The Studies Of Three Dimensional Earth’s Bow Shock MHD Simulations

The Earth’s bow shock is created because of the interaction of the supersonic and super-alfvenic solar wind with the magnetospheric obstacle, its location and shape depend on the property of the upstream solar wind, as well as the size and shape of the downstream magnetopause. Many studies indicate that the solar wind dynamic pressure and interplanetary magnetic field (IMF) are the two main contributing parameters to the global structure of the magnetopause, the position and shape of the Earth’s bow shock are primarily controlled by solar wind dynamic pressure, upstream Mach number(s), and the IMF orientation.In this paper, we primarily employ global MHD code Space Weather Modeling Framework (SWMF) to study the controlling factors on the Earth’s bow shock. We identify the bow shock surface according the Rankine-Hugoniot jump conditions. Then we propose a new bow shock model comprehensively taking account of the fast magnetic sonic Mach number, solar wind ram pressure, interplanetary magnetic field strength, and magnetopause curvature radius. By comparing the new model with one typical statistic model based on observation data and one physics-based simulation model, we find that the new global model of the bow shock is reliable, and can solve the problems that some models cannot describe the size and location of three-dimensional bow shock when the strength of interplanetary magnetic field is zero. We finally present a specific analysis to the size and two dimensional shape of bow shock under the conditions of different interplanetary magnetic field (IMF) and fast magnetic sonic mach numbers. We summarized our main results as follows:(1)With increase of fast magnetic sonic Mach number, the standoff distance of bow shock decreases under the condition of the northward interplanetary magnetic. However, the influence of fast magnetic sonic Mach number on standoff distance is weaker than under the southward IMF.(2)The size and location of bow shock in the equatorial plane and the meridian plane show an obvious asymmetry, and when the interplanetary magnetic field is turned from northward to southward, this asymmetry also changes;(3) For southward interplanetary magnetic field, when the absolute value of Bz is small, the shape of bow shock in the meridian plane is not a simple parabola, and there exists an obvious "distortion" which seems corresponding to the magnetopause cusp.(4) For northward interplanetary magnetic, the flaring angle of the bow shock will increase in the equatorial plane, but decrease in the meridian plane with the value of the fast magnetic sonic Mach numbers. However, under southward IMFs, the flaring angle of the bow shock will always increase when increasing the fast magnetic sonic Mach number.