The relation between gas density and velocity power spectra in galaxy clusters: qualitative treatment and cosmological simulations

TL;DR

This paper proposes a method to infer the velocity power spectrum of the intracluster medium in galaxy clusters from density fluctuations, calibrated with cosmological simulations, enabling new insights into cluster dynamics.

Contribution

It establishes a linear relation between density and velocity fluctuations in relaxed galaxy clusters and calibrates this relation using cosmological simulations.

Findings

The relation holds across a wide range of scales.

The calibration yields a dimensionless constant of about 1.

Density power spectra can serve as proxies for velocity spectra.

Abstract

We address the problem of evaluating the power spectrum of the velocity field of the ICM using only information on the plasma density fluctuations, which can be measured today by Chandra and XMM-Newton observatories. We argue that for relaxed clusters there is a linear relation between the rms density and velocity fluctuations across a range of scales, from the largest ones, where motions are dominated by buoyancy, down to small, turbulent scales: $(\delta\rho_k/\rho)^2 = \eta_1^2 (V_{1,k}/c_s)^2$, where $\delta\rho_k/\rho$ is the spectral amplitude of the density perturbations at wave number $k$, $V_{1,k}^2=V_k^2/3$ is the mean square component of the velocity field, $c_s$ is the sound speed, and $\eta_1$ is a dimensionless constant of order unity. Using cosmological simulations of relaxed galaxy clusters, we calibrate this relation and find $\eta_1\approx 1 \pm 0.3$. We argue that this value is set at large scales by buoyancy physics, while at small scales the density and velocity power spectra are proportional because the former are a passive scalar advected by the latter. This opens an interesting possibility to use gas density power spectra as a proxy for the velocity power spectra in relaxed clusters, across a wide range of scales.