Turbulence In Galaxy Clusters Research Articles

Quasi-two-dimensionality of three-dimensional, magnetically dominated, decaying turbulence

Decaying magnetohydrodynamic (MHD) turbulence is important in various astrophysical contexts, including early universe magnetic fields, star formation, turbulence in galaxy clusters, magnetospheres and solar corona. Previously known in the nonhelical case of magnetically dominated decaying turbulence, we show that magnetic reconnection is important also in the fully helical case and is likely the agent responsible for the inverse transfer of energy. Again, in the fully helical case, we find that there is a similarity in power law decay exponents in both 2.5D and 3D simulations. To understand this intriguing similarity, we investigate the possible quasi-two-dimensionalization of the 3D system. We perform Minkowski functional analysis and find that the characteristic length scales of a typical magnetic structure in the system are widely different, suggesting the existence of local anisotropies. Finally, we provide a quasi-two-dimensional hierarchical merger model which recovers the relevant power law scalings. In the nonhelical case, we show that a helicity-based invariant cannot constrain the system, and the best candidate is still anastrophy or vector potential squared, which is consistent with the quasi-two-dimensionalization of the system.

Turbulent heating in a stratified medium

ABSTRACT There is considerable evidence for widespread subsonic turbulence in galaxy clusters, most notably from Hitomi. Turbulence is often invoked to offset radiative losses in cluster cores, both by direct dissipation and by enabling turbulent heat diffusion. However, in a stratified medium, buoyancy forces oppose radial motions, making turbulence anisotropic. This can be quantified via the Froude number Fr, which decreases inward in clusters as stratification increases. We exploit analogies with MHD turbulence to show that wave–turbulence interactions increase cascade times and reduce dissipation rates ϵ ∝ Fr. Equivalently, for a given energy injection/dissipation rate ϵ, turbulent velocities u must be higher compared to Kolmogorov scalings. High-resolution hydrodynamic simulations show excellent agreement with the ϵ ∝ Fr scaling, which sets in for Fr ≲ 0.1. We also compare previously predicted scalings for the turbulent diffusion coefficient D ∝ Fr2 and find excellent agreement, for Fr ≲ 1. However, we find a different normalization, corresponding to stronger diffusive suppression by more than an order of magnitude. Our results imply that turbulent diffusion is more heavily suppressed by stratification, over a much wider radial range, than turbulent dissipation. Thus, the latter potentially dominates. Furthermore, this shift implies significantly higher turbulent velocities required to offset cooling, compared to previous models. These results are potentially relevant to turbulent metal diffusion in the galaxy groups and clusters (which is likewise suppressed), and to planetary atmospheres.

Magneto-thermal instability in galaxy clusters – I. Theory and two-dimensional simulations

ABSTRACT Determining the origin of turbulence in galaxy clusters, and quantifying its transport of heat, is an outstanding problem, with implications for our understanding of their thermodynamic history and structure. As the dilute plasma of the intracluster medium (ICM) is magnetized, heat and momentum travel preferentially along magnetic field lines. This anisotropy triggers a class of buoyancy instabilities that destabilize the ICM, and whose turbulent motions can augment or impede heat transport. We focus on the magneto-thermal instability (MTI), which may be active in the periphery of galaxy clusters. We aim to take a fresh look at the problem and construct a general theory that explains the MTI saturation mechanism and provides scalings and estimates for the turbulent kinetic energy, magnetic energy, and heat flux. We simulate MTI turbulence with a Boussinesq code, snoopy, which, in contrast to previous work, allows us to perform an extensive sampling of the parameter space. In two dimensions the saturation mechanism involves an inverse cascade that carries kinetic energy from the short MTI injection scales to larger scales, where it is arrested by the stable entropy stratification; at a characteristic ‘buoyancy scale’, the energy is dumped into large-scale g-modes, which subsequently dissipate. Consequently, the entropy stratification sets an upper limit on the size and strength of turbulent eddies. Meanwhile, the MTI conveys a substantial fraction of heat, despite the tangled geometry of the magnetic field. In a companion paper, these results are extended to three-dimensional flows, and compared to observations of real clusters.

Signature of Supersonic Turbulence in Galaxy Clusters Revealed by AGN-driven Hα Filaments

The hot intracluster medium (ICM) is thought to be quiescent with low observed velocity dispersions. Surface brightness fluctuations of the ICM also suggest that its turbulence is subsonic with a Kolmogorov scaling relation, indicating that the viscosity is suppressed and the kinetic energy cascades to small scales unscathed. However, recent observations of the cold gas filaments in galaxy clusters find that the scaling relations are steeper than that of the hot plasma, signaling kinetic energy losses and the presence of supersonic flows. In this work we use high-resolution simulations to explore the turbulent velocity structure of the cold filaments at the cores of galaxy clusters. Our results indicate that supersonic turbulent structures can be “frozen” in the cold gas that cools and fragments out of a fast, ∼107 K outflow driven by the central active galactic nucleus (AGN), when the radiative cooling time is shorter than the dynamical sound-crossing time. After the cold gas formation, however, the slope of the velocity structure function (VSF) flattens significantly over short, ∼10 Myr timescales. The lack of flattened VSF in observations of Hα filaments indicates that the Hα-emitting phase is short-lived for the cold gas in galaxy clusters. On the other hand, the ubiquity of supersonic turbulence revealed by observed filaments strongly suggests that supersonic outflows are an integral part of AGN–ICM interaction, and that AGN activity plays a crucial role at driving turbulence in galaxy clusters.

Exploring the relation between turbulent velocity and density fluctuations in the stratified intracluster medium

Context. The dynamics of the intracluster medium (ICM) is affected by turbulence driven by several processes, such as mergers, accretion and feedback from active galactic nuclei. Aims. X-ray surface brightness fluctuations have been used to constrain turbulence in galaxy clusters. Here, we use simulations to further investigate the relation between gas density and turbulent velocity fluctuations, with a focus on the effect of the stratification of the ICM. Methods. In this work, we studied the turbulence driven by hierarchical accretion by analysing a sample of galaxy clusters simulated with the cosmological code ENZO. We used a fixed scale filtering approach to disentangle laminar from turbulent flows. Results. In dynamically perturbed galaxy clusters, we found a relation between the root mean square of density and velocity fluctuations, albeit with a different slope than previously reported. The Richardson number is a parameter that represents the ratio between turbulence and buoyancy, and we found that this variable has a strong dependence on the filtering scale. However, we could not detect any strong relation between the Richardson number and the logarithmic density fluctuations, in contrast to results by recent and more idealised simulations. In particular, we find a strong effect from radial accretion, which appears to be the main driver for the gas fluctuations. The ubiquitous radial bias in the dynamics of the ICM suggests that homogeneity and isotropy are not always valid assumptions, even if the turbulent spectra follow Kolmogorov’s scaling. Finally, we find that the slope of the velocity and density spectra are independent of cluster-centric radii.

Troubled cosmic flows: turbulence, enstrophy, and helicity from the assembly history of the intracluster medium

ABSTRACT Both simulations and observations have shown that turbulence is a pervasive phenomenon in cosmic scenarios, yet it is particularly difficult to model numerically due to its intrinsically multiscale character which demands high resolutions. Additionally, turbulence is tightly connected to the dynamical state and the formation history of galaxies and galaxy clusters, producing a diverse phenomenology which requires large samples of such structures to attain robust conclusions. In this work, we use an adaptive mesh refinement (AMR) cosmological simulation to explore the generation and dissipation of turbulence in galaxy clusters, in connection to its assembly history. We find that major mergers, and more generally accretion of gas, is the main process driving turbulence in the intracluster medium. We have especially focused on solenoidal turbulence, which can be quantified through enstrophy. Our results seem to confirm a scenario for its generation which involves baroclinicity and compression at the external (accretion) and internal (merger) shocks, followed by vortex stretching downstream of them. We have also looked at the infall of mass to the cluster beyond its virial boundary, finding that gas follows trajectories with some degree of helicity, as it has already developed some vorticity in the external shocks.

A Multifiltering Study of Turbulence in a Large Sample of Simulated Galaxy Clusters

Abstract We present results from a large set of N-body/smoothed particle hydrodynamics (SPH) hydrodynamical cluster simulations aimed at studying the statistical properties of turbulence in the intracluster medium (ICM). The numerical hydrodynamical scheme employs an SPH formulation in which gradient errors are strongly reduced by using an integral approach. We consider both adiabatic and radiative simulations. We construct cluster subsamples according to the cluster dynamical status or gas physical modeling, from which we extract small-scale turbulent velocities obtained by applying different multiscale filtering methods to cluster velocities. The velocity power spectra of nonradiative relaxed clusters are mostly solenoidal and exhibit a peak at wavenumbers set by injection scales ≃r 200/10; at higher wavenumbers, the spectra are steeper than Kolmogorov. Cooling runs are distinguished by much shallower spectra, a feature which we interpret as the injection of turbulence at small scales due to the interaction of compact cool gas cores with the ICM. Turbulence in galaxy clusters is then characterized by multiple injection scales, with the small-scale driving source acting in addition to the large-scale injection mechanisms. Cooling runs of relaxed clusters exhibit enstrophy profiles with a power-law behavior over more than two decades in radius and a turbulent-to-thermal energy ratio ≲1%. In accordance with Hitomi observations, in the core of a highly relaxed cluster, we find a low level of gas motions. In addition, the estimated cluster radial profile of the sloshing oscillation period is in very good agreement with recent Fornax measurements, with the associated Froude number satisfying Fr ≲ 0.1 within r/r 200 ≲ 0.1. Our findings suggest that in cluster cores, ICM turbulence approaches a stratified anisotropic regime, with weak stirring motions dominated by gravity buoyancy forces and strongly suppressed along the radial direction. We conclude that turbulent heating cannot be considered the main heating source in cluster cores.

Constraining Gas Motions in the Intra-Cluster Medium

The detailed velocity structure of the diffuse X-ray emitting intra-cluster medium (ICM) remains one of the last missing key ingredients in understanding the microphysical properties of these hot baryons and constraining our models of the growth and evolution of structure on the largest scales in the Universe. Direct measurements of the gas velocities from the widths and shifts of X-ray emission lines were recently provided for the central region of the Perseus Cluster of galaxies by $Hitomi$, and upcoming high-resolution X-ray microcalorimeters onboard $XRISM$ and $Athena$ are expected to extend these studies to many more systems. In the mean time, several other direct and indirect methods have been proposed for estimating the velocity structure in the ICM, ranging from resonant scattering to X-ray surface brightness fluctuation analysis, the kinematic Sunyaev-Zeldovich effect, or using optical line emitting nebulae in the brightest cluster galaxies as tracers of the motions of the ambient plasma. Here, we review and compare the existing estimates of the velocities of the hot baryons, as well as the various overlapping physical processes that drive motions in the ICM, and discuss the implications of these measurements for constraining the viscosity and identifying the source of turbulence in clusters of galaxies.

MAPPING THE GAS TURBULENCE IN THE COMA CLUSTER: PREDICTIONS FOR ASTRO-H

ABSTRACT Astro-H will be able for the first time to map gas velocities and detect turbulence in galaxy clusters. One of the best targets for turbulence studies is the Coma cluster, due to its proximity, absence of a cool core, and lack of a central active galactic nucleus. To determine what constraints Astro-H will be able to place on the Coma velocity field, we construct simulated maps of the projected gas velocity and compute the second-order structure function, an analog of the velocity power spectrum. We vary the injection scale, dissipation scale, slope, and normalization of the turbulent power spectrum, and apply measurement errors and finite sampling to the velocity field. We find that even with sparse coverage of the cluster, Astro-H will be able to measure the Mach number and the injection scale of the turbulent power spectrum—the quantities determining the energy flux down the turbulent cascade and the diffusion rate for everything that is advected by the gas (metals, cosmic rays, etc.). Astro-H will not be sensitive to the dissipation scale or the slope of the power spectrum in its inertial range, unless they are outside physically motivated intervals. We give the expected confidence intervals for the injection scale and the normalization of the power spectrum for a number of possible pointing configurations, combining the structure function and velocity dispersion data. Importantly, we also determine that measurement errors on the line shift will bias the velocity structure function upward, and show how to correct this bias.

Developed turbulence and nonlinear amplification of magnetic fields in laboratory and astrophysical plasmas

The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe.

Chemical Enrichment RGS cluster Sample (CHEERS): Constraints on turbulence

Feedback from AGN, galactic mergers, and sloshing are thought to give rise to turbulence, which may prevent cooling in clusters. We aim to measure the turbulence in clusters of galaxies and compare the measurements to some of their structural and evolutionary properties. It is possible to measure the turbulence of the hot gas in clusters by estimating the velocity widths of their X-ray emission lines. The RGS Spectrometers aboard XMM-Newton are currently the only instruments provided with sufficient effective area and spectral resolution in this energy domain. We benefited from excellent 1.6Ms new data provided by the CHEERS project. The new observations improve the quality of the archival data and allow us to place constraints for some clusters, which were not accessible in previous work. One-half of the sample shows upper limits on turbulence less than 500km/s. For several sources, our data are consistent with relatively strong turbulence with upper limits on the velocity widths that are larger than 1000km/s. The NGC507 group of galaxies shows transonic velocities, which are most likely associated with the merging phenomena and bulk motions occurring in this object. Where both low- and high-ionization emission lines have good enough statistics, we find larger upper limits for the hot gas, which is partly due to the different spatial extents of the hot and cool gas phases. Our upper limits are larger than the Mach numbers required to balance cooling, suggesting that dissipation of turbulence may prevent cooling, although other heating processes could be dominant. The systematics associated with the spatial profile of the source continuum make this technique very challenging, though still powerful, for current instruments. The ASTRO-H and Athena missions will revolutionize the velocity estimates and discriminate between different spatial regions and temperature phases.

Particle reacceleration by compressible turbulence in galaxy clusters: effects of a reduced mean free path

Direct evidence for in situ particle acceleration mechanisms in the inter-galactic-medium (IGM) is provided by the diffuse Mpc--scale synchrotron emissions observed from galaxy clusters. It has been proposed that MHD turbulence, generated during cluster-cluster mergers, may be a source of particle reacceleration in the IGM. Calculations of turbulent acceleration must account self-consistently for the complex non--linear coupling between turbulent waves and particles. This has been calculated in some detail under the assumption that turbulence interacts in a collisionless way with the IGM. In this paper we explore a different picture of acceleration by compressible turbulence in galaxy clusters, where the interaction between turbulence and the IGM is mediated by plasma instabilities and maintained collisional at scales much smaller than the Coulomb mean free path. In this regime most of the energy of fast modes is channeled into the reacceleration of relativistic particles and the acceleration process approaches a universal behaviour being self-regulated by the back-reaction of the accelerated particles on turbulence itself. Assuming that relativistic protons contribute to several percent (or less) of the cluster energy, consistent with the FERMI observations of nearby clusters, we find that compressible turbulence at the level of a few percent of the thermal energy can reaccelerate relativistic electrons at GeV energies, that are necessary to explain the observed diffuse radio emission in the form of giant radio halos.

Magnetic turbulence in clusters of galaxies

AbstractGalaxy clusters are large laboratories for magnetic plasma turbulence and therefore permit us to confront our theoretical concepts of magnetogenesis with detailed observations. Magnetic turbulence in clusters can be studied via the radio-synchrotron emission from the intra-cluster medium in the form of cluster radio relics and halos. The power spectrum of turbulent magnetic fields can be examined via Faraday rotation analysis of extended radio sources. In case of the Hydra A cool core, the observed magnetic spectrum can be understood in terms of a turbulence-mediated feedback loop between gas cooling and the jet activity of the central galaxy. Finally, methods to measure higher-order statistics of the magnetic field using Stokes-parameter correlations are discussed, which permit us to determine the power spectrum of the magnetic tension force. This fourth-order statistical quantity offers a way to discriminate between different magnetic turbulence scenarios and different field structures using radio polarimetric observations.

Subgrid Modeling of AGN‐driven Turbulence in Galaxy Clusters

Hot, underdense bubbles powered by active galactic nuclei (AGN) are likely to play a key role in halting catastrophic cooling in the centers of cool-core galaxy clusters. We present three-dimensional simulations that capture the evolution of such bubbles, using an adaptive-mesh hydrodynamic code, FLASH3, to which we have added a subgrid model of turbulence and mixing. While pure-hydro simulations indicate that AGN bubbles are disrupted into resolution-dependent pockets of underdense gas, proper modeling of subgrid turbulence indicates that this a poor approximation to a turbulent cascade that continues far beyond the resolution limit. Instead, Rayleigh-Taylor instabilities act to effectively mix the heated region with its surroundings, while at the same time preserving it as a coherent structure, consistent with observations. Thus bubbles are transformed into hot clouds of mixed material as they move outwards in the hydrostatic intracluster medium (ICM), much as large airbursts lead to a distinctive ``mushroom cloud'' structure as they rise in the hydrostatic atmosphere of Earth. Properly capturing the evolution of such clouds has important implications for many ICM properties. In particular, it significantly changes the impact of AGN on the distribution of entropy and metals in cool-core clusters such as Perseus.

Compressible turbulence in galaxy clusters: physics and stochastic particle re-acceleration

We attempt to explain the non-thermal emission arising from galaxy clusters as a result of the re-acceleration of electrons by compressible turbulence induced by cluster mergers. On the basis of the available observational facts we put forward a simplified model of turbulence in clusters of galaxies focusing our attention on the compressible motions. In our model intracluster medium (ICM) is represented by a high-beta plasma in which turbulent motions are driven at large scales. The corresponding injection velocities are higher than the Alfvén velocity. As a result, the turbulence is approximately isotropic up to the scale at which the turbulent velocity gets comparable with the Alfvén velocity. These motions are most important for the energetic particle acceleration, but at the same time they are subjected to most of the plasma damping. Under the hypothesis that turbulence in the ICM is highly super-Alfvénic the magnetic field is passively advected and the field lines are bended on scales smaller than that of the classical, unmagnetized, ion–ion mean free path. This affects ion diffusion and the strength of the effective viscosity. Under these conditions the bulk of turbulence in hot (5–10 keV temperature) galaxy clusters is likely to be dissipated at collisionless scales via resonant coupling with thermal and fast particles. We use collisionless physics to derive the amplitude of the different components of the energy of the compressible modes, and review and extend the treatment of plasma damping in the ICM. We calculate the acceleration of both protons and electrons taking into account both transit time damping acceleration and non-resonant acceleration by large-scale compressions. We find that relativistic electrons can be re-accelerated in the ICM up to energies of several GeV provided that the rms velocity of the compressible turbulent-eddies is is the sound speed in the ICM. We find that under typical conditions ≈2–5 per cent of the energy flux of the cascading of compressible motions injected at large scales goes into the acceleration of fast particles and that this may explain the observed non-thermal emission from merging galaxy clusters.

Particle acceleration in galaxy clusters via MHD turbulence

AbstractSynchrotron emission extended on Mpc scales is detected in a number of massive galaxy clusters. The hot ICM becomes a collisionless–turbulent plasma on scales below 10–50 kpc and thus turbulence may accelerate the relativistic particles radiating in these sources. In this paper the injection, cascading and dissipation of hydro and MHD turbulence in galaxy clusters are briefly discussed. We also discuss the two most relevant mechanisms for stochastic particle acceleration produced by MHD turbulence in galaxy clusters, namely Alfvénic acceleration and Transit Time Damping acceleration from fast modes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Turbulence in clusters of galaxies and X-ray line profiles

Large-scale bulk motions and hydrodynamic turbulence in the intergalactic gas that fills clusters of galaxies significantly broaden X-ray emission lines. For lines of heavy ions (primarily helium-like and hydrogen-like iron ions), the hydrodynamic broadening is appreciably larger than the thermal broadening. Since clusters of galaxies have a negligible optical depth for resonant scattering in the forbidden and intercombination lines of these ions, these lines are not additionally broadened. At the same time, they are very intense, which allows deviations of the spectrum from the Gaussian spectrum in the line wings to be investigated. The line shape proves to be an important indicator of bulk hydrodynamic processes. Doppler probing of turbulence becomes possible, because the cryogenic detectors of the X-ray observatories now ready for launch and being planned will have a high energy resolution (from 5 eV for ASTRO-E2 to 1–2 eV for Constellation-X and XEUS). We use the spectral representation of a Kolmogorov cascade in the inertial range to calculate the characteristic shapes of radiation lines. Significant deviations in the line profiles from the Gaussian profile (shape asymmetry, additional peaks, sharp breaks in the exponential tails) are expected for large-scale turbulence. The kinematic SZ effect and the X-ray line profiles carry different information about the hydrodynamic velocity distribution in clusters of galaxies and complement each other, allowing the redshift, the peculiar velocity of the cluster, and the bulk velocity dispersion to be separated.

Nonthermal Emissions from Particles Accelerated by Turbulence in Clusters of Galaxies

We consider nonthermal emission from clusters of galaxies produced by particle acceleration by resonant scattering of Alfv\'{e}n waves driven by fluid turbulence through the Lighthill mechanism in the intracluster medium. We assume that the turbulence is driven by cluster mergers. We find that the resonant Alfv\'{e}n waves can accelerate electrons up to \gamma ~10^5 through resonant scattering. We also find that the turbulent resonant acceleration can give enough energy to electrons to produce the observed diffuse radio relic emission from clusters if the clusters have a pool of electrons with \gamma ~10^3. This mechanism can also explain the observed hard X-ray emission from clusters if the magnetic field in a cluster is small enough (~< \mu G) or the fluid turbulence spectrum is flatter than the Kolmogorov law. The fluid turbulence could be observed with Astro-E2 in the regions where diffuse radio emission is observed. Although non-gravitational heating before cluster formation (preheating) steepens a relation between radio luminosity and X-ray temperature, our predicted relation is still flatter than the observed one.

Generation and Implications of Post-Merger Turbulence in Clusters of Galaxies

Observations in X-ray and optical suggest that mergers of sub-clusters with galaxy clusters are quite common (for Coma see e.g., White et al. 1993; Colless &amp; Dunn 1996; Ishizaka &amp; Mineshige 1996). A merger leads to violent relaxation of the dissipationless dark matter resulting in a time-dependent gravitational potential. This in turn generates large-scale flows and shocks in the collisional baryonic intracluster gas (Takizawa &amp; Mineshige 1997). Both the large scale flows and the shocks will excite turbulence in the gas. We focus here on turbulence generated by shocks, which is less dependent on the specifics of the merger. This paper is based on a more detailed work (Goldman 1997).