Turbulence In Intracluster Medium Research Articles

Mapping the intracluster medium in the era of high-resolution X-ray spectroscopy

ABSTRACT High-resolution spectroscopy in soft X-rays will open a new window to map multiphase gas in galaxy clusters and probe physics of the intracluster medium (ICM), including chemical enrichment histories, circulation of matter and energy during large-scale structure evolution, stellar and black hole feedback, halo virialization, and gas mixing processes. An eV-level spectral resolution, large field of view, and effective area are essential to separate cluster emissions from the Galactic foreground and efficiently map the cluster outskirts. Several mission concepts that meet these criteria have been proposed recently, e.g. LEM, HUBS, and Super DIOS. This theoretical study explores what information on ICM physics could be recovered with such missions and the associated challenges. We emphasize the need for a comprehensive comparison between simulations and observations to interpret the high-resolution spectroscopic observations correctly. Using Line Emission Mapper (LEM) characteristics as an example, we demonstrate that it enables the use of soft X-ray emission lines (e.g. O vii/viii and Fe-L complex) from the cluster outskirts to measure the thermodynamic, chemical, and kinematic properties of the gas up to r200 and beyond. By generating mock observations with full backgrounds, analysing their images/spectra with observational approaches, and comparing the recovered characteristics with true ones from simulations, we develop six key science drivers for future missions, including the exploration of multiphase gas in galaxy clusters (e.g. temperature fluctuations, phase-space distributions), metallicity, ICM gas bulk motions and turbulence power spectra, ICM-cosmic filament interactions, and advances for cluster cosmology.

Physical cool-core condensation radius in massive galaxy clusters

Aims. We investigate the properties of cool cores in an optimally selected sample of 37 massive and X-ray-bright galaxy clusters, with regular morphologies, observed with Chandra. We started by measuring the density, temperature, and abundance radial profiles of their intracluster medium (ICM). From these independent quantities, we computed the cooling (tcool), free-fall (tff), and turbulence (teddy) timescales as a function of radius. Methods. By requiring the profile-crossing condition, tcool/teddy = 1, we measured the cool-core condensation radius, Rccc, within which the balancing feeding and feedback processes generate the turbulent condensation rain and related chaotic cold accretion (CCA). We also constrained the complementary (quenched) cooling flow radius, Rqcf, obtained via the condition tcool = 25 × tff, that encompasses the region of thermally unstable cooling. Results. We find that in our our massive cluster sample and in the limited redshift range considered (1.3 × 1014 < M500 < 16.6 × 1014 M⊙, 0.03 < z < 0.29), the distribution of Rccc peaks at ∼0.01 r500 and the entire range remains below ∼0.07 r500, with a very weak increase with redshift and no dependence on the cluster mass. We find that Rqcf is typically three times larger than Rccc, with a wider distribution, and growing more slowly along Rccc, according to an average relation Rqcf∝ Rccc0.46, with a large intrinsic scatter. Conclusions. We suggest that this sublinear relation can be understood as an effect of the micro rain of pockets of cooled gas flickering in the turbulent ICM, whose dynamical and thermodynamical properties are referred to as “macro weather”. Substituting the classical ad hoc cool-core radius R7.7 Gyr, we propose that Rqcf is an indicator of the size of global cool cores tied to the long-term macro weather, with the inner Rccc closely tracing the effective condensation rain and chaotic cold accretion (CCA) zone that feeds the central supermassive black hole (SMBH).

The nature of the motions of multiphase filaments in the centers of galaxy clusters

The intracluster medium (ICM) in the centers of galaxy clusters is heavily influenced by the “feedback” from supermassive black holes (SMBHs). Feedback can drive turbulence in the ICM and turbulent dissipation can potentially be an important source of heating. Due to the limited spatial and spectral resolutions of X-ray telescopes, direct observations of turbulence in the hot ICM have been challenging. Recently, we developed a new method to measure turbulence in the ICM using multiphase filaments as tracers. These filaments are ubiquitous in cluster centers and can be observed at very high resolution using optical and radio telescopes. We study the kinematics of the filaments by measuring their velocity structure functions (VSFs) over a wide range of scales in the centers of ∼10 galaxy clusters. We find features of the VSFs that correlate with the SMBHs activities, suggesting that SMBHs are the main driver of gas motions in the centers of galaxy clusters. In all systems, the VSF is steeper than the classical Kolmogorov expectation and the slopes vary from system to system. One theoretical explanation is that the VSFs we have measured so far mostly reflect the motion of the driver (jets and bubbles) rather than the cascade of turbulence. We show that in Abell 1795, the VSF of the outer filaments far from the SMBH flattens on small scales to a Kolmogorov slope, suggesting that the cascade is only detectable farther out with the current telescope resolution. The level of turbulent heating computed at small scales is typically an order of magnitude lower than that estimated at the driving scale. Even though SMBH feedback heavily influences the kinematics of the ICM in cluster centers, the level of turbulence it drives is rather low, and turbulent heating can only offset ≲ 10% of the cooling loss, consistent with the findings of numerical simulations.

Turbulence in the tail of a jellyfish galaxy

ABSTRACT When galaxies move through the intracluster medium (ICM) inside galaxy clusters, the ram pressure of the ICM can strip the gas from galaxies. The stripped gas forms tails on the trailing side. These galaxies are hence dubbed ‘jellyfish galaxies’. ESO 137-001 is a quintessential jellyfish galaxy located in the nearest rich cluster, the Norma cluster. Its spectacular multiphase tail has complex morphology and kinematics both from the imprinted galaxy’s interstellar medium (ISM) and as a result of the interactions between the stripped gas and the surrounding hot plasma, mediated by radiative cooling and magnetic fields. We study the kinematics of the multiphase tail using high-resolution observations of the ionized and the molecular gas in the entire structure. We calculate the velocity structure functions in moving frames along the tail and find that turbulence driven by Kelvin–Helmholtz (KH) instability quickly overwhelms the original ISM turbulence and saturates at ∼30 kpc. There is also a hint that the far end of the tail has possibly started to inherit pre-existing large-scale ICM turbulence likely caused by structure formation. Turbulence measured by the molecular gas is generally consistent with that measured by the ionized gas in the tail but has a slightly lower amplitude. Most of the measured turbulence is below the mean free path of the hot ICM (∼11 kpc). Using warm/cool gas as a tracer of the hot ICM, we find that the isotropic viscosity of the hot plasma must be suppressed below 0.01 per cent Spitzer level.

XMM-Newton view of the shock heating in an early merging cluster, CIZA J1358.9−4750

Abstract CIZA J1358.9−4750 is a nearby galaxy cluster in the early phase of a major merger. The two-dimensional temperature map using XMM-Newton EPIC-PN observation confirms the existence of a high-temperature region, which we call the “hot region,” in the “bridge region” connecting the two clusters. The ∼500 kpc wide region between the south-east and north-west boundaries also has higher pseudo-pressure compared to the unshocked regions, suggesting the existence of two shocks. The southern shock front is clearly visible in the X-ray surface brightness image and has already been reported by Kato et al. (2015, PASJ, 67, 71). The northern one, on the other hand, is newly discovered. To evaluate their Mach number, we constructed a three-dimensional toy merger model with overlapping shocked and unshocked components in the line of sight. The unshocked and pre-shock intracluster medium (ICM) conditions are estimated based on those outside the interacting bridge region, assuming point symmetry. The hot-region spectra are modeled with two-temperature thermal components, assuming that the shocked condition follows the Rankin–Hugoniot relation with the pre-shock condition. As a result, the shocked region is estimated to have a line-of-sight depth of ∼1 Mpc with a Mach number of ∼1.3 in the south-east shock and ∼1.7 in the north-west shock. The age of the shock waves is estimated to be ∼260 Myr. This three-dimensional merger model is consistent with the Sunyaev–Zel’dovich signal obtained using the Planck observation within the cosmic microwave background fluctuations. The total flow of the kinetic energy of the ICM through the south-east shock was estimated to be ∼2.2 × 1042 erg s−1. Assuming that $10\%$ of this energy is converted into ICM turbulence, the line–of–sight velocity dispersion is calculated to be ∼200 km s−1, which is basically resolvable via upcoming high spectral resolution observations.

Magneto-thermal instability in galaxy clusters – II. three-dimensional simulations

ABSTRACT In the intracluster medium (ICM) of galaxies, exchanges of heat across magnetic field lines are strongly suppressed. This anisotropic heat conduction, in the presence of a large-scale temperature gradient, destabilizes the outskirts of galaxy clusters via the magneto-thermal instability (MTI), which could drive observed ICM turbulence. In this paper we continue our investigation of the MTI with 3D simulations using the Boussinesq code snoopy. We redress two issues intrinsic to our previous 2D study: an inverse energy cascade and the impossibility of dynamo action. Contrary to 2D simulations, we find inconsequential transport of energy across scales (most energy is dissipated at the same scale as its injection) and that turbulent eddies are vertically elongated at or below the thermal conduction length yet relatively isotropic on larger scales. Similar to 2D, however, the saturated turbulent energy levels and the integral scale follow clear power-laws that depend on the thermal diffusivity, temperature gradient, and buoyancy frequency. We also show that the MTI amplifies magnetic fields, through a fluctuation dynamo, to equipartition strengths provided that the integral scale of MTI turbulence is larger than the viscous dissipation scale. Finally, we show that our scaling laws are consistent with extant observations of ICM turbulence if the thermal conductivity is reduced by a factor of ∼10 from its Spitzer value, and that the stable stratification significantly reduces the vertical elongation of MTI motions on global cluster scales.

Effects of Forcing on Shocks and Energy Dissipation in Interstellar and Intracluster Turbulences

Observations indicate that turbulence in the interstellar medium (ISM) is supersonic (M turb ≫ 1) and strongly magnetized (β ∼ 0.01–1), while in the intracluster medium (ICM) it is subsonic (M turb ≲ 1) and weakly magnetized (β ∼ 100). Here, M turb is the turbulent Mach number and β is the plasma beta. We study the properties of shocks induced in these disparate environments, including the distribution of the shock Mach number, M s , and the dissipation of the turbulent energy at shocks, through numerical simulations using a high-order, accurate code based on the weighted essentially nonoscillatory scheme. In particular, we investigate the effects of different modes of the forcing that drives turbulence: solenoidal, compressive, and a mixture of the two. In ISM turbulence, while the density distribution looks different with different forcings, the velocity power spectrum, P v , on small scales exhibits only weak dependence. Hence, the statistics of shocks depend weakly on forcing either. In the ISM models with M turb ≈ 10 and β ∼ 0.1, the fraction of the turbulent energy dissipated at shocks is estimated to be ∼15%, not sensitive to the forcing mode. In contrast, in ICM turbulence, P v as well as the density distribution show strong dependence on forcing. The frequency and average Mach number of shocks are greater for compressive forcing than for solenoidal forcing; so is the energy dissipation. The fraction of the ensuing shock dissipation is in the range of ∼10%–35% in the ICM models with M turb ≈ 0.5 and β ∼ 106. The rest of the turbulent energy should be dissipated through turbulent cascade.

LOFAR observations of galaxy clusters in HETDEX

Diffuse cluster radio sources, in the form of radio halos and relics, reveal the presence of cosmic rays and magnetic fields in the intracluster medium (ICM). These cosmic rays are thought to be (re)accelerated through the ICM turbulence and shock waves generated by cluster merger events. Here we characterize the presence of diffuse radio emission in known galaxy clusters in the HETDEX Spring Field, covering 424 deg2. For this, we developed a method to extract individual targets from LOFAR observations processed with the LoTSS DDF-pipeline software. This procedure enables improved calibration as well as the joint imaging and deconvolution of multiple pointings of selected targets. The calibration strategy can also be used for LOFAR low-band antenna and international-baseline observations. The fraction of Planck PSZ2 catalog clusters with any diffuse radio emission apparently associated with the ICM is 73 ± 17%. We detect a total of ten radio halos and twelve candidate halos in the HETDEX Spring Field. Of these ten radio halos, four are new discoveries, two of which are located in PSZ2 clusters. Five clusters host radio relics, two of which are new discoveries. The fraction of radio halos in Planck PSZ2 clusters is 31 ± 11%, or 62 ± 15% when including the candidate radio halos. Based on these numbers, we expect that there will be at least 183 ± 65 radio halos found in the LoTSS survey in PSZ2 clusters, in agreement with past predictions. The integrated flux densities for the radio halos were computed by fitting exponential models to the radio images. From these flux densities, we determine the cluster mass (M500) and Compton Y parameter (Y500) 150 MHz radio power (P150 MHz) scaling relations for Planck PSZ2-detected radio halos. Using bivariate correlated errors and intrinsic scatter orthogonal regression, we find slopes of 6.13 ± 1.11 and 3.32 ± 0.65 for the M500–P150 MHz and M500–P150 MHz relations, respectively. These values are consistent with the results of previous works.

An H α/X-ray orphan cloud as a signpost of intracluster medium clumping

ABSTRACT Recent studies have highlighted the potential significance of intracluster medium (ICM) clumping and its important implications for cluster cosmology and baryon physics. Many of the ICM clumps can originate from infalling galaxies, as stripped interstellar medium (ISM) mixing into the hot ICM. However, a direct connection between ICM clumping and stripped ISM has not been unambiguously established before. Here, we present the discovery of the first and still the only known isolated cloud (or orphan cloud [OC]) detected in both X-rays and H α in the nearby cluster A1367. With an effective radius of 30 kpc, this cloud has an average X-ray temperature of 1.6 keV, a bolometric X-ray luminosity of ∼3.1 × 1041 erg s−1, and a hot gas mass of ∼1010 M⊙. From the Multi-Unit Spectroscopic Explorer (MUSE) data, the OC shows an interesting velocity gradient nearly along the east-west direction with a low level of velocity dispersion of ∼80 km s−1, which may suggest a low level of the ICM turbulence. The emission line diagnostics suggest little star formation in the main H α cloud and a low-ionization (nuclear) emission-line regions like spectrum, but the excitation mechanisms remain unclear. This example shows that stripped ISM, even long after the initial removal from the galaxy, can still induce ICM inhomogeneities. We suggest that the magnetic field can stabilize the OC by suppressing hydrodynamic instabilities and thermal conduction. This example also suggests that at least some ICM clumps are multiphase in nature and implies that the ICM clumps can also be traced in H α. Thus, future deep and wide-field H α surveys can be used to probe the ICM clumping and turbulence.

A robust model for flux density calculations of radio halos in galaxy clusters: Halo-FDCA

Here we present Halo-FDCA, a robust open source Python package for modeling and estimating total flux densities of radio (mini) halos in galaxy clusters. Radio halos are extended ( ~200 - 1500 kpc in size) synchrotron emitting sources found in galaxy clusters that trace the presence of cosmic rays and magnetic fields in the intracluster medium (ICM). These sources are centrally located and have a low surface brightness. Their exact origin is still unknown but they are likely related to cosmic rays being re-accelerated in-situ by merger or sloshing driven ICM turbulence. The presented algorithm combines the numerical power of the Markov Chain Monte Carlo routine and multiple theoretical models to estimate the total radio flux density of a radio halo from a radio image and its associated uncertainty. This method introduces a flexible analytic fitting procedure to replace existing simplistic manual measurements prone to biases and inaccuracies. It allows to easily determine the properties of the emission and is particularly suitable for future studies of large samples of clusters.

Morphology of radio relics – I. What causes the substructure of synchrotron emission?

ABSTRACT High-resolution radio observations of cluster radio relics often show complex spatial and spectral features. However, it is not clear what these features reveal about the underlying magnetic field properties. We performed three-dimensional magnetohydrodynamical simulations of merger shock waves propagating through a magnetized, turbulent intracluster medium. Our model includes the diffusive shock acceleration (DSA) of cosmic ray electrons, their spatial advection and energy losses at run-time. With this set-up we can investigate the relation between radio substructure and pre-shock plasma conditions in the host cluster. We find that upstream turbulence plays a major role in shaping the properties of radio relics produced downstream. Within the assumption of DSA, we can reproduce the observed discrepancy between the X-ray derived Mach number of shocks, and the Mach number inferred from radio spectra. Our simulated spectral index maps and profiles across the radio relic also suggest that the standard deviation of the upstream magnetic field must be relatively small ($\sigma _B\le 1 \, \mu$G) in order to reproduce observations and therefore radio relics can potentially constrain the distribution of magnetic fields in galaxy clusters outskirts.

Radio and X-ray connection in radio mini-halos: Implications for hadronic models

Context. A large fraction of cool-core clusters are known to host diffuse, steep-spectrum radio sources, called radio mini-halos, in their cores. Mini-halos reveal the presence of relativistic particles on scales of hundreds of kiloparsecs, beyond the scales directly influenced by the central active galactic nucleus (AGN), but the nature of the mechanism that produces such a population of radio-emitting, relativistic electrons is still debated. It is also unclear to what extent the AGN plays a role in the formation of mini-halos by providing the seeds of the relativistic population. Aims. In this work we explore the connection between thermal and non-thermal components of the intra-cluster medium in a sample of radio mini-halos and we study the implications within the framework of a hadronic model for the origin of the emitting electrons. Methods. For the first time, we studied the thermal and non-thermal connection by carrying out a point-to-point comparison of the radio and the X-ray surface brightness in a sample of radio mini-halos. We extended the method generally applied to giant radio halos by considering the effects of a grid randomly generated through a Monte Carlo chain. Then we used the radio and X-ray correlation to constrain the physical parameters of a hadronic model and we compared the model predictions with current observations. Results. Contrary to what is generally reported in the literature for giant radio halos, we find that the mini-halos in our sample have super-linear scaling between radio and X-rays, which suggests a peaked distribution of relativistic electrons and magnetic field. We explore the consequences of our findings on models of mini-halos. We use the four mini-halos in the sample that have a roundish brightness distribution to constrain model parameters in the case of a hadronic origin of the mini-halos. Specifically, we focus on a model where cosmic rays are injected by the central AGN and they generate secondaries in the intra-cluster medium, and we assume that the role of turbulent re-acceleration is negligible. This simple model allows us to constrain the AGN cosmic ray luminosity in the range ∼1044−46 erg s−1 and the central magnetic field in the range 10–40 μG. The resulting γ-ray fluxes calculated assuming these model parameters do not violate the upper limits on γ-ray diffuse emission set by the Fermi-LAT telescope. Further studies are now required to explore the consistency of these large magnetic fields with Faraday rotation studies and to study the interplay between the secondary electrons and the intra-cluster medium turbulence.

Implications of the mild gas motion found with Hitomi in the core of the Perseus cluster

Based mainly on X-ray observations, we study the interactions between the intracluster medium (ICM) in clusters of galaxies and their member galaxies. Through (magneto)hydrodynamic and gravitational channels, moving galaxies are expected to drag the ICM around them, and then transfer some fraction of their dynamical energies on cosmological timescales to the ICM. This hypothesis is in line with several observations, including the possible cosmological infall of galaxies toward the cluster center, found over redshifts of z ∼ 1 to z ∼ 0. Further assuming that the energy lost by these galaxies is first converted into ICM turbulence and then dissipated, this picture can explain the subsonic and uniform ICM turbulence, measured with Hitomi in the core region of the Perseus cluster. The scenario may also explain several other unanswered problems regarding clusters of galaxies, such as what prevents the ICM from underoing the expected radiative cooling, how the various mass components in nearby clusters have attained different radial distributions, and how a thermal stability is realized between hot and cool ICM components that co-exist around cD galaxies. This view is also considered to pertain to the general scenario of galaxy evolution, including their environmental effects.

Kinematics of Filaments in Cooling Flow Clusters and Heating by Mixing

Abstract We compare a recent study of the kinematics of optical filaments in three cooling flow clusters of galaxies with previous numerical simulations of jet-inflated hot bubbles, and conclude that the velocity structure functions (VSFs) of the filaments better fit direct excitation by the jets than by turbulent cascade from the largest turbulent eddies. The observed VSFs of the optical filaments in the three clusters are steeper than that expected from a classical cascade in turbulent dissipation. Our three-dimensional hydrodynamical simulations show that as the jets inflate bubbles in the intracluster medium (ICM), they form vortexes in a large range of scales. These vortexes might drive the ICM turbulence with eddies of over more than an order of magnitude in size. A direct excitation of turbulence by the vortexes that the jets form and the slow turbulent dissipation imply that heating the ICM by mixing with hot bubbles is more efficient than heating by turbulent dissipation.

Turbulence in stratified atmospheres: implications for the intracluster medium

ABSTRACT The gas motions in the intracluster medium (ICM) are governed by turbulence. However, since the ICM has a radial profile with the centre being denser than the outskirts, ICM turbulence is stratified. Stratified turbulence is fundamentally different from Kolmogorov (isotropic, homogeneous) turbulence; kinetic energy not only cascades from large to small scales, but it is also converted into buoyancy potential energy. To understand the density and velocity fluctuations in the ICM, we conduct high-resolution (10242 × 1536 grid points) hydrodynamical simulations of subsonic turbulence (with rms Mach number $\mathcal {M}\approx 0.25$) and different levels of stratification, quantified by the Richardson number Ri, from Ri = 0 (no stratification) to Ri = 13 (strong stratification). We quantify the density, pressure, and velocity fields for varying stratification because observational studies often use surface brightness fluctuations to infer the turbulent gas velocities of the ICM. We find that the standard deviation of the logarithmic density fluctuations (σs), where s = ln (ρ/ < ρ($z$) >), increases with Ri. For weakly stratified subsonic turbulence (Ri ≲ 10, $\mathcal {M}\lt 1$), we derive a new σs–$\mathcal {M}$–Ri relation, $\sigma _\mathrm{ s}^2=\ln (1+b^2\mathcal {M}^4+0.09\mathcal {M}^2 \mathrm{Ri} H_\mathrm{ P}/H_\mathrm{ S})$, where b = 1/3–1 is the turbulence driving parameter, and HP and HS are the pressure and entropy scale heights, respectively. We further find that the power spectrum of density fluctuations, P(ρk/ < ρ >), increases in magnitude with increasing Ri. Its slope in k-space flattens with increasing Ri before steepening again for Ri ≳ 1. In contrast to the density spectrum, the velocity power spectrum is invariant to changes in the stratification. Thus, we find that the ratio between density and velocity power spectra strongly depends on Ri, with the total power in density and velocity fluctuations described by our σs–$\mathcal {M}$–Ri relation. Pressure fluctuations, on the other hand, are independent of stratification and only depend on $\mathcal {M}$.

Lessons learned from 19 years of high‐resolution X‐ray spectroscopy of galaxy clusters with the reflection grating spectrometer on board XMM‐Newton

AbstractThe intracluster medium (ICM) contains the vast majority of the baryonic matter in galaxy clusters and is heated to X‐ray radiating temperatures. X‐ray spectroscopy is therefore a key to understanding both the morphology and the dynamics of galaxy clusters. Here we recall crucial evolutionary problems of galaxy clusters unveiled by 19 years of high‐resolution X‐ray spectroscopy with the reflection grating spectrometer (RGS) on board XMM‐Newton. Its exquisite combination of effective area, spectral resolution, and excellent performance over two decades has enabled transformational science and important discoveries such as the lack of strong cooling flows, the constraints on ICM turbulence, and cooling–heating balance. The ability of RGS to resolve individual ICM spectral lines reveals in great detail the chemical enrichment in clusters by supernovae and asymptotic giant branch stars. RGS spectra clearly show that the ICM plasma is overall in thermal equilibrium, which is unexpected given the wealth of energetic phenomena such as jets from supermassive black holes and mergers.

Towards mapping turbulence in the intra-cluster medium

X-ray observations of the hot gas filling the intra-cluster medium (ICM) provide a wealth of information on the dynamics of clusters of galaxies. The global equilibrium of the ICM is believed to be ensured by non-thermal and thermal pressure support sources, among which gas movements and the dissipation of energy through turbulent motions. Accurate mapping of turbulence using X-ray emission lines is challenging due to the lack of spatially resolved spectroscopy. Only future instruments such as the X-ray Integral Field Unit (X-IFU) on Athena will have the spatial and spectral resolution to quantitatively investigate the ICM turbulence over a broad range of spatial scales. Powerful diagnostics for these studies are line shift and the line broadening maps, and the second-order structure function. When estimating these quantities, instruments will be limited by uncertainties of their measurements, and by the sampling variance (also known as cosmic variance) of the observation. Here, we extend the formalism started in our companion Paper I to include the effect of statistical uncertainties of measurements in the estimation of these line diagnostics, in particular for structure functions. We demonstrate that statistics contribute to the total variance through different terms, which depend on the geometry of the detector, the spatial binning and the nature of the turbulent field. These terms are particularly important when probing the small scales of the turbulence. An application of these equations is performed for the X-IFU, using synthetic turbulent velocity maps of a Coma-like cluster. Results are in excellent agreement with the formulas both for the structure function estimation (≤3%) and its variance (≤10%). The expressions derived here and in Paper I are generic, and ensure an estimation of the total errors in any X-ray measurement of turbulent structure functions. They also open the way for optimisations in the upcoming instrumentation and in observational strategies.

Turbulence decay in the density-stratified intracluster medium

Abstract Turbulence evolution in a density-stratified medium differs from that of homogeneous isotropic turbulence described by the Kolmogorov picture. We evaluate the degree of this effect in the intracluster medium (ICM) with hydrodynamical simulations. We find that the buoyancy effect induced by ICM density stratification introduces qualitative changes to the turbulence energy evolution, morphology, and the density fluctuation–turbulence Mach number relation, and likely explains the radial dependence of the ICM turbulence amplitude as found previously in cosmological simulations. A new channel of energy flow between the kinetic and the potential energy is opened up by buoyancy. When the gravitational potential is kept constant with time, this energy flow leaves oscillations to the energy evolution, and leads to a balanced state of the two energies where both asymptote to power-law time evolution with slopes shallower than that for the turbulence kinetic energy of homogeneous isotropic turbulence. We discuss that the energy evolution can differ more significantly from that of homogeneous isotropic turbulence when there is a time variation of the gravitational potential. Morphologically, ICM turbulence can show a layered vertical structure and large horizontal vortical eddies in the central regions with the greatest density stratification. In addition, we find that the coefficient in the linear density fluctuation–turbulence Mach number relation caused by density stratification is in general a variable with position and time.

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.

Role of intracluster supernovae in radio mini-haloes in galaxy clusters

Abstract A possibility of generating a population of cosmic ray particles accelerated in supernovae type Ia (SNIa) remnants in the intracluster medium (ICM) is discussed. The presently constrained host-less SNIa rates in the clusters are found to be sufficient to fill a few hundred kpc region with cosmic ray electrons within their typical synchrotron lifetime of 100 Myr. The SNIa have already been considered potential sources of excess Fe abundance in cool-core clusters, distributed heating and turbulence in ICM. A good fraction of total radio power from mini-haloes can be sourced from the SNIa energy deposited in the ICM with required energy conversion efficiency ≤1 per cent. The radio power estimated from low Mach-number shock acceleration in SNIa remnants is consistent with the observations within the uncertainties in the estimates. Some observational properties of the radio mini-haloes are broadly consistent with the SNIa scenario. It is also speculated that radio powers and possibly detections of mini-haloes are linked to star formation and merger histories of the clusters.