The numerical results from a physics-based global magnetohydrodynamic (MHD) model are used to examine the effect of the interplanetary magnetic field (IMF), solar wind dynamic pressure, and dipole tilt angle on the size and shape of the magnetopause. The subsolar magnetopause is identified using the plasma velocity and density, the cusps are identified using the thermal pressure, and the whole shape of the magnetopause is determined with the three-dimensional streamlines traced through the simulation domain. The magnetopause surface obtained from the simulations is fitted with a three-dimensional surface function controlled by ten configuration parameters, which provide a description of the subsolar magnetopause, the cusp geometry, the flaring angle, the azimuthal asymmetry, the north-south asymmetry, and the twisting angle of the magnetopause. Effects of the IMF, solar wind dynamic pressure, and dipole tilt angle on the configuration parameters are analyzed and fitted by relatively simple functions. It is found that the solar wind dynamic pressure mainly affects the magnetopause size; the IMF mainly controls the magnetopause flaring angle, azimuthal asymmetry, and twisting angle; and the dipole tilt angle mainly affects the magnetopause north-south asymmetry and the cusp geometry. The model is validated by comparing with available empirical models and observational results, and it is demonstrated that the new model can describe the magnetopause for typical solar wind conditions.

Using a 3D multispecies magnetohydrodynamic model, we investigated the effect of the solar wind dynamic pressure (Pd) with different densities and velocities on the subsolar standoff distance (r0) of the Martian magnetic pileup boundary (MPB). We fixed the solar maximum condition, the strongest crustal field located in the dayside region, and the Parker spiral interplanetary magnetic field at Mars. We simulated 35 cases with a Pd range of 0.1494 to 7.323 nPa (solar wind number density n ∈ [1, 9] cm−3, and solar wind velocity V ∈ [−258, −1344] km s−1). The main results are as follows. (1) r0 decreases with increasing Pd according to the power-law relations. For the same Pd, a higher solar wind velocity (lower density) results in a larger r0 of the Martian MPB. (2) A higher solar wind density leads to a lower ratio of the compressed magnetic field strength to the crustal field strength and a larger plasma β under the same Pd. This indicates that the thermal pressure at the Martian MPB plays a significant role for the compressed magnetic field. Because the magnetic pileup process is stronger for a higher solar wind velocity, the magnetic pressure at the Martian MPB is increased. As a result, the thermal pressure decreases and r0 of the Martian MPB increases. (3) We present a new formula of r0 with the parameters of the solar wind dynamic pressure, number density, and velocity.

Using global MHD simulations, we construct a 3D parametric Martian bow shock model that employs a generalized conic section function defined by seven parameters. Effects of the solar wind dynamic pressure (P d ), the magnetosonic Mach number (M MS), and the intensity and the orientation of the interplanetary magnetic field (IMF) on the seven parameters are examined based on 250 simulation cases. These 250 cases have a P d range of 0.36–9.0 nPa (the solar wind number density varying from 3.5 to 12 cm−3 and the solar wind speed varying from 250 to 670 km s−1), an M MS range of 2.8–7.9, and an IMF strength range from zero to 10 nT. The results from our parametric model show several things. (1) The size of the Martian bow shock is dominated by P d . When P d increases, the bow shock moves closer to Mars, and the flaring of the bow shock decreases. (2) The M MS has a similar effect on the bow shock as P d but with different coefficients. (3) The effects of IMF components on the bow shock position are associated with the draping and pileup of the IMF around the Martian ionosphere; hence, we find that both the subsolar standoff distance and the flaring angle of the bow shock increase with the field strength of the IMF components that are perpendicular to the solar wind flow direction (B Y and B Z in the MSO coordinate system). The parallel IMF component (B X ) has little effect on the subsolar standoff distance but affects the flaring angle. (4) The cross section of the bow shock is elongated in the direction perpendicular to the IMF on the Y–Z plane, and the elongation degree is enhanced with increasing intensities of B Y and B Z . The north–south (dawn–dusk) asymmetry is controlled by the cone angle when the IMF is on the X–Z (X–Y) plane. These results show a good agreement with the previous empirical and theoretical models. The current parametric model is obtained under solar maximum conditions with the strongest Martian crustal magnetic field located at the subsolar point. In fact, the bow shock shape can also be affected by both the solar extreme ultraviolet radiation and the orientation of crustal magnetic anomalies to the Sun, which should be considered in future models.