The Dynamic Venusian Bow Shock Model With the Nonlinear Effect of Magnetosonic Mach Number Based on Venus Express Observations

Utilizing the 8.5-year Venus Express observations, we investigate the effects of solar wind magnetosonic Mach number $\left(M_{MS}\right)$, solar extreme ultraviolet (EUV) radiation, solar wind dynamic pressure $\left(P_d\right)$ and interplanetary magnetic field (IMF) on the shape of the Venusian bow shock. Our statistical analysis yields several findings: (a) The spatial scale of the Venusian bow shock varies in a nonlinear manner with $M_{MS}$ and shows a linear correlation with the EUV flux. (b) After the variance of the bow shock size caused by different $M_{MS}$ and EUV are considered, the bow shock size shows no apparent correlation with the IMF intensity, IMF cone angle and solar wind dynamic pressure. (c) The angle between the IMF and the shock normal $\left({\theta }_{Bn}\right)$ emerges as a significant factor shaping the bow shock's local distance. A two-parameter ($M_{MS}$ and EUV) dynamic bow shock model is consequently constructed. This dynamic model not only elucidates the typical behavior of the bow shock under normal solar wind conditions but also unveils the anomalously distant bow shock location characterized by extremely low $M_{MS}$.