ABSTRACT Heating of virialized gas by streaming cosmic rays (CRs) may be energetically important in galaxy haloes, 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 $\boldsymbol {k \cdot B }\ne 0$ are strongly affected by CR diffusion. When the streaming time is shorter than the CR diffusion time, thermally unstable modes (with $\boldsymbol {k \cdot B }\ne 0$) are waves propagating at a speed ∝ the Alfvén speed. Halo gas in photoionization equilibrium is thermally stable independent of CR pressure, while gas in collisional ionization equilibrium is unstable for physically realistic parameters. In gravitationally stratified plasmas, the oscillation frequency of thermally overstable modes can be higher in the presence of CR streaming than the buoyancy/free-fall frequency. This may modify the critical tcool/tff at which multiphase gas is present. The criterion for convective instability of a stratified, CR-heated medium can be written in the familiar Schwarzschild form dseff/dz < 0, where seff is an effective entropy involving the gas and CR pressures. We discuss the implications of our results for the thermal evolution and multiphase structure of galaxy haloes, groups, and clusters.
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Turbulent Cosmic Ray–Mediated Shocks in the Hot Ionized Interstellar Medium
Abstract The structure of shocks and turbulence are strongly modified during the acceleration of cosmic rays (CRs) at a shock wave. The pressure and the collisionless viscous stress decelerate the incoming thermal gas and thus modify the shock structure. A CR streaming instability ahead of the shock generates the turbulence on which CRs scatter. The turbulent magnetic field in turn determines the CR diffusion coefficient and further affects the CR energy spectrum and pressure distribution. The dissipation of turbulence contributes to heating the thermal gas. Within a multicomponent fluid framework, CRs and thermal gas are treated as fluids and are closely coupled to the turbulence. The system equations comprise the gas dynamic equations, the CR pressure evolution equation, and the turbulence transport equations, and we adopt typical parameters for the hot ionized interstellar medium. It is shown that the shock has no discontinuity but possesses a narrow but smooth transition. The self-generated turbulent magnetic field is much stronger than both the large-scale magnetic field and the preexisting turbulent magnetic field. The resulting CR diffusion coefficient is substantially suppressed and is more than three orders smaller near the shock than it is far upstream. The results are qualitatively consistent with certain observations.
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- Award ID(s):
- 1655280
- NSF-PAR ID:
- 10355939
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 932
- Issue:
- 1
- ISSN:
- 0004-637X
- Page Range / eLocation ID:
- 65
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Subsonic, compressive turbulence transfers energy to cosmic rays (CRs), a process known as nonresonant reacceleration. It is often invoked to explain the observed ratios of primary to secondary CRs at ∼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 streaming is included, reacceleration rates depend on plasma
β . Due to streaming-modified phase shifts between CR and gas variables, they are slower than canonical reacceleration rates in low-β environments like the interstellar medium but remain unchanged in high-β environments like the intracluster medium. We also quantify the streaming energy-loss rate in our simulations. For sub-Alfvénic turbulence, it is resolution dependent (hence unconverged in large-scale simulations) and heavily suppressed compared to the isotropic loss ratev A· ∇P CR/P CR∼v A/L 0, due to misalignment between the mean field and isotropic CR gradients. Unlike acceleration efficiencies, CR losses are almost independent of magnetic field strength overβ ∼ 1–100 and are, therefore, not the primary factor behind lower acceleration rates when streaming is included. While this paper is primarily concerned with how turbulence affects CRs, in a follow-up paper we consider how CRs affect turbulence by diverting energy from the MHD cascade, altering the pathway to gas heating and steepening the turbulent spectrum. -
Abstract We study the propagation of mildly relativistic cosmic rays (CRs) in multiphase interstellar medium environments with conditions typical of nearby disk galaxies. We employ the techniques developed in Armillotta et al. to postprocess three high-resolution TIGRESS magnetohydrodynamic simulations modeling local patches of star-forming galactic disks. Together, the three simulations cover a wide range of gas surface density, gravitational potential, and star formation rate (SFR). Our prescription for CR propagation includes the effects of advection by the background gas, streaming along the magnetic field at the local ion Alfvén speed, and diffusion relative to the Alfvén waves, with the diffusion coefficient set by the balance between streaming-driven Alfvén wave excitation and damping mediated by local gas properties. We find that the combined transport processes are more effective in environments with higher SFR. These environments are characterized by higher-velocity hot outflows (created by clustered supernovae) that rapidly advect CRs away from the galactic plane. As a consequence, the ratio of midplane CR pressure to midplane gas pressures decreases with increasing SFR. We also use the postprocessed simulations to make predictions regarding the potential dynamical impacts of CRs. The relatively flat CR pressure profiles near the midplane argue that they would not provide significant support against gravity for most of the ISM mass. However, the CR pressure gradients are larger than the other pressure gradients in the extraplanar region (∣ z ∣ > 0.5 kpc), suggesting that CRs may affect the dynamics of galactic fountains and/or winds. The degree of this impact is expected to increase in environments with lower SFR.more » « less
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Abstract We investigate acceleration and propagation processes of high-energy particles inside hot accretion flows. The magnetorotational instability (MRI) creates turbulence inside accretion flows, which triggers magnetic reconnection and may produce non-thermal particles. They can be further accelerated stochastically by the turbulence. To probe the properties of such relativistic particles, we perform magnetohydrodynamic simulations to obtain the turbulent fields generated by the MRI, and calculate orbits of the high-energy particles using snapshot data of the MRI turbulence. We find that the particle acceleration is described by a diffusion phenomenon in energy space with a diffusion coefficient of the hard-sphere type: Dε ∝ ε2, where ε is the particle energy. Eddies in the largest scale of the turbulence play a dominant role in the acceleration process. On the other hand, the stochastic behaviour in configuration space is not usual diffusion but superdiffusion: the radial displacement increases with time faster than that in the normal diffusion. Also, the magnetic field configuration in the hot accretion flow creates outward bulk motion of high-energy particles. This bulk motion is more effective than the diffusive motion for higher energy particles. Our results imply that typical active galactic nuclei that host hot accretion flows can accelerate CRs up to ε ∼ 0.1−10 PeV.
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ABSTRACT We derive a consistent set of moment equations for cosmic ray (CR)-magnetohydrodynamics, assuming a gyrotropic distribution function (DF). Unlike previous efforts, we derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that is valid in both the nearly isotropic DF and/or strong-scattering regimes, and the arbitrarily anisotropic DF or free-streaming regimes, as well as allowing for anisotropic scattering and transport/magnetic field structure. We present the appropriate two-moment closure and equations for various choices of evolved variables, including the CR phase space DF f, number density n, total energy e, kinetic energy ϵ, and their fluxes or higher moments, and the appropriate coupling terms to the gas. We show that this naturally includes and generalizes a variety of terms including convection/fluid motion, anisotropic CR pressure, streaming, diffusion, gyro-resonant/streaming losses, and re-acceleration. We discuss how this extends previous treatments of CR transport including diffusion and moment methods and popular forms of the Fokker–Planck equation, as well as how this differs from the analogous M1-RHD equations. We also present two different methods for incorporating a reduced speed of light (RSOL) to reduce time-step limitations: In both, we carefully address where the RSOL (versus true c) must appear for the correct behaviour to be recovered in all interesting limits, and show how current implementations of CRs with an RSOL neglect some additional terms.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3847/1538-4357/ac6ddc
