Pressure Dependence of Atmospheric Loss by Impact-induced Vapor Expansion

Introduction: The large number of impacts would have many consequences on the evolution of planetary atmospheres. Melosh and Vickery [1] analytically estimated the lower limit of impactor mass and velocity which could blow off all the atmosphere above the tangent plane to the impact point and suggested the possibility of the substantial atmospheric loss on Mars by impacts during the heavy bombardment. In their estimate, the mass of the atmospheric loss is to be proportional to the planetary atmospheric pressure. Several groups performed numerical calculations using an analytical model or hydrodynamic codes to evaluate the effect on the atmospheric mass by impacts more quantitatively [2-4]. However, they focus mostly on the effect under the present Earth atmosphere, i.e atmospheric pressure is about 1 bar. The atmospheric pressure differs by the planets (~90 bar for Venus and ~10 mbar for Mars), and is the quantity that could change greatly through its evolution. In order to discuss the atmospheric loss by impacts through the evolution of the atmospheres, it is required to consider the effect by the atmospheric pressure on the mass of the atmospheric loss by impacts. We carried out several runs with various atmospheric pressure by using a 2-D cylindrical hydrocode and investigated the dependence of the mass of the atmospheric loss on the atmospheric pressure. Numerical Calculations: We considered a vapor expansion in a planetary atmosphere, which is gravitationally bound to the planet. The atmosphere is assumed to be isothermal. The vapor cloud, which is generated by the impact, is considered to be homogeneous and at rest initially within a hemisphere centered at the impact point. We approximated both the atmosphere and vapor cloud as an ideal gas. To calculate the motion of the atmosphere with the vapor expansion and the mass of atmospheric loss, we developed a 2-D cylindrical hydrocode. This code is based on the algorithm CIP (Cubic Interpolated Propagation) [5]. The entire computational region is resolved into 180×180 grids. The spatial interval is 0.1 rv for the initial vapor cloud, where rv is the initial vapor radius. The interval in the other region increases by a geometric series. We normalized hydrodynamic equations and initial conditions by using appropriate scales and then derived four dimensionless parameters as follows,