Mirror-wave Structures in the Solar Wind: Grad-Shafranov Reconstruction, MHD, and Hall MHD Simulations with Double-polytropic Energy Closures

Mirror-mode waves with anticorrelated density and magnetic field are widely observed in the solar wind and planetary magnetospheres. In this study we analyze the characteristics of three mirror-wave events observed by the Magnetospheric Multiscale Mission in the Earth's magnetosheath based on the Grad-Shafranov (GS) reconstruction model with temperature anisotropy. The GS scheme solves steady, two-dimensional MHD equations with field-aligned flow from the plasma and magnetic field measurements taken by a single spacecraft traversing across a coherent field structure. The reconstructed 2D plasma and field maps are obtained in the de Hoffmann-Teller frame and on the plane perpendicular to the invariant axis. The energy closures are a set of empirical energy laws with two polytropic exponents inferred from the observed mirror events which are in the ranges of gamma(perpendicular to) = 0.6 similar to 0.89 and gamma(parallel to) = 0.99 similar to 1.35. It is shown that the mirror waves are nonpropagating with linear magnetic field polarization and possess anticorrelated density, temperatures, and magnetic field with the widths of 10-40 ion inertial lengths. The double-polytropic MHD and Hall MHD simulations of mirror instability show consistent results with the GS reconstructions in terms of field-line geometry, phase relations and the sizes of mirror waves, etc.