Effect Of The Radiation Pressure On Planetary Exospheres: Analytical Approach And Application To Earth, Mars and Hot Jupiters

Abstract:

The atomic Hydrogen is one of the most abundant species in many planetary exospheres, such as on Earth, on planets in the Solar System and on Hot Jupiters. Because the exosphere is a quasi-collisionless medium, the atomic Hydrogen can reach several planetary radii without collisions and its motion is only determined by external forces such as the gravity and the radiation pressure. However, the exosphere still remains a complex medium : 1) to model because, on one hand, this is a region of interaction between the interplanetary medium and the planetary atmosphere and, on another hand, the fluid approach is not appropriate and a kinetic should be used instead, 2) to observe because of the extremely low densities. Currently, the most used analytical model to determine the neutral density profiles is the well-known Chamberlain’s one, which however includes only the gravity. We have developed an analytical model based on the previous work by Bishop and Chamberlain (1989) with a Hamiltonian approach, taking into account both the gravity and the radiation pressure. We extend their previous 1D model (density profiles on the Sun-planet axis only) into a 2D model depending on the distance from the planet and the zenith angle to derive density profiles (Beth et al. 2015b, in review). Moreover, we derived an analytical formula for the thermal escape to compare with the classical Jeans’ escape flux.

We thus show that the radiation pressure induces :

1. Strong density asymmetries at high altitudes in the planetary exospheres, leading to the phenomenon of “geotail” at Earth,
2. Natural existence of an external limit (or exopause) for the exosphere, whose location is analytically determined,
3. Increase of the exospheric densities compared with Chamberlain profiles without radiation pressure (e.g. up to +150% at 5 Martian radius),
4. Significant increase of the thermal escape flux (up to 30/35% for Earth/Mars today), until a “blow-off” regime with a constant escape flux for an extreme radiation pressure. The influence of the radiation pressure on the escape flux may thus bring conditions on the size of primary atmospheres, because of a strong radiation pressure in the Sun’s young years.
5. Same effects on exoplanets, in particular on the hot Jupiters that are also subject to additional effects : centrifugal force and stellar gravity.