Origin and loss of nebula-captured hydrogen envelopes from 'sub'- to 'super-Earths' in the habitable zone of Sun-like stars

We investigate the origin and loss of captured hydrogen envelopes from protoplanets having masses in a range between 'sub-Earth'-like bodies of 0.1 M-circle plus and 'super-Earths' with 5 M-circle plus in the habitable zone at 1 au of a Sun-like G star, assuming that their rocky cores had formed before the nebula gas dissipated. We model the gravitational attraction and accumulation of nebula gas around a planet's core as a function of protoplanetary luminosity during accretion and calculate the resulting surface temperature by solving the hydrostatic structure equations for the protoplanetary nebula. Depending on nebular properties, such as the dust grain depletion factor, planetesimal accretion rates, and resulting luminosities, for planetary bodies of 0.1-1 M-circle plus we obtain hydrogen envelopes with masses between similar to 2.5 x 10(19) and 1.5 x 10(26) g. For 'super-Earths' with masses between 2 and 5 M-circle plus more massive hydrogen envelopes within the mass range of similar to 7.5 x 10(23)-1.5 x 10(28) g can be captured from the nebula. For studying the escape of these accumulated hydrogen-dominated protoatmospheres, we apply a hydrodynamic upper atmosphere model and calculate the loss rates due to the heating by the high soft-X-ray and extreme ultraviolet (XUV) flux of the young Sun/star. The results of our study indicate that under most nebula conditions 'sub-Earth' and Earth-mass planets can lose their captured hydrogen envelopes by thermal escape during the first similar to 100 Myr after the disc dissipated. However, if a nebula has a low dust depletion factor or low accretion rates resulting in low protoplanetary luminosities, it is possible that even protoplanets with Earth-mass cores may keep their hydrogen envelopes during their whole lifetime. In contrast to lower mass protoplanets, more massive 'super-Earths', which can accumulate a huge amount of nebula gas, lose only tiny fractions of their primordial hydrogen envelopes. Our results agree with the fact that Venus, Earth, and Mars are not surrounded by dense hydrogen envelopes, as well as with the recent discoveries of low density 'super-Earths' that most likely could not get rid of their dense protoatmospheres.