Thermal mass loss of protoplanetary cores with hydrogen-dominated   atmospheres: The influences of ionization and orbital distance
  We investigate the loss rates of the hydrogen atmospheres of terrestrial planets with a range of masses and orbital distances by assuming a stellar extreme ultraviolet (EUV) luminosity that is 100 times stronger than that of the current Sun. We apply a 1D upper atmosphere radiation absorption and hydrodynamic escape model that takes into account ionization, dissociation and recombination to calculate hydrogen mass loss rates. We study the effects of the ionization, dissociation and recombination on the thermal mass loss rates of hydrogen-dominated super-Earths and compare the results to those obtained by the energy-limited escape formula which is widely used for mass loss evolution studies. Our results indicate that the energy-limited formula can to a great extent over- or underestimate the hydrogen mass loss rates by amounts that depend on the stellar EUV flux and planetary parameters such as mass, size, effective temperature, and EUV absorption radius. 
N. V. Erkaev, H. Lammer, P. Odert, K. G. Kislyakova, C. P. Johnstone,   M. G\"udel, M. L. Khodachenko
astro-ph.EP