Kelvin-Helmholtz instabilities at the sloshing cold fronts in the Virgo cluster as a measure for the effective ICM viscosity

Sloshing cold fronts (CFs) arise from minor merger triggered gas sloshing. Their detailed structure depends on the properties of the intra-cluster medium (ICM): hydrodynamical simulations predict the CFs to be distorted by Kelvin-Helmholtz instabilities (KHIs), but aligned magnetic fields, viscosity, or thermal conduction can suppress the KHIs. Thus, observing the detailed structure of sloshing CFs can be used to constrain these ICM properties. Both smooth and distorted sloshing CFs have been observed, indicating that the KHI is suppressed in some clusters, but not in all. Consequently, we need to address at least some sloshing clusters individually before drawing general conclusions about the ICM properties. We present the first detailed attempt to constrain the ICM properties in a specific cluster from the structure of its sloshing CF. Proximity and brightness make the Virgo cluster an ideal target. We combine observations and Virgo-specific hydrodynamical sloshing simulations. Here we focus on a Spitzer-like temperature dependent viscosity as a mechanism to suppress the KHI, but discuss the alternative mechanisms in detail. We identify the CF at 90 kpc north and north-east of the Virgo center as the best location in the cluster to observe a possible KHI suppression. For viscosities $\gtrsim$ 10% of the Spitzer value KHIs at this CF are suppressed. We describe in detail the observable signatures at low and high viscosities, i.e. in the presence or absence of KHIs. We find indications for a low ICM viscosity in archival XMM-Newton data and demonstrate the detectability of the predicted features in deep Chandra observations.Comment: Accepted for ApJ; 15 pages, 11 figures. A movie can be found here: http://www.hs.uni-hamburg.de/DE/Ins/Per/Roediger/research.html#Virgo-viscou

Numerical simulation of liquid sloshing in a partially filled container with inclusion of compressibility effects

A numerical scheme of study is developed to model compressible two-fluid flows simulating liquid sloshing in a partially filled tank. For a two-fluid system separated by an interface as in the case of sloshing, not only a Mach-uniform scheme is required, but also an effective way to eliminate unphysical numerical oscillations near the interface. By introducing a preconditioner, the governing equations expressed in terms of primitive variables are solved for both fluids (i.e. water, air, gas etc.) in a unified manner. In order to keep the interface sharp and to eliminate unphysical numerical oscillations in unsteady fluid flows, the non-conservative implicit Split Coefficient Matrix Method (SCMM) is modified to construct a flux difference splitting scheme in the dual time formulation. The proposed numerical model is evaluated by comparisons between numerical results and measured data for sloshing in an 80% filled rectangular tank excited at resonance frequency. Through similar comparisons, the investigation is further extended by examining sloshing flows excited by forced sway motions in two different rectangular tanks with 20% and 83% filling ratios. These examples demonstrate that the proposed method is suitable to capture induced free surface waves and to evaluate sloshing pressure loads acting on the tank walls and ceiling

Stirring Up the Pot: Can Cooling Flows In Galaxy Clusters Be Quenched By Gas Sloshing?

X-ray observations of clusters of galaxies reveal the presence of edges in surface brightness and temperature, known as "cold fronts". In relaxed clusters with cool cores, these commonly observed edges have been interpreted as evidence for the "sloshing" of the core gas in the cluster's gravitational potential. Such sloshing may provide a source of heat to the cluster core by mixing hot gas from the cluster outskirts with the cool core gas. Using high-resolution $N$-body/Eulerian hydrodynamics simulations, we model gas sloshing in galaxy clusters initiated by mergers with subclusters. The simulations include merger scenarios with gas-filled and gasless subclusters. The effect of changing the viscosity of the intracluster medium is also explored. We find that sloshing can facilitate heat inflow to the cluster core, provided that there is a strong enough disturbance. In adiabatic simulations, we find that sloshing can raise the entropy floor of the cluster core by nearly an order of magnitude in the strongest cases. If the ICM is viscous, the mixing of gases with different entropies is decreased and consequently the heat flux to the core is diminished. In simulations where radiative cooling is included, we find that though eventually a cooling flow develops, sloshing can prevent the significant buildup of cool gas in the core for times on the order of a Gyr for small disturbances and a few Gyr for large ones. If repeated encounters with merging subclusters sustain the sloshing of the central core gas as is observed, this process can provide a relatively steady source of heat to the core, which can help to prevent a significant cooling flow.Comment: 22 pages, 26 figures, "emulateapj" format. The version accepted by ApJ, with proof correction

Cluster Core Heating from Merging Subclusters

Though feedback from central active galactic nuclei provides an attractive solution to the problem of overcooling in galaxy cluster cores, another possible source of heating may come from ``sloshing'' of the cluster core gas initiated by mergers. We present a set of simulations of galaxy cluster mergers with subclusters in order to determine the amount of heating provided by the mechanism of sloshing, exploring a parameter space over mass ratio, impact parameter, and viscosity of the intracluster medium (ICM). Our results show that for sloshing caused by mergers with gasless subclusters cooling may be partially offset by heating from sloshing, but this mechanism is less effective if the ICM is viscous.Comment: To appear in proceedings of "The Monster's Fiery Breath", Eds. Sebastian Heinz & Eric Wilcots (AIP conference series). 4 pages, 3 figure

Eigenvalue bounds of mixed Steklov problems

We study bounds on the Riesz means of the mixed Steklov-Neumann and Steklov-Dirichlet eigenvalue problem on a bounded domain $\Omega$ in $\mathbb{R}^n$. The Steklov-Neumann eigenvalue problem is also called the sloshing problem. We obtain two-term asymptotically sharp lower bounds on the Riesz means of the sloshing problem and also provide an asymptotically sharp upper bound for the Riesz means of mixed Steklov-Dirichlet problem. The proof of our results for the sloshing problem uses the average variational principle and monotonicity of sloshing eigenvalues. In the case of Steklov-Dirichlet eigenvalue problem, the proof is based on a well-known bound on the Riesz means of the Dirichlet fractional Laplacian and an inequality between the Dirichlet and Navier fractional Laplacian. The two-term asymptotic results for the Riesz means of mixed Steklov eigenvalue problems are discussed in the appendix which in particular show the asymptotic sharpness of the bounds we obtain.Comment: An appendix by by F. Ferrulli and J. Lagac\'e is added; some changes in the introduction are mad

What fraction of the density fluctuations in the Perseus cluster core is due to gas sloshing rather than AGN feedback?

Deep Chandra observations of the core of the Perseus cluster show a plethora of complex structure. It has been found that when the observed density fluctuations in the intracluster medium are converted into constraints on AGN induced turbulence, the resulting turbulent heating rates are sufficient to balance cooling locally throughout the central 220kpc. However while the signatures of AGN feedback (inflated bubbles) dominate the central 60kpc in X-ray images, beyond this radius the intracluster medium is increasingly shaped by the effects of gas sloshing, which can also produce subtle variations in X-ray surface brightness. We use mock Chandra observations of gas sloshing simulations to investigate what fraction of the observed density fluctuations in the core of the Perseus galaxy cluster may originate from sloshing rather than AGN induced feedback. Outside 60kpc, we find that the observed level of the density fluctuations is broadly consistent with being produced by sloshing alone. If this is the case, AGN-generated turbulence is likely to be insufficient in combating cooling outside 60kpc.Comment: 9 pages, 5 figures, accepted for publication in MNRA

Damping of liquid sloshing by foams: from everyday observations to liquid transport

We perform experiments on the sloshing dynamics of liquids in a rectangular container submitted to an impulse. We show that when foam is placed on top of the liquid the oscillations of the free interface are significantly damped. The ability to reduce sloshing and associated splashing could find applications in numerous industrial processes involving liquid transport.Comment: Accepted for publication in Journal of Visualizatio

Large scale gas sloshing out to half the virial radius in the strongest cool core REXCESS galaxy cluster, RXJ2014.8-2430

We search the cool core galaxy clusters in the REXCESS sample for evidence of large scale gas sloshing, and find clear evidence for sloshing in RXJ2014.8-2430, the strongest cool core cluster in the REXCESS cluster sample. The residuals of the surface brightness distribution from the azimuthal average for RXJ2014 show a prominent swirling excess feature extending out to an abrupt surface brightness discontinuity at 800 kpc from the cluster core (half the virial radius) to the south, which the XMM-Newton observations confirm to be cold, low entropy gas. The gas temperature is significantly higher outside this southern surface brightness discontinuity, indicating that this is a cold front 800 kpc from the cluster core. Chandra observations of the central 200 kpc show two clear younger cold fronts on opposite sides of the cluster. The scenario appears qualitatively consistent with simulations of gas sloshing due to minor mergers which raise cold, low entropy gas from the core to higher radius, resulting in a swirling distribution of opposing cold fronts at increasing radii. However the scale of the observed sloshing is much larger than that which has been simulated at present, and is similar to the large scale sloshing recently observed in the Perseus cluster and Abell 2142.Comment: 5 pages, 5 figures. Accepted for publication in MNRA

Candidates for a possible third-generation gravitational wave detector: comparison of ring-Sagnac and sloshing-Sagnac speedmeter interferometers

Speedmeters are known to be quantum non-demolition devices and, by potentially providing sensitivity beyond the standard quantum limit, become interesting for third generation gravitational wave detectors. Here we introduce a new configuration, the sloshing-Sagnac interferometer, and compare it to the more established ring-Sagnac interferometer. The sloshing-Sagnac interferometer is designed to provide improved quantum noise limited sensitivity and lower coating thermal noise than standard position meter interferometers employed in current gravitational wave detectors. We compare the quantum noise limited sensitivity of the ring-Sagnac and the sloshing-Sagnac interferometers, in the frequency range, from 5 Hz to 100 Hz, where they provide the greatest potential benefit. We evaluate the improvement in terms of the unweighted noise reduction below the standard quantum limit, and by finding the range up to which binary black hole inspirals may be observed. The sloshing-Sagnac was found to give approximately similar or better sensitivity than the ring-Sagnac in all cases. We also show that by eliminating the requirement for maximally-reflecting cavity end mirrors with correspondingly-thick multi-layer coatings, coating noise can be reduced by a factor of approximately 2.2 compared to conventional interferometers