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 between sub-Earth'-like bodies of 0.1$M_{\oplus}$ up to super-Earths’ with 5$M_{\oplus }$ in the HZ of a Sun like G star, assuming their rocky cores had formed before the nebula dissipated. We model the gravitational accumulation of nebula gas around a 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 and resulting luminosities, for planetary bodies of 0.1–1$M_{\oplus }$ we obtain hydrogen envelopes with masses between $\sim 2.5\times {10}^{19}$–$1.5\times {10}^{26}$ g. For super-Earths' with masses between 2--5$M_{\oplus}$ hydrogen envelopes within the mass range of $\sim 7.5\times 10^{23}$--$1.5\times 10^{28}$ g can be captured. To study the escape of these hydrogen-dominated protoatmospheres, we apply a hydrodynamic upper atmosphere model and calculate the loss rates due to the heating by the high XUV flux of the young star. Our results indicate that under most nebula conditions sub-Earth’ and Earth-mass planets can lose their envelopes by thermal escape during the first $100$ Myr after the disk 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, super-Earths' accumulate a huge amount of nebula gas and lose only tiny fractions of their primordial 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 protoatmospheres.