Turbulent density and pressure fluctuations in the stratified intracluster medium (2010.12602v2)

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 ($\mathrm{Fr}\perp$). 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 ($256^2\times 384$ -- $1024^2\times1536$ resolution elements), in which we scan the parameter space of subsonic rms Mach number ($\mathcal{M}$), $\mathrm{Fr}\perp$, and the ratio of entropy and pressure scale heights ($R_{PS}=H_P/H_S$), relevant to the ICM. We develop a new scaling relation between the standard deviation of logarithmic density fluctuations ($\sigma_s$, where $s=\ln(\rho/\left<\rho\right>)$), $\mathcal{M}$, and $\mathrm{Fr}{\perp}$, valid till $\mathrm{Fr}\perp\ll1$:~$\sigma_s^2=\ln\left(1+b^2\mathcal{M}^4+0.10/(\mathrm{Fr}\perp+0.25/\sqrt{\mathrm{Fr}\perp})^2\mathcal{M}^2R_{PS}\right)$, where $b\sim1/3$ for solenoidal turbulence driving studied here. We further find that logarithmic pressure fluctuations $\sigma_{(\ln{P}/\left<P\right>)}$ are independent of stratification and scale according to the relation $\sigma_{(\ln{\bar{P}})}^2=\ln\left(1+b^2\gamma^2\mathcal{M}^4\right)$, where $\bar{P}=P/\left<P\right>$ and $\gamma$ is the adiabatic index of the gas.

• The paper details a novel scaling relation for logarithmic density fluctuations based on subsonic, stratified turbulence simulations.
• It shows that strong stratification induces velocity anisotropy, sharply reducing vertical motions compared to horizontal flows.
• The research offers scaling laws that improve the interpretation of X-ray and SZ observations, refining estimates of intracluster turbulence.

Overview of "Turbulent Density and Pressure Fluctuations in the Stratified Intracluster Medium"

This paper explores the intricate dynamics of turbulence within the intracluster medium (ICM), focusing on how density and pressure fluctuations interact with the stratified nature of this environment. The authors, Mohapatra, Federrath, and Sharma, employ high-resolution hydrodynamic simulations to explore the parameter space that characterizes subsonic, stratified turbulence, emphasizing the range of the perpendicular Froude number ($\mathrm{Fr}_\perp$), Mach number ($\mathcal{M}$), and the pressure-entropy scale height ratio ($R_{PS}$). The paper addresses the limitations of classic turbulence models by recognizing the unique conditions in the ICM, thereby providing scaling relations that could significantly improve our understanding of turbulent gas motions in galaxy clusters.

Key Contributions

1. Density and Pressure Fluctuation Scaling: The paper extends previous work on turbulence in the ICM to the strong stratification limit, offering a new scaling relation for the standard deviation of logarithmic density fluctuations, $\sigma_s$. This relation is given by:

$$\sigma_s^2 = \ln\left(1 + b^2\mathcal{M}^4 + \frac{0.10 \mathcal{M}^2 R_{PS}}{\left(\mathrm{Fr}_\perp + 0.25/\sqrt{\mathrm{Fr}_\perp}\right)^2}\right)$$

Here, $b\approx 1/3$ for solenoidal driving. Importantly, pressure fluctuations $\sigma_{\ln(\bar{P})}$ are shown to be independent of stratification, scaling purely with $\mathcal{M}$ according to $$\sigma_{\ln(\bar{P})}^2 = \ln(1 + b^2\gamma^2\mathcal{M}^4)$$.

1. Velocity Anisotropy: The authors measure the anisotropy in turbulent eddies due to stratification, pointing out that for strong stratification ($\mathrm{Fr}_\perp \ll 1$), the vertical component of velocity ($v_z$) decreases sharply relative to the horizontal components ($v_\perp$). This anisotropy is a key factor in the energy dynamics, as buoyancy forces dominate over large scales, confining motions to nearly two-dimensional layers.
2. Implications for Observations: The research carries significant implications for interpreting X-ray and Sunyaev-Zel'dovich (SZ) effect observations of the ICM. The derived scaling relations between density/pressure fluctuations and turbulent velocities provide a more nuanced framework for inferring ICM dynamics, especially considering the invariance of pressure fluctuations to stratification effects.
3. Robustness Under Different Physical Conditions: The simulations consider various configurations of the ICM, taking into account the effects of different Mach numbers, stratification levels, and thermodynamic profiles. The findings remain consistent across these conditions, suggesting that the derived relations are robust and broadly applicable within the ICM context.

Practical and Theoretical Implications

Theoretical implications primarily revolve around advancing the physical understanding of turbulence under anisotropic stratification, challenging the traditional use of Kolmogorov theory which assumes isotropy. Practically, these findings could refine methods of estimating ICM turbulence from observable quantities, potentially impacting cosmological studies that utilize galaxy clusters as probes. Future SZ and X-ray observations with high angular resolution will benefit from these enhanced models, allowing researchers to better constrain the velocities and thermodynamics of the ICM.

Future Directions

The paper paves the way for future research to incorporate additional physics such as magnetic fields, radiative cooling, and more complex driving mechanisms in turbulence simulations. Additionally, this work encourages the development of observational techniques to validate the proposed scaling laws and anisotropy effects, especially in light of advanced facilities anticipated in the near future.

Overall, this paper offers a comprehensive examination of turbulence within the stratified settings of the ICM, significantly contributing to both theoretical frameworks and practical methodologies for observational astrophysics.