DISCRETE VELOCITY MODEL FOR AN ESCAPING SINGLE-COMPONENT ATMOSPHERE

The structure of an escaping single-component planetary atmosphere is computed by direct numerical integration the nonlinear Boltzmann equation. The transition from collision-dominated behavior deep in the atmosphere to nearly collisionless behavior at great altitudes is therefore treated self-consistently for the first time. We consider a hypothetical planet having the same mass and radius as the Earth, surrounded by an atmosphere of atoms having the same mass and total hard-sphere collision cross-section as atomic hydrogen. The atmosphere is initially hydrostatic and isothermal, at a temperature of 1000 K. As the computation progresses, the atmosphere gradually escapes. Eventually, a quasi-steady state is reached in which the density decreases significantly more rapidly than the initial barometric distribution, and the temperature decreases nearly 200 K between the planetary surface and an altitude of 10,000 km. The bulk upward flow speed increases with altitude above the exobase. However, because the most energetic particles escape and are not replenished, the atmosphere gradually cools, and the deep, collision-dominated portion of the atmosphere settles towards the planet’s surface. The high-velocity tail of the velocity distribution function is quite anisotropic over a large range of altitudes, and remains largely depleted of incoming unbound particles even well below the exobase. At the highest altitudes in our simulation, the population of escaping unbound particles is considerably enhanced by the streaming of such particles from the warmer and denser regions below. The computed escape flux is at least 30% greater than the Jeans flux as a result of this effect. It is suggested that computations similar to this one may prove useful for studying atmospheric escape from the primeval terrestrial planets, comets and Pluto.