Turbulence in the intracluster medium: simulations, observables & thermodynamics

We conduct two kinds of homogeneous isotropic turbulence simulations relevant for the intracluster medium (ICM): (i) pure turbulence runs without radiative cooling; (ii) turbulent heating$+$radiative cooling runs with global thermal balance. For pure turbulence runs in the subsonic regime, the rms density and surface brightness (SB) fluctuations vary as the square of the rms Mach number ($\mathcal{M}_{\text{rms}}$). However, with thermal balance, the density and SB fluctuations $(\delta SB/SB)$ are much larger. These scalings have implications for translating SB fluctuations into a turbulent velocity, particularly for cool cores. For thermal balance runs with large (cluster core) scale driving, both the hot and cold phases of the gas are supersonic. For small scale (one order of magnitude smaller than the cluster core) driving, multiphase gas forms on a much longer timescale but $\mathcal{M}_{\text{rms}}$ is smaller. Both small and large scale driving runs have velocities larger than the Hitomi results from the Perseus cluster. Thus turbulent heating as the dominant heating source in cool cluster cores is ruled out if multiphase gas is assumed to condense out from the ICM. Next we perform thermal balance runs in which we partition the input energy into thermal and turbulent parts and tune their relative magnitudes. The contribution of turbulent heating has to be $\lesssim 10\%$ in order for turbulence velocities to match Hitomi observations. If the dominant source of multiphase gas is not cooling from the ICM (but say uplift from the central galaxy), the importance of turbulent heating cannot be excluded.Comment: MNRAS accepted version; for movies see: http://www.mso.anu.edu.au/~rajsekha/BT_movies.htm

Multiphase condensation in cluster halos: interplay of cooling, buoyancy and mixing

Gas in the central regions of cool-core clusters and other massive halos has a short cooling time ($\lesssim1~\mathrm{Gyr}$). Theoretical models predict that this gas is susceptible to multiphase condensation, in which cold gas is expected to condense out of the hot phase if the ratio of the thermal instability growth time scale ($t_{\mathrm{ti}}$) to the free-fall time ($t_{\mathrm{ff}}$) is $t_{\mathrm{ti}}/t_{\mathrm{ff}}\lesssim10$. The turbulent mixing time $t_{\mathrm{mix}}$ is another important time scale: if $t_{\mathrm{mix}}$ is short enough, the fluctuations are mixed before they can cool. In this study, we perform high-resolution ($512^2\times768$--$1024^2\times1536$ resolution elements) hydrodynamic simulations of turbulence in a stratified medium, including radiative cooling of the gas. We explore the parameter space of $t_{\mathrm{ti}}/t_{\mathrm{ff}}$ and $t_{\mathrm{ti}}/t_{\mathrm{mix}}$ relevant to galaxy and cluster halos. We also study the effect of the steepness of the entropy profile, the strength of turbulent forcing and the nature of turbulent forcing (natural mixture vs. compressive modes) on multiphase gas condensation. We find that larger values of $t_{\mathrm{ti}}/t_{\mathrm{ff}}$ or $t_{\mathrm{ti}}/t_{\mathrm{mix}}$ generally imply stability against multiphase gas condensation, whereas larger density fluctuations (e.g., due to compressible turbulence) promote multiphase gas condensation. We propose a new criterion $\min(t_{\mathrm{ti}}/\min(t_{\mathrm{mix}},t_\mathrm{ff}))\lesssim c_2\times\exp(c_1\sigma_s)$ for when the halo becomes multiphase, where $\sigma_s$ denotes the amplitude of logarithmic density fluctuations and $c_1\simeq6$, $c_2\simeq1.8$ from an empirical fit to our results.Comment: MNRAS-accepted version, 16+2 (appendix) pages, 11 figures, simulation movies available at this playlist on youtube: https://youtube.com/playlist?list=PLuaNgQ1v_KMZlkKXdB7hcaQ7-hb0hmY7

Turbulence in stratified atmospheres: implications for the intracluster medium

The gas motions in the intracluster medium (ICM) are governed by stratified turbulence. 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 ($1024^2\times 1536$ 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 $\mathrm{Ri}$, from $\mathrm{Ri}=0$ (no stratification) to $\mathrm{Ri}=13$ (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 ($\sigma_s$), where s=\ln(\rho/\left), increases with $\mathrm{Ri}$. For weakly stratified subsonic turbulence ($\mathrm{Ri}\lesssim10$, $\mathcal{M}<1$), we derive a new $\sigma_s$--$\mathcal{M}$--$\mathrm{Ri}$ relation, $\sigma_s^2=\ln(1+b^2\mathcal{M}^4+0.09\mathcal{M}^2\mathrm{Ri}H_P/H_S)$, 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(\rho_k/\left), increases in magnitude with increasing $\mathrm{Ri}$, whereas the velocity power spectrum is invariant. Thus, the ratio between density and velocity power spectra strongly depends on $\mathrm{Ri}$. Pressure fluctuations, on the other hand, are independent of stratification and only depend on $\mathcal{M}$.Comment: MNRAS accepted version. For simulation movies see: https://www.youtube.com/watch?v=fYXbwO73Ef

Multiphase turbulence in galactic halos: effect of the driving

Supernova explosions, active galactic nuclei jets, galaxy--galaxy interactions and cluster mergers can drive turbulence in the circumgalactic medium (CGM) and in the intracluster medium (ICM). However, the exact nature of turbulence forced by these sources and its impact on the different statistical properties of the CGM/ICM and their global thermodynamics is still unclear. To investigate the effects of different types of forcing, we conduct high resolution ($1008^3$ resolution elements) idealised hydrodynamic simulations with purely solenoidal (divergence-free) forcing, purely compressive (curl-free) forcing, and natural mixture forcing (equal fractions of the two components). The simulations also include radiative cooling. We study the impact of the three different forcing modes (sol, comp, mix) on the morphology of the gas, its temperature and density distributions, sources and sinks of enstrophy, i.e., solenoidal motions, as well as the kinematics of hot ($\sim10^7~\mathrm{K}$) X-ray emitting and cold ($\sim10^4~\mathrm{K}$) H$\alpha$ emitting gas. We find that compressive forcing leads to stronger variations in density and temperature of the gas as compared to solenoidal forcing. The cold phase gas forms large-scale filamentary structures for compressive forcing and misty, small-scale clouds for solenoidal forcing. The cold phase gas has stronger large-scale velocities for compressive forcing. The natural mixture forcing shows kinematics and gas distributions intermediate between the two extremes, the cold-phase gas occurs as both large-scale filaments and small-scale misty clouds.Comment: 21 pages, 12 figures, accepted for publication in MNRAS. Simulation movies are available at this link: https://www.youtube.com/watch?v=qBsJti2R0HY&list=PLuaNgQ1v_KMaovGyz-7jbFha-HvoXpG2

Turbulent density and pressure fluctuations in the stratified intracluster medium

ABSTRACT Turbulent gas motions are observed in the intracluster medium (ICM). The ICM is density-stratified, with the gas density being highest at the centre of the cluster and decreasing radially outwards. As a result of this, Kolmogorov (homogeneous, isotropic) turbulence theory does not apply to the ICM. The gas motions are instead explained by anisotropic stratified turbulence, with the stratification quantified by the perpendicular Froude number (Fr⊥). These turbulent motions are associated with density and pressure fluctuations, which manifest as perturbations in X-ray surface brightness maps of the ICM and as thermal Sunyaev–Zeldovich effect (SZ) fluctuations, respectively. In order to advance our understanding of the relations between these fluctuations and the turbulent gas velocities, we have conducted 100 high-resolution hydrodynamic simulations of stratified turbulence (2562 × 384–10242 × 1536 resolution elements), in which we scan the parameter space of subsonic rms Mach number ($\mathcal {M}$), Fr⊥, and the ratio of entropy and pressure scale heights (RPS = HP/HS), relevant to the ICM. We develop a new scaling relation between the standard deviation of logarithmic density fluctuations (σs, where s = ln (ρ/$\langle$ρ$\rangle$)), $\mathcal {M}$, and Fr⊥, which covers both the strongly stratified (Fr⊥ ≪ 1) and weakly stratified (Fr⊥ ≫ 1) turbulence regimes: $\sigma _{\rm s}^2=\ln (1+b^2\mathcal {M}^4+0.10/(\mathrm{Fr}_\perp +0.25/\sqrt{\mathrm{Fr}_\perp })^2\mathcal {M}^2R_{\rm PS})$, where b ∼ 1/3 for solenoidal turbulence driving studied here. We further find that logarithmic pressure fluctuations σ(ln P/ &amp;lt; P &amp;gt;) are independent of stratification and scale according to the relation $\sigma _{(\ln {\bar{P}})}^2=\ln (1+b^2\gamma ^2\mathcal {M}^4)$, where $\bar{P}=P/\left\langle P \right\rangle$ and γ is the adiabatic index of the gas. We have tested these scaling relations to be valid over the parameter ranges $\mathcal {M} = 0.01$–0.40, Fr⊥ = 0.04–10.0, and RPS = 0.33–2.33.</jats:p

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/ &amp;lt; ρ($z$) &amp;gt;), 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/ &amp;lt; ρ &amp;gt;), 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 $\mathcal {M}$.</jats:p

Characterizing the turbulent multiphase haloes with periodic box simulations

ABSTRACT Turbulence in the intracluster medium (ICM) is driven by active galactic nuclei (AGNs) jets, by mergers, and in the wakes of infalling galaxies. It not only governs gas motion but also plays a key role in the ICM thermodynamics. Turbulence can help seed thermal instability by generating density fluctuations, and mix the hot and cold phases together to produce intermediate temperature gas (104–107 K) with short cooling times. We conduct high resolution (3843–7683 resolution elements) idealized simulations of the multiphase ICM and study the effects of turbulence strength, characterized by fturb (0.001–1.0), the ratio of turbulent forcing power to the net radiative cooling rate. We analyse density and temperature distribution, amplitude and nature of gas perturbations, and probability of transitions across the temperature phases. We also study the effects of mass and volume weighted thermal heating and weak ICM magnetic fields. For low fturb, the gas is distribution is bimodal between the hot and cold phases. The mixing between different phases becomes more efficient with increasing fturb, producing larger amounts of the intermediate temperature gas. Strong turbulence (fturb ≥ 0.5) generates larger density fluctuations and faster cooling, The rms logarithmic pressure fluctuation scaling with Mach number $\sigma _{\ln {\bar{P}}}^2\approx \ln (1+b^2\gamma ^2\mathcal {M}^4)$ is unaffected by thermal instability and is the same as in hydro turbulence. In contrast, the density fluctuations characterized by $\sigma _s^2$ are much larger, especially for $\mathcal {M}\lesssim 0.5$. In magnetohydrodynamic runs, magnetic fields provide significant pressure support in the cold phase but do not have any strong effects on the diffuse gas distribution, and nature and amplitude of fluctuations.</jats:p