Overcoming the Limitations of the Energy-limited Approximation for Planet Atmospheric Escape
Abstract
Studies of planetary atmospheric composition, variability, and evolution require appropriate theoretical and numerical tools to estimate key atmospheric parameters, among which the mass-loss rate is often the most important. In evolutionary studies, it is common to use the energy-limited formula, which is attractive for its simplicity but ignores important physical effects and can be inaccurate in many cases. To overcome this problem, we consider a recently developed grid of about 7000 one-dimensional upper-atmosphere hydrodynamic models computed for a wide range of planets with hydrogen-dominated atmospheres from which we extract the mass-loss rates. The grid boundaries are [1:39] {M}\oplus in planetary mass, [1:10] {R}\oplus in planetary radius, [300:2000] K in equilibrium temperature, [0.4:1.3] {M}⊙ in host star’s mass, [0.002:1.3] au in orbital separation, and about [1026:5×1030] erg s-1 in stellar X-ray and extreme ultraviolet luminosity. We then derive an analytical expression for the atmospheric mass-loss rates based on a fit to the values obtained from the grid. The expression provides the mass-loss rates as a function of planetary mass, planetary radius, orbital separation, and incident stellar high-energy flux. We show that this expression is a significant improvement to the energy-limited approximation for a wide range of planets. The analytical expression presented here enables significantly more accurate planetary evolution computations without increasing computing time.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- October 2018
- DOI:
- 10.3847/2041-8213/aae586
- arXiv:
- arXiv:1810.06920
- Bibcode:
- 2018ApJ...866L..18K
- Keywords:
-
- planets and satellites: atmospheres;
- planets and satellites: gaseous planets;
- planets and satellites: general;
- planets and satellites: physical evolution;
- Astrophysics - Earth and Planetary Astrophysics
- E-Print:
- 7 pages, 3 Figures, 2 Tables, published