Efficient acceleration of cosmic rays (via the mechanism of diffusive shock acceleration) requires turbulent, amplified magnetic fields in the shock's upstream region. We present results of multidimensional particle-in-cell simulations aimed at observing the magnetic field amplification that is expected to arise from the cosmic-ray current ahead of the shock, and the impact on the properties of the upstream interstellar medium. We find that the initial structure and peak strength of the amplified field is somewhat sensitive to the choice of parameters, but that the field growth saturates in a similar manner in all cases: the back-reaction on the cosmic rays leads to modification of their rest-frame distribution and also a net transfer of momentum to the interstellar medium, substantially weakening their relative drift while also implying the development of a modified shock. The upstream medium becomes turbulent, with significant spatial fluctuations in density and velocity, the latter in particular leading to moderate upstream heating; such fluctuations will also have a strong influence on the shock structure.
Large-scale galactic winds driven by stellar feedback are one phenomenon that influences the dynamical and chemical evolution of a galaxy, redistributing material throughout the circumgalatic medium. Non-thermal feedback from galactic cosmic rays (CRs) -high-energy charged particles accelerated in supernovae and young stars - can impact the efficiency of wind driving. The streaming instability limits the speed at which they can escape. However, in the presence of turbulence, the streaming instability is subject to suppression that depends on the magnetization of turbulence given by its Alfvén …
Using a multi-fluid approach, we investigate streaming and thermal instabilities of the electron-ion plasma with homogeneous cold cosmic rays propagating perpendicular to the background magnetic field. Perturbations are considered to be also across the magnetic field. The back-reaction of cosmic rays resulting in strong streaming instabilities is taken into account. It is shown that for sufficiently short wavelength perturbations, the growth rates can exceed the growth rate of cosmic-ray streaming instability along the magnetic field found by Nekrasov & Shadmehri (2012), which is in its turn c…
We examine the effects of streaming cosmic rays upstream of a strong, parallel collisionless shock. We include explicitly the inertia of the cosmic rays in our analysis, which was neglected in previous work. For parameters relevant to the acceleration of cosmic rays at a supernova blast wave, we find no MHD fluid instability that would lead to the amplification of the magnetic field above that given by the compression at the shock. We show how to recover, from our own analysis, the cosmic-ray-driven MHD fluid instability found by previous authors. We conclude that including the inertia and dyn…
A new nonthermal phenomenon caused by streaming cosmic rays (CRs) in the universe is proposed. The streaming CRs drive the return current of thermal electrons to compensate for the CR current. Then, electric fields are induced by the resistivity of the return current. It is shown that the resistive electric fields can accelerate secondary electrons generated by the streaming CRs. This is the self-discharge by streaming CRs. In this work, the self-discharge condition and the condition for runaway acceleration of secondary electrons are presented. The self-discharge makes high-energy secondary e…
We demonstrate that cosmic rays form filamentary structures in the precursors of supernova remnant shocks due to their self-generated magnetic fields. The cosmic-ray filamentation results in the growth of a long wavelength instability, and naturally couples the rapid non-linear amplification on small scales to larger length scales. Hybrid magnetohydrodynamics--particle simulations are performed to confirm the effect. The resulting large scale magnetic field may facilitate the scattering of high energy cosmic rays as required to accelerate protons beyond the knee in the cosmic-ray spectrum at s…
We study the streaming instability of GeV$-100~$GeV cosmic rays (CRs) and its damping in the turbulent interstellar medium (ISM). We find that the damping of streaming instability is dominated by ion-neutral collisional damping in weakly ionized molecular clouds, turbulent damping in the highly ionized warm medium, and nonlinear Landau damping in the Galactic halo. Only in the Galactic halo, is the streaming speed of CRs close to the Alfvén speed. Alfvénic turbulence plays an important role in both suppressing the streaming instability and regulating the diffusion of streaming CRs via magnetic…
Using the multi-fluid approach, we investigate streaming and thermal instabilities of the electron-ion plasma with homogeneous cold cosmic rays drifting perpendicular to the background magnetic field. Perturbations across the magnetic field are considered. The back-reaction of cosmic rays resulting in the streaming instability is taken into account. The thermal instability is shown not to be subject to the action of cosmic rays in the model under consideration. The dispersion relation for the thermal instability has been derived which includes sound velocities of plasma and cosmic rays, Alfvén…
The cosmic rays non-resonant streaming instability is believed to be the source of substantial magnetic field amplification. In this work we investigate the effects of the ambient plasma temperature on the instability and derive analytical expressions of its growth rate in the hot, demagnetized regime of interaction. To study its non-linear evolution we perform hybrid-PIC simulations for a wide range of temperatures. We find that in the cold limit about two-thirds of the cosmic rays drift kinetic energy is converted into magnetic energy. Increasing the temperature of the ambient plasma can sub…
Subsonic, compressive turbulence transfers energy to cosmic rays (CRs), a process known as non-resonant reacceleration. It is often invoked to explain observed ratios of primary to secondary CRs at $\sim \rm GeV$ energies, assuming wholly diffusive CR transport. However, such estimates ignore the impact of CR self-confinement and streaming. We study these issues in stirring box magnetohydrodynamic (MHD) simulations using Athena++, with field-aligned diffusive and streaming CR transport. For diffusion only, we find CR reacceleration rates in good agreement with analytic predictions. When stream…
It is recently proposed that cosmic rays generate a seed magnetic field in the early universe. In this paper, we propose another generation mechanism of magnetic fields by cosmic rays, which is the Biermann battery driven by resistive heating induced by the streaming of cosmic rays. This mechanism is dominant in small-scale, low-temperature, and strongly-ionized regions, compared with other previously proposed mechanisms. Because cosmic rays are expected to be accelerated after the death of the first stars, this mechanism can work during structure formation in the early universe. We show that …
Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs and demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M_A^4 dependence.…
The observed bimodality in radio luminosity in galaxy clusters is puzzling. We investigate the possibility that cosmic-ray (CR) streaming in the intra-cluster medium can 'switch off' hadronically induced radio and gamma-ray emission. For self-confined CRs, this depends on the source of MHD wave damping: if only non-linear Landau damping operates, then CRs stream on the slow Alfvenic timescale, but if turbulent wave damping operates, super-Alfvenic streaming is possible. As turbulence increases, it promotes outward streaming more than it enables inward turbulent advection. Curiously, the CR flu…
Galactic outflows play an important role in galactic evolution. Despite their importance, a detailed understanding of the physical mechanisms responsible for the driving of these winds is lacking. In an effort to gain more insight into the nature of these flows, we perform global three-dimensional magneto-hydrodynamical simulations of an isolated Milky Way-size starburst galaxy. We focus on the dynamical role of cosmic rays injected by supernovae, and specifically on the impact of the streaming and anisotropic diffusion of cosmic rays along the magnetic fields. We find that these microphysical…
High-energy gamma ray emission has been detected recently from supernovae remnants (SNRs) and their surroundings. The existence of molecular clouds near some of the SNRs suggests that the gamma rays originate predominantly from p-p interactions with cosmic rays accelerated at a closeby SNR shock wave. Here we investigate the acceleration of cosmic rays and the gamma ray production in the cloud self-consistently by taking into account the interactions of the streaming instability and the background turbulence both at the shock front and in the ensuing propagation to the clouds. We focus on the …
Cosmic rays (CRs) are thought to play a dynamically important role in several key aspects of galaxy evolution, including the structure of the interstellar medium, the formation of galactic winds, and the non-thermal pressure support of halos. We introduce a numerical model solving for the CR streaming instability and acceleration of CRs at shocks with a fluid approach in the adaptive mesh refinement code ramses. CR streaming is solved with a diffusion approach and its anisotropic nature is naturally captured. We introduce a shock finder for the ramses code that automatically detects shock disc…
We use analytic calculations and time-dependent spherically-symmetric simulations to study the properties of isothermal galactic winds driven by cosmic-rays (CRs) streaming at the Alfvén velocity. The simulations produce time-dependent flows permeated by strong shocks; we identify a new linear instability of sound waves that sources these shocks. The shocks substantially modify the wind dynamics, invalidating previous steady state models: the CR pressure $p_c$ has a staircase-like structure with $dp_c/dr \simeq 0$ in most of the volume, and the time-averaged CR energetics are in many cases bet…
Heating of virialized gas by streaming cosmic rays (CRs) may be energetically important in galaxy halos, groups and clusters. We present a linear thermal stability analysis of plasmas heated by streaming CRs. We separately treat equilibria with and without background gradients, and with and without gravity. We include both CR streaming and diffusion along the magnetic-field direction. Thermal stability depends strongly on the ratio of CR pressure to gas pressure, which determines whether modes are isobaric or isochoric. Modes with $\mathbf{k \cdot B }\neq 0$ are strongly affected by CR diffusi…
We obtain the angular distribution of the cosmic rays reaching an observer from an individual source and after propagation through a turbulent magnetic field, for different ratios between the source distance and the diffusion length. We study both the high-energy quasi-rectilinear regime as well as the transition towards the diffusive regime at lower energies where the deflections become large. We consider the impact of energy losses, showing that they tend to enhance the anisotropy of the source at a given energy. We also discuss lensing effects, in particular those that could result from the…
We investigate the streaming and thermal instabilities of the electron-ion plasma with homogeneous cold cosmic rays drifting perpendicular to the background magnetic field in the multi-fluid approach. One-dimensional perturbations along the magnetic field are considered. The induced return current of the background plasma and back-reaction of cosmic rays are taken into account. It is shown that the cosmic ray back-reaction results in the streaming instability having considerably larger growth rates than that due to the return current of the background plasma. This increase is by a factor of th…
How and where cosmic rays are produced, and how they diffuse through various turbulent media, represent fundamental problems in astrophysics with far reaching implications, both in terms of our theoretical understanding of high-energy processes in the Milky Way and beyond, and the successful interpretation of space-based and ground based GeV and TeV observations. For example, recent and ongoing detections, e.g., by Fermi (in space) and HESS (in Namibia), of $γ$-rays produced in regions of dense molecular gas hold important clues for both processes. In this paper, we carry out a comprehensive n…
This paper considers turbulent damping of Alfven waves in magnetized plasmas. We identify two cases of damping, one related to damping of cosmic rays streaming instability, the other related to damping of Alfven waves emitted by a macroscopic wave source, e.g. stellar atmosphere. The physical difference between the two cases is that in the former case the generated waves are emitted in respect to the local direction of magnetic field, in the latter in respect to the mean field. The scaling of damping is different in the two cases. We the regimes of turbulence ranging from subAlfvenic to superA…
External cosmic rays impinging upon circumstellar disks associated with young stellar objects provide an important source of ionization, and as such, play an important role in disk evolution and planet formation. However, these incoming cosmic rays are affected by a variety of physical processes internal to stellar/disk systems, including modulation by turbulent magnetic fields. Globally, these fields naturally provide both a funneling effect, where cosmic rays from larger volumes are focused into the disk region, and a magnetic mirroring effect, where cosmic rays are repelled due to the incre…
The propagation of cosmic rays (CRs) in turbulent interstellar magnetic fields is typically described as a spatial diffusion process. This formalism predicts only a small deviation from an isotropic CR distribution in the form of a dipole in the direction of the CR density gradient or relative background flow. We show that the existence of a global CR dipole moment necessarily generates a spectrum of higher multipole moments in the local CR distribution. These "anomalous" anisotropies are a direct consequence of Liouville's theorem in the presence of a local turbulent magnetic field. We show t…
Cosmic rays (CRs) are a dynamically important component of the interstellar medium (ISM) of galaxies. The $\sim$GeV CRs that carry most CR energy and pressure are likely confined by self-generated turbulence, leading them to stream along magnetic field lines at the ion Alfvén speed. However, the consequences of self-confinement for CR propagation on galaxy scales remain highly uncertain. In this paper, we use a large ensemble of magnetohydrodynamical turbulence simulations to quantify how the basic parameters describing ISM turbulence -- the sonic Mach number, $\mathcal{M}$ (plasma compressibi…
We investigate the diffusion of cosmic rays (CR) close to their sources. Propagating individual CRs in purely isotropic turbulent magnetic fields with maximal scale of spatial variations Lmax, we find that CRs diffuse anisotropically at distances r <~ Lmax from their sources. As a result, the CR densities around the sources are strongly irregular and show filamentary structures. We determine the transition time t* to standard diffusion as t* ~ 10^4 yr (Lmax/150 pc)^b (E/PeV)^(-g) (Brms/4 muG)^g, with b ~ 2 and g = 0.25-0.5 for a turbulent field with Kolmogorov power spectrum. We calculate the …
Cosmic rays (CRs) may be used to infer properties of intervening cosmic magnetic fields. Conversely, understanding the effects of magnetic fields on the propagation of high-energy CRs is crucial to elucidate their origin. In the present work we investigate the role of intracluster magnetic fields on the propagation of CRs with energies between $10^{16}$ and $10^{18.5}$ eV. We look for possible signatures of a transition in the CR propagation regime, from diffusive to ballistic. Finally, we discuss the consequences of the confinement of high-energy CRs in clusters and superclusters for the prod…
Cosmic ray anisotropy has been observed in a wide energy range and at different angular scales by a variety of experiments over the past decade. However, no comprehensive or satisfactory explanation has been put forth to date. The arrival distribution of cosmic rays at Earth is the convolution of the distribution of their sources and of the effects of geometry and properties of the magnetic field through which particles propagate. It is generally believed that the anisotropy topology at the largest angular scale is adiabatically shaped by diffusion in the structured interstellar magnetic field…
I conduct simple analytical estimates and conclude that mixing by vortices is a more efficient process to transfer the cosmic ray energy of jet-inflated bubbles to the intracluster medium (ICM) than streaming of cosmic rays along magnetic field lines. Jets and the bubbles they inflate transfer heat to the ambient gas in cooling flows in cluster of galaxies and in galaxies. The internal energy of the jet-inflated bubbles is dominate by very hot thermal gas and/or cosmic rays. Cosmic rays that stream along magnetic field lines that connect the bubbles with the ICM heat the ICM as their energy is…
The equation governing the streaming of a quantity down its gradient superficially looks similar to the simple constant velocity advection equation. In fact, it is the same as an advection equation if there are no local extrema in the computational domain or at the boundary. However, in general when there are local extrema in the computational domain it is a non-trivial nonlinear equation. The standard upwind time evolution with a CFL-limited time step results in spurious oscillations at the grid scale. These oscillations, which originate at the extrema, propagate throughout the computational …
We investigate the damping of Alfvén waves generated by the cosmic ray resonant streaming instability in the context of the cosmic ray escape and propagation in the proximity of supernova remnants. We consider ion-neutral damping, turbulent damping and non linear Landau damping in the warm ionized and warm neutral phases of the interstellar medium. For the ion-neutral damping, up-to-date damping coefficients are used. We investigate in particular whether the self-confinement of cosmic rays nearby sources can appreciably affect the grammage. We show that the ion-neutral damping and the turbulen…
We constrain the energy at which the transition from Galactic to extragalactic cosmic rays occurs by computing the anisotropy at Earth of cosmic rays emitted by Galactic sources. Since the diffusion approximation starts to loose its validity for E/Z >~ 10^(16-17) eV, we propagate individual cosmic rays (CRs) using Galactic magnetic field models and taking into account both their regular and turbulent components. The turbulent field is generated on a nested grid which allows spatial resolution down to fractions of a parsec. Assuming sufficiently frequent Galactic CR sources, the dipole amplitud…
Recent studies have found that cosmic ray transport plays an important role in feedback processes such as star formation and the launching of galactic winds. Although cosmic ray buoyancy is widely held to be a destabilizing force in galactic disks, the effect of cosmic ray transport on the stability of stratified systems has yet to be analyzed. We perform a stability analysis of a stratified layer for three different cosmic ray transport models: decoupled (Classic Parker), coupled with $γ_c=4/3$ but not streaming (Modified Parker), and finally coupled with streaming at the Alfvén speed. When t…
This paper deals with the cosmic-ray penetration into molecular clouds and with the related gamma--ray emission. High energy cosmic rays interact with the dense gas and produce neutral pions which in turn decay into two gamma rays. This makes molecular clouds potential sources of gamma rays, especially if they are located in the vicinity of a powerful accelerator that injects cosmic rays in the interstellar medium. The amplitude and duration in time of the cosmic--ray overdensity around a given source depend on how quickly cosmic rays diffuse in the turbulent galactic magnetic field. For these…
The hot, X-ray-emitting intracluster medium (ICM) is the dominant baryonic constituent of clusters of galaxies. In the cores of many clusters, radiative energy losses from the ICM occur on timescales significantly shorter than the age of the system. Unchecked, this cooling would lead to massive accumulations of cold gas and vigorous star formation, in contradiction to observations. Various sources of energy capable of compensating these cooling losses have been proposed, the most promising being heating by the supermassive black holes in the central galaxies through inflation of bubbles of rel…
Cosmic rays are thought to escape their sources streaming along the local magnetic field lines. We show that this phenomenon generally leads to the excitation of both resonant and non-resonant streaming instabilities. The self-generated magnetic fluctuations induce particle diffusion in extended regions around the source, so that cosmic rays build up a large pressure gradient. By means of two-dimensional (2D) and three-dimensional (3D) hybrid particle-in-cell simulations, we show that such a pressure gradient excavates a cavity around the source and leads to the formation of a cosmic-ray domin…
The propagation of high-energy cosmic rays through giant molecular clouds constitutes a fundamental process in astronomy and astrophysics. The diffusion of cosmic-rays through these magnetically turbulent environments is often studied through the use of energy-dependent diffusion coefficients, although these are not always well motivated theoretically. Now, however, it is feasible to perform detailed numerical simulations of the diffusion process computationally. While the general problem depends upon both the field structure and particle energy, the analysis may be greatly simplified by dimen…
Background radiation fields pervade the Universe, and above a certain energy any $γ$-ray flux emitted by an extragalactic source should be attenuated due to $e^+e^-$ pair production. The opacity could be alleviated if photons oscillated into hypothetical axion-like particles (ALPs) in ambient magnetic fields, leading to a $γ$-ray excess especially at high optical depths that could be detected with imaging air Cherenkov telescopes (IACTs). Here, we introduce a method to search for such a signal in $γ$-ray data and to estimate sensitivities for future observations. Different magnetic fields clos…
Streaming cosmic rays can power the exponential growth of a seed magnetic field by exciting a non-resonant instability that feeds on their bulk kinetic energy. By generating the necessary turbulent magnetic field, it is thought to play a key role in the confinement and acceleration of cosmic rays at shocks. In this work we present hybrid-Particle-In-Cell simulations of the non-resonant mode including Monte Carlo collisions, and investigate the interplay between the pressure anisotropies produced by the instability and particle collisions in the background plasma. Simulations of poorly ionized …
Low-energy cosmic rays, in particular protons with energies below 1 GeV, are significant drivers of the thermochemistry of molecular clouds. However, these cosmic rays are also greatly impacted by energy losses and magnetic field transport effects in molecular gas. Explaining cosmic ray ionization rates of $10^{-16}$ s$^{-1}$ or greater in dense gas requires either a high external cosmic ray flux, or local sources of MeV-GeV cosmic ray protons. We present a new local source of low-energy cosmic rays in molecular clouds: first order Fermi-acceleration of protons in regions undergoing turbulent …
Arrival directions of ultra-high energy cosmic rays from the direction of ten brightest radio sources lying within 50 Mpc from our Galaxy were studied by using recent models of the largescale Galactic magnetic field. A detailed study, where also small-scale turbulent magnetic field component was implemented, is presented for the radiogalaxy Virgo A. This radiogalaxy is located far from the Galactic plane which leads to a unique image of this UHECR source candidate, if the flux is composed from a mixture of intermediate mass nuclei. We present a method suitable for identifying cosmic rays arriv…
Supernova remnants are believed to be the main sources of galactic Cosmic Rays (CR). Within this framework, particles are accelerated at supernova remnant shocks and then released in the interstellar medium. The mechanism through which CRs are released and the way in which they propagate still remain open issues. The main difficulty is the high non-linearity of the problem: CRs themselves excite the magnetic turbulence that confines them close to their sources. We solve numerically the coupled differential equations describing the evolution in space and time of the escaping particles and of th…
Stochastic acceleration of cosmic rays in second order Fermi processes is usually considered too slow to reach ultra-high energies, except in specific cases. In this paper we present the energy spectrum obtained from second order Fermi acceleration in highly turbulent magnetic fields as e.g.\ found in the outskirts of AGN jets in situations where it can be sufficiently fast to accelerate particles to the highest observed energies. We parametrize the resulting non-power-law spectra and show that these can describe the cosmic ray energy spectrum and mass-composition data at the highest energies …
Cosmic ray transport on galactic scales depends on the detailed properties of the magnetized, multiphase interstellar medium (ISM). In this work, we post-process a high-resolution TIGRESS magnetohydrodynamic simulation modeling a local galactic disk patch with a two-moment fluid algorithm for cosmic ray transport. We consider a variety of prescriptions for the cosmic rays, from a simple purely diffusive formalism with constant scattering coefficient, to a physically-motivated model in which the scattering coefficient is set by critical balance between streaming-driven Alfvén wave excitation an…
The origin of the ultrahigh energy cosmic ray remains being a mystery. However, a considerable progress has been made in the past few years due to the good quality data recorded by current cosmic ray observatories. One of the recent achievements is obtaining firm observational evidence about the extragalactic origin of the most energetic cosmic rays by the Pierre Auger observatory. On the other hand, it is believed that there is a non-null turbulent magnetic field that fills the intergalactic medium. Therefore, the presence of the intergalactic magnetic field can play an important role on the …
The maximum magnetic field strength generated by Weibel-type plasma instabilities is estimated for typical conditions in the interstellar medium. The relevant kinetic dispersion relations are evaluated by conducting a parameter study both for Maxwellian and for suprathermal particle distributions showing that micro Gauss magnetic fields can be generated. It is shown that, depending on the streaming velocity and the plasma temperatures, either the longitudinal or a transverse instability will be dominant. In the presence of an ambient magnetic field, the filamentation instability is typically s…
The propagation of particles accelerated at supernova remnant shocks and escaping the parent remnants is likely to proceed in a strongly non-linear regime, due to the efficient self-generation of Alfvén waves excited through streaming instability near the sources. Depending on the amount of neutral hydrogen present in the regions around the sites of supernova explosions, cosmic rays may accumulate an appreciable grammage in the same regions and get self-confined for non-negligible times, which in turn results in an enhanced rate of production of secondaries. Here we calculate the contribution …
We study non-thermal emissions from cool cores in galaxy clusters. We adopted a recent model, in which cosmic-rays (CRs) prevail in the cores and stably heat them through CR streaming. The non-thermal emissions come from the interaction between CR protons and intracluster medium (ICM). Comparison between the theoretical predictions and radio observations shows that the overall CR spectra must be steep, and most of the CRs in the cores are low-energy CRs. Assuming that the CRs are injected through AGN activities, we study the nature of the shocks that are responsible for the CR acceleration. Th…
