skip to main content

Title: The cosmic-ray staircase: the outcome of the cosmic-ray acoustic instability

Recently, cosmic rays (CRs) have emerged as a leading candidate for driving galactic winds. Small-scale processes can dramatically affect global wind properties. We run two-moment simulations of CR streaming to study how sound waves are driven unstable by phase-shifted CR forces and CR heating. We verify linear theory growth rates. As the sound waves grow non-linear, they steepen into a quasi-periodic series of propagating shocks; the density jumps at shocks create CR bottlenecks. The depth of a propagating bottleneck depends on both the density jump and its velocity; ΔPc is smaller for rapidly moving bottlenecks. A series of bottlenecks creates a CR staircase structure, which can be understood from a convex hull construction. The system reaches a steady state between growth of new perturbations, and stair mergers. CRs are decoupled at plateaus, but exert intense forces and heating at stair jumps. The absence of CR heating at plateaus leads to cooling, strong gas pressure gradients and further shocks. If bottlenecks are stationary, they can drastically modify global flows; if their propagation times are comparable to dynamical times, their effects on global momentum and energy transfer are modest. The CR acoustic instability is likely relevant in thermal interfaces between cold more » and hot gas, as well as galactic winds. Similar to increased opacity in radiative flows, the build-up of CR pressure due to bottlenecks can significantly increase mass outflow rates, by up to an order of magnitude. It seeds unusual forms of thermal instability, and the shocks could have distinct observational signatures, on ∼kpc scales.

« less
 ;  ;
Award ID(s):
Publication Date:
Journal Name:
Monthly Notices of the Royal Astronomical Society
Page Range or eLocation-ID:
p. 4464-4493
Oxford University Press
Sponsoring Org:
National Science Foundation
More Like this

    We use analytical 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 pc has a staircase-like structure with dpc/dr ≃ 0 in most of the volume, and the time-averaged CR energetics are in many cases better approximated by pc ∝ ρ1/2, rather than the canonical pc ∝ ρ2/3. Accounting for this change in CR energetics, we analytically derive new expressions for the mass-loss rate, momentum flux, wind speed, and wind kinetic power in galactic winds driven by CR streaming. We show that streaming CRs are ineffective at directly driving cold gas out of galaxies, though CR-driven winds in hotter ISM phases may entrain cool gas. For the same physical conditions, diffusive CR transport (Paper I) yields mass-loss rates that are a few-100 times larger than streaming transport, and asymptotic wind powers that are a factor of ≃4 larger. We discuss the implications of our results for galactic wind theory and observations; strongmore »shocks driven by CR-streaming-induced instabilities produce gas with a wide range of densities and temperatures, consistent with the multiphase nature of observed winds. We also quantify the applicability of the isothermal gas approximation for modelling streaming CRs and highlight the need for calculations with more realistic thermodynamics.

    « less
  2. 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
  3. 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 certainmore »observations.« less

    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 Mach number. While previous simulations that relied on a simplified model of CR transport have shown that super-Alfvénic streaming of CRs enhances galactic winds, in this paper we take into account a realistic model of streaming suppression. We perform three-dimensional magnetohydrodynamic simulations of a section of a galactic disc and find that turbulent damping dependent on local magnetization of turbulent interstellar medium (ISM) leads to more spatially extended gas and CR distributions compared to the earlier streaming calculations, and that scale heights of these distributions increase for stronger turbulence. Our results indicate that the star formation rate increases with the level of turbulence in the ISM. We also find that the instantaneous windmore »mass loading is sensitive to local streaming physics with the mass loading dropping significantly as the strength of turbulence increases.

    « less

    Cosmic rays (CRs) are an important component in the interstellar medium, but their effect on the dynamics of the disc–halo interface (<10 kpc from the disc) is still unclear. We study the influence of CRs on the gas above the disc with high-resolution FIRE-2 cosmological simulations of late-type L⋆ galaxies at redshift z ∼ 0. We compare runs with and without CR feedback (with constant anisotropic diffusion κ∥ ∼ 3 × 1029 cm2 s−1 and streaming). Our simulations capture the relevant disc–halo interactions, including outflows, inflows, and galactic fountains. Extra-planar gas in all of the runs satisfies dynamical balance, where total pressure balances the weight of the overlying gas. While the kinetic pressure from non-uniform motion (≳1 kpc scale) dominates in the mid-plane, thermal and bulk pressures (or CR pressure if included) take over at large heights. We find that with CR feedback, (1) the warm (∼104 K) gas is slowly accelerated by CRs; (2) the hot (>5 × 105 K) gas scale height is suppressed; (3) the warm-hot (2 × 104–5 × 105 K) medium becomes the most volume-filling phase in the disc–halo interface. We develop a novel conceptual model of the near-disc gas dynamics in low-redshift L⋆ galaxies: with CRs, the disc–halo interface is filled with CR-driven warm winds and hotmore »superbubbles that are propagating into the circumgalactic medium with a small fraction falling back to the disc. Without CRs, most outflows from hot superbubbles are trapped by the existing hot halo and gravity, so typically they form galactic fountains.

    « less