Viscous Kelvin-Helmholtz instabilities in highly ionised plasmas

Transport coefficients in highly ionised plasmas like the intra-cluster medium (ICM) are still ill-constrained. They influence various processes, among them the mixing at shear flow interfaces due to the Kelvin-Helmholtz instability (KHI). The observed structure of potential mixing layers can be used to infer the transport coefficients, but the data interpretation requires a detailed knowledge of the long-term evolution of the KHI under different conditions. Here we present the first systematic numerical study of the effect of constant and temperature-dependent isotropic viscosity over the full range of possible values. We show that moderate viscosities slow down the growth of the KHI and reduce the height of the KHI rolls and their rolling-up. Viscosities above a critical value suppress the KHI. The effect can be quantified in terms of the Reynolds number Re = U{\lambda}/{\nu}, where U is the shear velocity, {\lambda} the perturbation length, and {\nu} the kinematic viscosity. We derive the critical Re for constant and temperature dependent, Spitzer-like viscosities, an empirical relation for the viscous KHI growth time as a function of Re and density contrast, and describe special behaviours for Spitzer-like viscosities and high density contrasts. Finally, we briefly discuss several astrophysical situations where the viscous KHI could play a role, i.e., sloshing cold fronts, gas stripping from galaxies, buoyant cavities, ICM turbulence, and high velocity clouds.Comment: Accepted by MNRAS. 22 pages, 21 figure

Shear thickening in densely packed suspensions of spheres and rods confined to few layers

We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-induced effect, viscosity curves show shear thickening that retains bulk behavior down to samples as thin as two particle diameters for spheres, below which the suspension is jammed. Rods exhibit similar behavior commensurate with the particle width, but they show additional effects when the thickness is reduced below about a particle length as they are forced to align; the stress increases for decreasing gap size at fixed shear rate while the shear thickening regime gradually transitions to a Newtonian scaling regime. This weakening of shear thickening as an ordered configuration is approached contrasts with the strengthening of shear thickening when the packing fraction is increased in the disordered bulk limit, despite the fact that both types of confinement eventually lead to jamming.Comment: 21 pages, 14 figures. submitted to the Journal of Rheolog

Stripped elliptical galaxies as probes of ICM physics: II. Stirred, but mixed? Viscous and inviscid gas stripping of the Virgo elliptical M89

Elliptical galaxies moving through the intra-cluster medium (ICM) are progressively stripped of their gaseous atmospheres. X-ray observations reveal the structure of galactic tails, wakes, and the interface between the galactic gas and the ICM. This fine-structure depends on dynamic conditions (galaxy potential, initial gas contents, orbit in the host cluster), orbital stage (early infall, pre-/post-pericenter passage), as well as on the still ill-constrained ICM plasma properties (thermal conductivity, viscosity, magnetic field structure). Paper I describes flow patterns and stages of inviscid gas stripping. Here we study the effect of a Spitzer-like temperature dependent viscosity corresponding to Reynolds numbers, Re, of 50 to 5000 with respect to the ICM flow around the remnant atmosphere. Global flow patterns are independent of viscosity in this Reynolds number range. Viscosity influences two aspects: In inviscid stripping, Kelvin-Helmholtz instabilities (KHIs) at the sides of the remnant atmosphere lead to observable horns or wings. Increasing viscosity suppresses KHIs of increasing length scale, and thus observable horns and wings. Furthermore, in inviscid stripping, stripped galactic gas can mix with the ambient ICM in the galaxy's wake. This mixing is suppressed increasingly with increasing viscosity, such that viscously stripped galaxies have long X-ray bright, cool wakes. We provide mock X-ray images for different stripping stages and conditions. While these qualitative results are generic, we tailor our simulations to the Virgo galaxy M89 (NGC 4552), where Re~ 50 corresponds to a viscosity of 10% of the Spitzer level. Paper III compares new deep Chandra and archival XMM-Newton data to our simulations.Comment: ApJ in press. 16 pages, 16 figures. Text clarified, conclusions unchange

Stripped elliptical galaxies as probes of ICM physics : III. Deep Chandra observation of NGC 4552 - Measuring the viscosity of the intracluster medium

We present results from a deep (200 ks) Chandra observation of the early-type galaxy NGC 4552 (M89) which is falling into the Virgo cluster. Previous shallower X-ray observations of this galaxy showed a remnant gas core, a tail to the South of the galaxy, and twin `horns' attached to the northern edge of the gas core [machacek05a]. In our deeper data, we detect a diffuse, low surface brightness extension to the previously known tail, and measure the temperature structure within the tail. We combine the deep Chandra data with archival XMM-Newton observations to put a strong upper limit on the diffuse emission of the tail out to a large distance (10×the radius of the remnant core) from the galaxy center. In our two previous papers [roediger15a,roediger15b], we presented the results of hydrodynamical simulations of ram pressure stripping specifically for M89 falling into the Virgo cluster and investigated the effect of ICM viscosity. In this paper, we compare our deep data with our specifically tailored simulations and conclude that the observed morphology of the stripped tail in NGC 4552 is most similar to the inviscid models. We conclude that, to the extent the transport processes can be simply modeled as a hydrodynamic viscosity, the ICM viscosity is negligible. More generally, any micro-scale description of the transport processes in the high-β plasma of the cluster ICM must be consistent with the efficient mixing observed in the stripped tail on macroscopic scales

The infall of the Virgo elliptical galaxy M60 toward M87 and the gaseous structures produced by Kelvin-Helmholtz instabilities

We present Chandra observations of hot gas structures, characteristic of gas stripping during infall, in the Virgo cluster elliptical galaxy M60 (NGC4649) located 1 Mpc east of M87. 0.5−2 keV Chandra X-ray images show a sharp leading edge in the surface brightness 12.4±0.1 kpc north and west of the galaxy center in the direction of M87 characteristic of a merger cold front due to M60's motion through the Virgo ICM. We measured a temperature of 1.00±0.02 keV for abundance 0.5Z⊙ inside the edge and 1.37+0.35−0.19 keV for abundance 0.1Z⊙ in the Virgo ICM free stream region. We find that the observed jump in surface brightness yields a density ratio of 6.44+1.04−0.67 between gas inside the edge and in the cluster free stream region. If the edge is a cold front due solely to the infall of M60 in the direction of M87, we find a pressure ratio of 4.7+1.7−1.4 and Mach number 1.7±0.3. For 1.37 keV Virgo gas we find a total infall velocity for M60 of 1030±180 kms−1. We calculate the motion in the plane of the sky to be 1012+183−192 km−1 implying an inclination angle ξ=11±3 degrees. Surface brightness profiles show the presence of a faint diffuse gaseous tail. We identify filamentary, gaseous wing structures caused by the galaxy's motion through the ICM. The structure and dimensions of these wings are consistent with simulations of Kelvin-Helmholtz instabilities as expected if the gas stripping is close to inviscid