Conservation of total escape from hydrodynamic planetary atmospheres

- More efficient escape leads to increased cooling in a hydrodynamic atmosphere.
- The upper atmosphere shrinks under increased cooling.
- The total escape rate is conserved (nearly a constant) for a hydrodynamic atmosphere under the same level of heating.

Atmosphere escape is one key process controlling the evolution of planets. However, estimating the escape rate in any detail is difficult because there are many physical processes contributing to the total escape rate. Here we show that as a result of energy conservation the total escape rate from hydrodynamic planetary atmospheres where the outflow remains subsonic is nearly constant under the same stellar XUV photon flux when increasing the escape efficiency from the exobase level, consistent with the energy-limited escape approximation. Thus the estimate of atmospheric escape in a planetʼs evolution history can be greatly simplified.