Slow mode waves and mirror instability in gyrotropic Hall magnetohydrodynamic model

Recently the nonlinear magnetohydrodynamic (MHD) model corrected by pressure anisotropy and Hall current arising from the ion inertia is applied to construct slow or mirror mode structures and compare with the observation in the Earth's magnetosphere [K. Stasiewicz, Phys. Rev. Lett. 93, 125004 (2004)]. A serious issue is also raised of whether the Hall MHD model is appropriate for describing the high beta plasma and is capable of reproducing the wave dispersion found in kinetic theory [O. Pokhotelov, Phys. Rev. Lett. 95, 129501 (2005)]. In this paper we give an overview of the characteristics of linear slow mode waves and mirror instability within the context of the gyrotropic Hall MHD model closed with various energy equations. The properties examined include the phase speed, the compressibility of plasma density and magnetic field, the magnetic polarization of slow mode waves, as well as the criteria for mirror instability and their dependences on pressure anisotropy, plasma beta, propagation angle, and energy closures. The analyses help to clarify the applicability and limitation with applying the gyrotropic Hall MHD model to the observed slow or mirror mode structures.