Atmospheric erosion and replenishment induced by impacts upon the Earth and Mars during a heavy bombardment

Consequences of a heavy bombardment for the atmospheres of Earth and Mars are investigated with a stochastic model. The main result is the dominance of the accumulation. The atmospheric pressure is strongly increasing both for Earth and Mars in the course of an enhanced bombardment. The effect of atmospheric erosion is found to be minor, regarding escape during meteorite entry, in the expanding vapor plume, and ejection due to free-surface motion. The initial atmospheric surface pressure if comparable to the modern value turns out as a less important additive constant of the final pressure. Impactor retention and atmospheric erosion are parametrized in terms of scaling laws, compatible with recent numerical simulations. The dependence on impactor size, atmospheric and planetary parameters is analyzed among alternative models and numerical results. The stochastic model is fed with the net replenishment originating from impactor material and the loss of preexisting atmospheric gas. Major input parameters are the total cumulative impactor mass and the relative mass of atmophile molecules in comets and asteroids. Input size distributions of the impactor ensemble correspond to presently observed main belt asteroids and KBOs. Velocity distributions are taken from dynamical simulations for the Nice model. Depending on the composition of large cometary impactors, the Earth could acquire a more massive atmosphere, a few bars in terms of surface pressure, mostly as CO and CO₂. For Mars accumulation of 1–4 bars of CO and CO₂ requires an asteroidal ‘late veneer’ of the order of 10²⁴ g containing 2% atmophiles.