Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The subgrid-scale energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure ($\beta_\mathrm{p} = 0.25, 1, 2.5, 5, 25$) and sonic Mach numbers ($M_s = 2, 2.5, 4$). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and $\alpha-\beta-\gamma$ closures. We find only mediocre performance of the kinetic eddy-viscosity and $\alpha-\beta-\gamma$ closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlation and constant coefficient values over time and and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.Comment: 15 pages, 6 figures; to be published in New Journal of Physic

A morphological analysis of the substructures in radio relics

Recent observations of radio relics - diffuse radio emission in galaxy clusters - have revealed that these sources are not smooth but consist of structures in the form of threads and filaments. We investigate the origin of these filamentary structures and the role of projection effects. To this end, we have developed a tool that extracts the filamentary structures from background emission. Moreover, it is capable of studying both two-dimensional and three-dimensional objects. We apply our structure extractor to, both, observations and cosmological simulations of radio relics. Using Minkowski functionals, we determine the shape of the identified structures. In our 2D analysis, we find that the brightest structures in the observed and simulated maps are filaments. Our analysis of the 3D simulation data shows that radio relics do not consist of sheets but only of filaments and ribbons. Furthermore, we did not find any measurable projection effects that could hide any sheet-like structures in projection. We find that, both, the magnetic field and the shock front consist of filaments and ribbons that cause filamentary radio emission.Comment: 20 pages, 22 figures, accepted for publication in MNRA