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 (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.

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

“…Next, we validate our method against more idealised simulations. As previously discussed, due to the different nature of the simulations, it is not feasible to apply the very same algorithm that Mohapatra et al 2020Mohapatra et al , 2021a used in their studies to our cluster sample. For instance, in Mohapatra et al and Shi & Zhang, the Mach number and the Richardson number were parameters of the simulation.…”

“…After filtering for density fluctuations, we obtained the logarithmic perturbations both performing a fixed-scale filtering method, with a scale L ≈ 43.6 kpc and computing the mean density on a slice at a given z coordinate, which is the method that Mohapatra et al 2020Mohapatra et al , 2021a used in their studies. We plot the results in Fig.…”

“…The Richardson number, Ri, is central to our study, but, in contrast to some previous work in which the authors considered Ri as an input parameter of the simulation (Mohapatra et al 2020, Shi & Zhang 2019, we had to compute it a-posteriori following Eq. 1.…”

“…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).…”

“…In this paper we explore the character of the turbulence in realistic, stratified ICM generated in high-resolution, cosmological simulations of galaxy clusters. We mainly focus on the relation between density and velocity fluctuations, their dependence on the Richardson number (see Mohapatra et al 2020), and the anisotropy of the turbulent velocity field.…”