Star formation in galaxies appears to be self-regulated by energetic feedback processes. Among the most promising agents of feedback are cosmic rays (CRs), the relativistic ion population of interstellar and intergalactic plasmas. In these environments, energetic CRs are virtually collisionless and interact via collective phenomena mediated by kinetic-scale plasma waves and large-scale magnetic fields. The enormous separation of kinetic and global astrophysical scales requires a hydrodynamic description. Here, we develop a new macroscopic theory for CR transport in the self-confinement picture, which includes CR diffusion and streaming. The interaction between CRs and electromagnetic fields of Alfvénic turbulence provides the main source of CR scattering, and causes CRs to stream along the magnetic field with the Alfvén velocity if resonant waves are sufficiently energetic. However, numerical simulations struggle to capture this effect with current transport formalisms and adopt regularization schemes to ensure numerical stability. We extent the theory by deriving an equation for the CR momentum density along the mean magnetic field and include a transport equation for the Alfvén-wave energy. We account for energy exchange of CRs and Alfvén waves via the gyroresonant instability and include other wave damping mechanisms. Using numerical simulations we demonstrate that our new theory enables stable, self-regulated CR transport. The theory is coupled to magneto-hydrodynamics, conserves the total energy and momentum, and correctly recovers previous macroscopic CR transport formalisms in the steady-state flux limit. Because it is free of tunable parameters, it holds the promise to provide predictable simulations of CR feedback in galaxy formation.1 The Legendre polynomials are eigenfunctions of the pitch-angle Laplace operator ∂ t f | scatt = ∂ µ [ν(1 − µ 2 )/2 ∂ µ f ]. This operator describes pitch-angle diffusion and ν denotes the scattering frequency. Note that this simple Laplacian resembles the actual scattering operator as discussed in equation (51).
Cosmic-ray-driven (CR-driven) instabilities play a decisive role during particle acceleration at shocks and CR propagation in galaxies and galaxy clusters. These instabilities amplify magnetic fields and modulate CR transport so that the intrinsically collisionless CR population is tightly coupled to the thermal plasma and provides dynamical feedback. Here, we show that CRs with a finite pitch angle drive electromagnetic waves (along the background magnetic field) unstable on intermediate scales between the gyroradii of CR ions and electrons as long as CRs are drifting with a velocity less than half of the Alfvén speed of electrons. By solving the linear dispersion relation, we show that this new instability typically grows faster by more than an order of magnitude in comparison to the commonly discussed resonant instability at the ion gyroscale. We find the growth rate for this intermediate-scale instability and identify the growing modes as background ion-cyclotron modes in the frame that is comoving with the CRs. We confirm the theoretical growth rate with a particle-in-cell simulation and study the nonlinear saturation of this instability. We identify three important astrophysical applications of this intermediate-scale instability, which is expected to (1) modulate CR transport and strengthen CR feedback in galaxies and galaxy clusters, (2) enable electron injection into the diffusive shock acceleration process, and (3) decelerate CR escape from the sites of particle acceleration, which would generate gamma-ray halos surrounding CR sources such as supernova remnants.
Recent observations with the MeerKAT radio telescope reveal a unique population of faint nonthermal filaments pervading the central molecular zone (CMZ). Some of those filaments are organized into groups of almost parallel filaments, seemingly sorted by their length, so that their morphology resembles a harp with radio emitting "strings". We argue that the synchrotron emitting GeV electrons of these radio harps have been consecutively injected by the same source (a massive star or pulsar) into spatially intermittent magnetic fiber bundles within a magnetic flux tube or via time-dependent injection events. After escaping from this source, the propagation of cosmic ray (CR) electrons inside a flux tube is governed by the theory of CR transport. We propose to use observations of radio harp filaments to gain insight into the specifics of CR propagation along magnetic fields of which there are two principle modes: CRs could either stream with self-excited magneto-hydrodynamical waves or diffuse along the magnetic field. To disentangle these possibilities, we conduct hydrodynamical simulations of either purely diffusing or streaming CR electrons and compare the resulting brightness distributions to the observed synchrotron profiles of the radio harps. We find compelling evidence that CR streaming is the dominant propagation mode for GeV CRs in one of the radio harps. Observations at higher angular resolution should detect more radio harps and may help to disentangle projection effects of the possibly three-dimensional flux-tube structure of the other radio harps.
We present a new numerical algorithm to solve the recently derived equations of two-moment cosmic ray hydrodynamics (CRHD). The algorithm is implemented as a module in the moving mesh Arepo code. Therein, the anisotropic transport of cosmic rays (CRs) along magnetic field lines is discretised using a path-conservative finite volume method on the unstructured time-dependent Voronoi mesh of Arepo. The interaction of CRs and gyroresonant Alfvén waves is described by short-timescale source terms in the CRHD equations. We employ a custom-made semi-implicit adaptive time stepping source term integrator to accurately integrate this interaction on the small light-crossing time of the anisotropic transport step. Both the transport and the source term integration step are separated from the evolution of the magneto-hydrodynamical equations using an operator split approach. The new algorithm is tested with a variety of test problems, including shock tubes, a perpendicular magnetised discontinuity, the hydrodynamic response to a CR overpressure, CR acceleration of a warm cloud, and a CR blast wave, which demonstrate that the coupling between CR and magneto-hydrodynamics is robust and accurate. We demonstrate the numerical convergence of the presented scheme using new linear and non-linear analytic solutions.
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