Turbulence decay in the density-stratified intracluster medium

Shi, Xun; Zhang, Congyao

doi:10.1093/mnras/stz1392

Cited by 16 publications

(12 citation statements)

References 53 publications

(68 reference statements)

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“…This scaling is equivalent to multiplying δρ 2 buoyancy with f scale (see Equation (18c)). Shi & Zhang (2019) study the decay of a turbulent velocity field in a stratified medium and find that normalised density dispersion σρ is smaller than the saturated value initially, stays roughly constant, and saturates after t 1/N to σρ = 0.59M as turbulence decays with time and M decreases (see their figure 8). Their temporal behaviour is consistent with our σ s -M-Ri relation, since the density fluctuations due to buoyancy with moderate stratification only depend on the driving scale and the entropy scale height (Eq.…”

Section: Density Fluctuation σ S As a Function Of Rimentioning

confidence: 99%

“…At late times Ri 10, σ s decreases linearly with decreasing M ( fig. 8 in Shi & Zhang 2019) as we enter the strongly stratified regime, and vertical displacement and σ s are suppressed. This regime will be investigated further in a follow-up study.…”

Section: Density Fluctuation σ S As a Function Of Rimentioning

confidence: 99%

“…For NCC clusters, we consider driving by mergers with L driv ≈ 1 Mpc and v L driv ≈ 1000 km/s. Here we use the Brunt-Vaisala frequency N from figure 1 in Shi & Zhang (2019). Note that Ri = N 2 L 2 driv /v 2 L driv is sensitive to the choice of L driv and v L driv .…”

Section: Introductionmentioning

confidence: 99%

“…Moderately stratified turbulence with Ri 10 governs both cool and non-cool core clusters. darnini (2019); Shi & Zhang (2019) include gravitational stratification in their models. However, these simulations mostly cannot resolve the Ozmidov length l O (the length scale where turbulent shear and stratification terms are equal in magnitude) within the inertial range of turbulence.…”

Section: Introductionmentioning

confidence: 99%

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Turbulence in stratified atmospheres: implications for the intracluster medium

Mohapatra

Federrath

Sharma

2020

Monthly Notices of the Royal Astronomical Society

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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 (1024 2 × 1536 grid points) hydrodynamical simulations of subsonic turbulence (with rms Mach number M ≈ 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 (σ s ), where s = ln(ρ/ ρ(z) ), increases with Ri. For weakly stratified subsonic turbulence (Ri 10, M < 1), we derive a new σ s -M-Ri relation, σ 2 s = ln 1 + b 2 M 4 + 0.09M 2 RiH P /H S , where b = 1/3-1 is the turbulence driving parameter, and H P and H S are the pressure and entropy scale heights respectively. We further find that the power spectrum of density fluctuations, P(ρ k / 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 σ s -M-Ri relation. Pressure fluctuations, on the other hand, are independent of stratification and only depend on M.

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Section: Density Fluctuation σ S As a Function Of Rimentioning

confidence: 99%

Section: Density Fluctuation σ S As a Function Of Rimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Turbulence in stratified atmospheres: implications for the intracluster medium

Mohapatra

Federrath

Sharma

2020

Monthly Notices of the Royal Astronomical Society

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“…There are previous works investigating turbulence in a stratified ICM-like medium (Zhuravleva et al 2014b;Gaspari et al 2014;Valdarnini 2019;Shi & Zhang 2019;Mohapatra et al 2020). However, they focused on idealised plasma flows, or were limited to the innermost regions of galaxy clusters (≤ 500 kpc).…”

Section: Introductionmentioning

confidence: 99%

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

Simonte

Vazza

Brighenti

et al. 2022

A&A

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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.

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Towards mapping turbulence in the intra-cluster medium

Clerc

Cucchetti

Pointecouteau

et al. 2019

A&A

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Context. X-ray observations of galaxy clusters provide insights into the nature of gaseous turbulent motions, their physical scales, and the fundamental processes to which they are related. Spatially-resolved, high-resolution spectral measurements of X-ray emission lines provide diagnostics on the nature of turbulent motions in emitting atmospheres. Since they are acting on scales comparable to the size of the objects, the uncertainty on these physical parameters is limited by the number of observational measurements, through sample variance. Aims. We propose a different and complementary approach to repeating numerical simulations for the computation of sample variance (i.e. Monte-Carlo sampling) by introducing new analytical developments for lines diagnosis. Methods. We considered the model of a “turbulent gas cloud”, consisting in isotropic and uniform turbulence described by a universal Kolmogorov power-spectrum with random amplitudes and phases in an optically thin medium. Following a simple prescription for the four-term correlation of Fourier coefficients, we derived generic expressions for the sample mean and variance of line centroid shift, line broadening, and projected velocity structure function. We performed a numerical validation based on Monte-Carlo simulations for two popular models of gas emissivity based on the β-model. Results. Generic expressions for the sample variance of line centroid shifts and broadening in arbitrary apertures are derived and match the simulations within their range of applicability. Generic expressions for the mean and variance of the structure function are provided and verified against simulations. An application to the Athena/X-IFU (Advanced Telescope for High-ENergy Astrophysics/X-ray Integral Field Unit) and XRISM/Resolve (X-ray Imaging and Spectroscopy Mission) instruments forecasts the potential of sensitive, spatially-resolved spectroscopy to probe the inertial range of turbulent velocity cascades in a Coma-like galaxy cluster. Conclusions. The formulas provided are of generic relevance and can be implemented in forecasts for upcoming or current X-ray instrumentation and observing programmes.

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Turbulence decay in the density-stratified intracluster medium

Cited by 16 publications

References 53 publications

Turbulence in stratified atmospheres: implications for the intracluster medium

Turbulence in stratified atmospheres: implications for the intracluster medium

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

Towards mapping turbulence in the intra-cluster medium

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