The Matryoshka Run: A Eulerian Refinement Strategy to Study the Statistics of Turbulence in Virialized Cosmic Structures

Abstract

We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at redshift z=0. The development of turbulence is ensured as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. We achieve a large dynamic range of spatial scales through a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h −1 kpc across the virial volume. The probability density functions of various velocity derived quantities exhibit the features characteristic of fully developed compressible turbulence observed in dedicated periodic-box simulations. Shocks generate only 60% of the total vorticity within R vir /3 region and 40% beyond that. We compute second and third order, longitudinal and transverse, structure functions for both solenoidal and compressional components, in the cluster core, virial region and beyond. The structure functions exhibit a well defined inertial range of turbulent cascade. The injection scale is comparable to the virial radius but increases towards the outskirts. Within R vir /3, the spectral slope of the solenoidal component is close to Kolmogorov's, but for the compressional component is substantially steeper and close to Burgers'; the flow is mostly solenoidal and statistically rigorously consistent with fully developed, homogeneous and isotropic turbulence. Small scale anisotropy appears due to numerical artifact. Towards the virial region, the flow becomes increasingly compressional, the structure functions flatter and modest genuine anisotropy appear particularly close to the injection scale. In comparison, mesh adaptivity based on Lagrangian refinement and the same finest resolution, leads to lack of turbulent power on small scale and excess thereof on large scales, with the discrepancy growing towards the outer cluster regions, while producing unreliable density weighted structure functions throughout.

Turbulence and vorticity in Galaxy clusters generated by structure formation

“…Our results here, as well as previous cluster simulations are roughly consistent with the behaviour of solenoidal turbulence fol-lowing the classic, Kolmogorov picture in which |δ v| ∝ L 1/3 n ((e.g., Ryu et al 2008;Xu et al 2011;Vazza et al 2011a;Miniati 2014). Consequently, while the r.m.s turbulent velocity or the total turbulent pressure depend on Ln, the solenoidal kinetic energy cascade flux, defined as:…”

“…Previous studies (Ryu et al 2008;Vazza et al 2014;Miniati 2014;Schmidt et al 2014) and our results below suggest that ICM turbulent motions are predominantly solenoidal in character. The distinguishing property of solenoidal turbulence is, of course, that the motions are rotational; that is, they have non-vanishing local vorticity, ω = ∇ × v = 0.…”

“…The generation of shocks and turbulence in simulated flows may be subject to spurious numerical effects, especially when adaptive mesh refinement is concerned (e.g., Miniati 2014;Schmidt et al 2015). We wanted to avoid spurious effects caused by an uneven grid structure over time or space in the cluster formation region; the imposed fixed mesh refinement scheme puts 100 percent of the inner sub-volume uniformly sampled at 14/h kpc ≈ 20 kpc.…”

“…Power spectra and structure functions constructed from simulation cluster-wide velocity fields typically suggest outer coherence scales ∼ 1 Mpc (e.g., Vazza et al 2009b;Miniati 2014). While these scales correctly capture dominant, energy containing processes for the entire cluster, they do not, as emphasized above, necessarily discriminate against non-random, so, non-turbulent motions.…”

“…These motions may be driven by processes originating on galactic scales (e.g., star burst winds, AGN outflows and bubbles, (e.g., O'Neill et al 2009;Morsony et al 2010;Mendygral et al 2012;Gaspari et al 2012)), possibly ICM-based magneto-thermal instabilities (e.g., Kunz et al 2011;ZuHone et al 2013), but especially by cluster-scale processes associated with cluster formation out of cosmological, large-⋆ Email:franco.vazza@hs.uni-hamburg.de scale structure (e.g., Dolag et al 2005;Vazza et al 2006;Ryu et al 2008;Lau et al 2009;Vazza et al 2011a;ZuHone 2011;Miniati 2014;Schmidt et al 2014). …”