XUV exposed non-hydrostatic hydrogen-rich upper atmospheres of   terrestrial planets. Part I: Atmospheric expansion and thermal escape
  The recently discovered low-density "super-Earths" Kepler-11b, Kepler-11f, Kepler-11d, Kepler-11e, and planets such as GJ 1214b represent most likely planets which are surrounded by dense H/He envelopes or contain deep H2O oceans also surrounded by dense hydrogen envelopes. Although these "super-Earths" are orbiting relatively close to their host stars, they have not lost their captured nebula-based hydrogen-rich or degassed volatile-rich steam protoatmospheres. Thus it is interesting to estimate the maximum possible amount of atmospheric hydrogen loss from a terrestrial planet orbiting within the habitable zone of late main sequence host stars. For studying the thermosphere structure and escape we apply a 1-D hydrodynamic upper atmosphere model which solves the equations of mass, momentum and energy conservation for a planet with the mass and size of the Earth and for a "super-Earth" with a size of 2 R_Earth and a mass of 10 M_Earth. We calculate volume heating rates by the stellar soft X-ray and EUV radiation and expansion of the upper atmosphere, its temperature, density and velocity structure and related thermal escape rates during planet's life time. Moreover, we investigate under which conditions both planets enter the blow-off escape regime and may therefore experience loss rates which are close to the energy-limited escape. Finally we discuss the results in the context of atmospheric evolution and implications for habitability of terrestrial planets in general. 
N. V. Erkaev, H. Lammer, P. Odert, Yu. N. Kulikov, K. G. Kislyakova,   M. L. Khodachenko, M. G\"udel, A. Hanslmeier, H. Biernat
astro-ph.EP