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1. Thermal instability of halo gas heated by streaming cosmic rays

   https://doi.org/10.1093/mnras/staa385  

   Kempski, Philipp ; Quataert, Eliot ( April 2020 , Monthly Notices of the Royal Astronomical Society)

   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 formmore »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.« less
2. Turbulent Reacceleration of Streaming Cosmic Rays

   https://doi.org/10.3847/1538-4357/aca021  

   Bustard, Chad ; Oh, S. Peng ( December 2022 , The Astrophysical Journal)

   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 plasmaβ. Due to streaming-modified phase shifts between CR and gas variables, they are slower than canonical reacceleration rates in low-βenvironments like the interstellar medium but remain unchanged in high-βenvironments 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/L₀, 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 primarilymore »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.

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3. Acceleration and escape processes of high-energy particles in turbulence inside hot accretion flows

   https://doi.org/10.1093/mnras/stz329  

   Kimura, Shigeo S. ; Tomida, Kengo ; Murase, Kohta ( February 2019 , Monthly Notices of the Royal Astronomical Society)

   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 tomore »ε ∼ 0.1−10 PeV.

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4. A consistent reduced-speed-of-light formulation of cosmic ray transport valid in weak- and strong-scattering regimes

   https://doi.org/10.1093/mnras/stab2635  

   Hopkins, Philip F ; Squire, Jonathan ; Butsky, Iryna S ( December 2021 , Monthly Notices of the Royal Astronomical Society)

   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 themore »correct behaviour to be recovered in all interesting limits, and show how current implementations of CRs with an RSOL neglect some additional terms.« less
5. But what about...: cosmic rays, magnetic fields, conduction, and viscosity in galaxy formation

   https://doi.org/10.1093/mnras/stz3321  

   Hopkins, Philip F ; Chan, T K ; Garrison-Kimmel, Shea ; Ji, Suoqing ; Su, Kung-Yi ; Hummels, Cameron B ; Kereš, Dušan ; Quataert, Eliot ; Faucher-Giguère, Claude-André ( March 2020 , Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We present and study a large suite of high-resolution cosmological zoom-in simulations, using the FIRE-2 treatment of mechanical and radiative feedback from massive stars, together with explicit treatment of magnetic fields, anisotropic conduction and viscosity (accounting for saturation and limitation by plasma instabilities at high β), and cosmic rays (CRs) injected in supernovae shocks (including anisotropic diffusion, streaming, adiabatic, hadronic and Coulomb losses). We survey systems from ultrafaint dwarf ($M_{\ast }\sim 10^{4}\, \mathrm{M}_{\odot }$, $M_{\rm halo}\sim 10^{9}\, \mathrm{M}_{\odot }$) through Milky Way/Local Group (MW/LG) masses, systematically vary uncertain CR parameters (e.g. the diffusion coefficient κ and streaming velocity), and study a broad ensemble of galaxy properties [masses, star formation (SF) histories, mass profiles, phase structure, morphologies, etc.]. We confirm previous conclusions that magnetic fields, conduction, and viscosity on resolved ($\gtrsim 1\,$ pc) scales have only small effects on bulk galaxy properties. CRs have relatively weak effects on all galaxy properties studied in dwarfs ($M_{\ast } \ll 10^{10}\, \mathrm{M}_{\odot }$, $M_{\rm halo} \lesssim 10^{11}\, \mathrm{M}_{\odot }$), or at high redshifts (z ≳ 1–2), for any physically reasonable parameters. However, at higher masses ($M_{\rm halo} \gtrsim 10^{11}\, \mathrm{M}_{\odot }$) and z ≲ 1–2, CRs can suppress SF and stellar masses by factorsmore »∼2–4, given reasonable injection efficiencies and relatively high effective diffusion coefficients $\kappa \gtrsim 3\times 10^{29}\, {\rm cm^{2}\, s^{-1}}$. At lower κ, CRs take too long to escape dense star-forming gas and lose their energy to collisional hadronic losses, producing negligible effects on galaxies and violating empirical constraints from spallation and γ-ray emission. At much higher κ CRs escape too efficiently to have appreciable effects even in the CGM. But around $\kappa \sim 3\times 10^{29}\, {\rm cm^{2}\, s^{-1}}$, CRs escape the galaxy and build up a CR-pressure-dominated halo which maintains approximate virial equilibrium and supports relatively dense, cool (T ≪ 106 K) gas that would otherwise rain on to the galaxy. CR ‘heating’ (from collisional and streaming losses) is never dominant.« less