search was launched to identify events behind interplanetary shocks that could be explained by our new solution and not classical diffusive shock acceleration. Two new SMFR acceleration events were identified in situ for the first time within heliocentric distances of 1 astronomical unit (au) in Helios A data. A Metropolis–Hastings algorithm is employed to fit the new solution to the energetic proton fluxes so that the relative strength of the transport coefficients associated with each SMFR acceleration mechanism can be determined. We conclude that the second-order Fermi mechanism for particle acceleration by SMFRs is more important than first-order Fermi acceleration due to the mean compression of the SMFRs regions during these new events. Furthermore, with the aid of SMFR parameters determined via the Grad–Shafranov reconstruction method, we find that second-order Fermi SMFR acceleration is dominated by the turbulent motional electric field parallel to the guide/background field. Finally, successful reproduction of energetic proton flux data during these SMFR acceleration events also required efficient particle escape from the SMFR acceleration regions.
-
Large-scale magnetic fields thread through the electrically conducting matter of the interplanetary and interstellar medium, stellar interiors and other astrophysical plasmas, producing anisotropic flows with regions of high-Reynolds-number turbulence. It is common to encounter turbulent flows structured by a magnetic field with a strength approximately equal to the root-mean-square magnetic fluctuations. In this work, direct numerical simulations of anisotropic magnetohydrodynamic (MHD) turbulence influenced by such a magnetic field are conducted for a series of cases that have identical resolution, and increasing grid sizes up to $2048^3$ . The result is a series of closely comparable simulations at Reynolds numbers ranging from 1400 up to 21 000. We investigate the influence of the Reynolds number from the Lagrangian viewpoint by tracking fluid particles and calculating single-particle and two-particle statistics. The influence of Alfvénic fluctuations and the fundamental anisotropy on the MHD turbulence in these statistics is discussed. Single-particle diffusion curves exhibit mildly superdiffusive behaviours that differ in the direction aligned with the magnetic field and the direction perpendicular to it. Competing alignment processes affect the dispersion of particle pairs, in particular at the beginning of the inertial subrange of time scales. Scalings for relative dispersion, which become clearer in the inertial subrange for a larger Reynolds number, can be observed that are steeper than indicated by the Richardson prediction.more » « less
-
null (Ed.)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.more » « less
