Electron Heating in Low Mach Number Perpendicular shocks. II. Dependence on the Pre-Shock Conditions [HEAP]


Recent X-ray observations of merger shocks in galaxy clusters have shown that the post-shock plasma is two-temperature, with the protons being hotter than the electrons. In this work, the second of a series, we investigate by means of two-dimensional particle-in-cell simulations the efficiency of electron irreversible heating in perpendicular low Mach number shocks. We consider values of plasma beta (ratio of thermal and magnetic pressures) in the range $4\lesssim \beta_{p0}\lesssim 32$ and sonic Mach number (ratio of shock speed to pre-shock sound speed) in the range $2\lesssim M_{s}\lesssim 5$, as appropriate for galaxy cluster shocks. As shown in Paper I, magnetic field amplification – induced by shock compression of the pre-shock field, or by strong proton cyclotron and mirror modes accompanying the relaxation of proton temperature anisotropy – can drive the electron temperature anisotropy beyond the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance, and allows for efficient entropy production. We find that the post-shock electron temperature $T_{e2}$ exceeds the adiabatic expectation $T_{e2,\rm ad}$ by an amount $(T_{e2}-T_{e2,\rm ad})/T_{e0}\simeq 0.044 \,M_s (M_s-1)$ (here, $T_{e0}$ is the pre-shock temperature), which depends only weakly on the plasma beta, over the range $4\lesssim \beta_{p0}\lesssim 32$ which we have explored, and on the proton-to-electron mass ratio (the coefficient of $\simeq 0.044$ is measured for our fiducial $m_i/m_e=49$, and we estimate that it will decrease to $\simeq 0.03$ for the realistic mass ratio). Our results have important implications for current and future observations of galaxy cluster shocks in the radio band (synchrotron emission and Sunyaev-Zel’dovich effect) and at X-ray frequencies.

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X. Guo, L. Sironi and R. Narayan
Tue, 12 Dec 17

Comments: 22 pages, 16 figures, 4 tables, 3 appendices; submitted to ApJ

Perpendicular relativistic shocks in magnetized pair plasma [HEAP]


Perpendicular relativistic ($\gamma_0=10$) shocks in magnetized pair plasmas are investigated using two dimensional Particle-in-Cell simulations. A systematic survey, from unmagnetized to strongly magnetized shocks, is presented accurately capturing the transition from Weibel-mediated to magnetic-reflection-shaped shocks. This transition is found to occur for upstream flow magnetizations $10^{-3}<\sigma<10^{-2}$ at which a strong perpendicular net current is observed in the precursor, driving the so-called current-filamentation instability. The global structure of the shock and shock formation time are discussed. The MHD shock jump conditions are found in good agreement with the numerical results, except for $10^{-4} < \sigma < 10^{-2}$ where a deviation up to 10\% is observed. The particle precursor length converges toward the Larmor radius of particles injected in the upstream magnetic field at intermediate magnetizations. For $\sigma>10^{-2}$, it leaves place to a purely electromagnetic precursor following from the strong emission of electromagnetic waves at the shock front.
Particle acceleration is found to be efficient in weakly magnetized perpendicular shocks in agreement with previous works, and is fully suppressed for $\sigma > 10^{-2}$. Diffusive Shock Acceleration is observed only in weakly magnetized shocks, while a dominant contribution of Shock Drift Acceleration is evidenced at intermediate magnetizations. The spatial diffusion coefficients are extracted from the simulations allowing for a deeper insight into the self-consistent particle kinematics and scale with the square of the particle energy in weakly magnetized shocks.
These results have implications for particle acceleration in the internal shocks of AGN jets and in the termination shocks of Pulsar Wind Nebulae.

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I. Plotnikov, A. Grassi and M. Grech
Mon, 11 Dec 17

Comments: 23 pages, 18 figures, 2 appendices, submitted to MNRAS

Magnetorotational instability in eccentric disks [HEAP]


Eccentric disks arise in such astrophysical contexts as tidal disruption events, but it is unknown whether the magnetorotational instability (MRI), which powers accretion in circular disks, operates in eccentric disks as well. We examine the linear evolution of unstratified, incompressible MRI in an eccentric disk orbiting a point mass. We consider vertical modes of wavenumber $k$ on a background flow with uniform eccentricity $e$ and vertical Alfv\’en speed $v_\mathrm A$ along an orbit with mean motion $n$. We find two mode families, one with dominant magnetic components, the other with dominant velocity components; the former is unstable at $(1-e)^3f^2\lesssim3$, where $f\equiv kv_\mathrm A/n$, the latter at $e\gtrsim0.8$. For $f^2\lesssim3$, MRI behaves much like in circular disks, but the growth per orbit declines slowly with increasing $e$; for $f^2\gtrsim3$, modes grow by parametric amplification, which is resonant for $0<e\ll1$. MRI growth and the attendant angular momentum and energy transport happen chiefly near pericenter, where orbital shear dominates magnetic tension.

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C. Chan, J. Krolik and T. Piran
Thu, 7 Dec 17

Comments: 13 pages, 6 figures, 2 appendices, submitted to ApJ

Astrophysical gyrokinetics: Turbulence in pressure-anisotropic plasmas at ion scales and beyond [HEAP]


We present a theoretical framework for describing electromagnetic kinetic turbulence in a multi-species, magnetized, pressure-anisotropic plasma. Turbulent fluctuations are assumed to be small compared to the mean field, to be spatially anisotropic with respect to it, and to have frequencies small compared to the ion cyclotron frequency. At scales above the ion Larmor radius, the theory reduces to the pressure-anisotropic generalization of kinetic reduced magnetohydrodynamics (KRMHD) formulated by Kunz et al. (2015). At scales at and below the ion Larmor radius, three main objectives are achieved. First, we analyse the linear response of the pressure-anisotropic gyrokinetic system, and show it to be a generalisation of previously explored limits. The effects of pressure anisotropy on the stability and collisionless damping of Alfvenic and compressive fluctuations are highlighted, with attention paid to the spectral location and width of the frequency jump that occurs as Alfven waves transition into kinetic Alfven waves. Secondly, we derive and discuss a general free-energy conservation law, which captures both the KRMHD free-energy conservation at long wavelengths and dual cascades of kinetic Alfven waves and ion entropy at sub-ion-Larmor scales. We show that non-Maxwellian features in the distribution function change the amount of phase mixing and the efficiency of magnetic stresses, and thus influence the partitioning of free energy amongst the cascade channels. Thirdly, a simple model is used to show that pressure anisotropy can cause large variations in the ion-to-electron heating ratio due to the dissipation of Alfvenic turbulence. Our theory provides a foundation for determining how pressure anisotropy affects the turbulent fluctuation spectra, the differential heating of particle species, and the ratio of parallel and perpendicular phase mixing in space and astrophysical plasmas.

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M. Kunz, I. Abel, K. Klein, et. al.
Thu, 7 Dec 17

Comments: 56 pages, 5 figures, submitted to Journal of Plasma Physics (submitted 28 Nov 2017); abstract abridged

Heating and cooling of coronal loops with turbulent suppression of parallel heat conduction [SSA]


Using the “enthalpy-based thermal evolution of loops” (EBTEL) model, we investigate the hydrodynamics of the plasma in a flaring coronal loop in which heat conduction is limited by turbulent scattering of the electrons that transport the thermal heat flux. The EBTEL equations are solved analytically in each of the two (conduction-dominated and radiation-dominated) cooling phases. Comparison of the results with typical observed cooling times in solar flares shows that the turbulent mean free-path $\lambda_T$ lies in a range corresponding to a regime in which classical (collision-dominated) conduction plays at most a limited role. We also consider the magnitude and duration of the heat input that is necessary to account for the enhanced values of temperature and density at the beginning of the cooling phase and for the observed cooling times. We find through numerical modeling that in order to produce a peak temperature $\simeq 1.5 \times 10^7$~K and a 200~s cooling time consistent with observations, the flare heating profile must extend over a significant period of time; in particular, its lingering role must be taken into consideration in any description of the cooling phase. Comparison with observationally-inferred values of post-flare loop temperatures, densities, and cooling times thus leads to useful constraints on both the magnitude and duration of the magnetic energy release in the loop, as well as on the value of the turbulent mean free-path $\lambda_T$.

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N. Bian, A. Emslie, D. Horne, et. al.
Fri, 1 Dec 17

Comments: 16 pages, 4 figures, to be published in The Astrophysical Journal

Laminar and turbulent dynamos in chiral magnetohydrodynamics. II. Simulations [CL]


Using numerical simulations, we study laminar and turbulent dynamos in chiral magnetohydrodynamics with an extended set of equations that accounts for an additional electric current due to the chiral magnetic effect (CME). This quantum relativistic phenomenon originates from an asymmetry between left- and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the chiral dynamics of the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability; (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral $\alpha_\mu$ effect (which is not related to kinetic helicity and becomes dominant at large fluid and magnetic Reynolds numbers); and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2) during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the revealed new chiral effects in the relativistic plasmas of the early Universe and of proto-neutron stars are discussed.

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J. Schober, I. Rogachevskii, A. Brandenburg, et. al.
Wed, 29 Nov 17

Comments: 21 pages, 20 figures; submitted to ApJ

Development of Tearing Instability in a Current Sheet Forming by Sheared Incompressible Flow [CL]


Sweet-Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it forms. Formation can occur due to sheared, sub-Alfv\’enic incompressible flows which narrow the sheet. Standard tearing theory (Furth et al. 1963; Coppi et al. 1976; Rutherford 1973) is not immediately applicable to such forming sheets for two reasons: first, because the flow introduces terms not present in the standard calculation; second, because the changing equilibrium introduces time dependence to terms which are constant in the standard calculation, complicating the formulation of an eigenvalue problem. This paper adapts standard tearing mode analysis to confront these challenges. In an initial phase when any perturbations are primarily governed by ideal MHD, a coordinate transformation reveals that the flow compresses and stretches perturbations. A multiple scale formulation describes how linear tearing mode theory (Furth et al. 1963; Coppi et al. 1976) can be applied to an equilibrium changing under flow, showing that tearing eigenfunctions grow slowly due to the flow and undergo exponential growth at a rate given by standard scalings with time dependence added. In the nonlinear Rutherford stage, the coordinate transformation shows that standard theory can be adapted by adding to the stationary rates time dependence and an additional term due to the strengthening equilibrium magnetic field. Overall, this understanding supports the use of flow-free scalings with slight modifications to study tearing in a forming sheet.

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E. Tolman, N. Loureiro and D. Uzdensky
Mon, 27 Nov 2017

Comments: submitted for publication