Characterizing turbulence in galaxy clusters: defining turbulent energies and assessing multi-scale versus fixed-scale filters

TL;DR

This work develops a fixed-scale real-space filtering framework to disentangle bulk motions from turbulence in the intracluster medium and to define scale-dependent magnetic and kinetic energies using second and third order moments. Applied to a GPU-accelerated Arepo/IllustrisTNG simulation of a massive cluster merger from the PICO-Clusters suite, it shows that turbulent pressure on scales below ~160 kpc peaks at ~5% during core passage and decays to ~2% within ~1.3 Gyr, aligning with XRISM trends and suggesting low turbulence in relaxed clusters. The authors critically assess multiscale iterative filters, demonstrating they can produce artifacts and misidentify scales, and argue for fixed-scale filtering as a clearer, more robust basis for comparing simulations with observations from XRISM and future X-ray missions; they also provide an open GPU-accelerated pipeline for applying these methods to large cosmological datasets. Overall, the study clarifies turbulence generation during major mergers and strengthens connections between high-resolution simulations and observations of galaxy clusters. The work lays groundwork for improved interpretation of turbulence in the ICM and informs planning for XRISM and next generation X-ray telescopes.

Abstract

Disentangling turbulence and bulk motions in the intracluster medium (ICM) of galaxy clusters is inherently ambiguous, as the plasma is continuously stirred by different processes on disparate scales. This poses a serious problem in the interpretation of both observations and numerical simulations. In this paper, we use filtering operators in real space to separate bulk motion from turbulence at different scales. We show how filters can be used to define consistent kinetic and magnetic energies for the bulk and turbulent component. We apply our GPU-accelerated filtering pipeline to a simulation of a major galaxy cluster merger, which is part of the PICO-Clusters suite of zoom-in cosmological simulations of massive clusters using the moving mesh code Arepo and the IllustrisTNG galaxy formation model. We find that during the merger the turbulent pressure fraction on physical scales $\lesssim$160 kpc reaches a maximum of 5%, before decreasing to 2% after $\sim$1.3 Gyr from the core passage. These low values are consistent with recent observations of clusters with XRISM, and suggest that unless a cluster was recently perturbed by a major merger, turbulence levels are low. We then re-examine the popular multiscale iterative filter method. In our tests, we find that its use can introduce artifacts, and that it does not reliably disentangle fluctuations living on widely separated length scales. Rather, we believe it is more fruitful to use fixed-scale filters and turbulent energies to compare between simulations and observations. This work significantly improves our understanding of turbulence generation by major mergers in galaxy clusters, which can be probed by XRISM and next-generation X-ray telescopes, allowing us to connect high-resolution cosmological simulations to observations.

Figures (16)

• Figure 1: Decomposition of the gas density, gas velocity and magnetic field of Halo3 before the merger ($z=0.51$) for a filter scale of $\ell=30 ~ kpc$ (represented by a beam of radius $\ell$ in the top left corner). From top to bottom: slices of the total field, bulk and turbulent components across the center of the cluster. The coordinates are in physical units with respect to the center of mass of the cluster, while dashed lines denote the virial radius $R_{200,\mathrm{c}}$. The colorbars are in common for each column. The cluster appears to be relatively relaxed, with a roughly spherical shape.
• Figure 2: Filtered energy densities of the merging clusters for a filter scale of $\ell=30 ~ kpc$ (represented by a beam of radius $\ell$ in the top left corner). From top to bottom: total density field; kinetic (left) and magnetic (right) turbulent dispersion; bulk (left) and turbulent (right) kinetic energy densities; turbulent momentum along merger axis (left) and cross kinetic energy density (right). Dashed circles are drawn at $R_{200,\mathrm{c}}$ of the two halos, while the contours represent the projected shock surfaces. Velocities are computed with respect to the center of mass of the two clusters. The velocity dispersion is larger in the periphery than in the core, while both the magnetic field dispersion and turbulent kinetic energy peak near the center and far from merger shocks.
• Figure 3: Decomposition of the magnetic energy according to Eq. \ref{['eq:mag_energy_decomposition']} as a function of the filtering length $\ell$ after integrating over the volume. Top: two-dimensional slice of a three-dimensional Kolmogorov synthetic magnetic field. Bottom: the blue line is the filtered total energy of the synthetic turbulent field, the orange line is the energy of the smooth component, while the green is the energy of the turbulent field. The black squares show the analytical result of Eq. \ref{['eq:turbulent_energy_integrated']} obtained by applying the Gaussian filter with scale $\ell$ to the Fourier components of the synthetic field, and computing the energy of the modes.
• Figure 4: Decomposition of the density, velocity (in the rest system of the main cluster) and magnetic field of Halo3 during the merger ($z=0.27$) for a filter scale of $30 ~ kpc$ (represented by a beam of radius $\ell$ in the top left corner). The layout of the figure is the same as in Fig. \ref{['fig:before_all_fields']}. The cluster is highly disturbed by the infall of the less massive companion (along the horizontal axis, from the right side). The infall is accompanied by a large-scale inflow, without however significant small-scale fluctuations. The magnetic field remains more homogeneously distributed throughout the volume.
• Figure 5: Time evolution of the filtered kinetic and magnetic energies during the major merger. Left column: kinetic (top) and magnetic energy (bottom) and their decomposition according to Eqs. \ref{['eq:filt_mag_energy_volume']} and \ref{['eq:filt_kin_energy_volume']} for a fiducial filter scale of $30 ~ kpc$ corresponding to a cutoff wavelength of $\simeq$160 kpc. The vertical lines correspond to the time of the snapshots shown in Figs. \ref{['fig:before_all_fields']} and \ref{['fig:during_all_fields']}. Right column: bulk and turbulent energies for different filter scales. For the scales considered, the turbulent kinetic energy is always subdominant compared to the bulk throughout the merger, while the reverse is true for the turbulent magnetic energy.