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We investigate the origin and loss of captured hydrogen envelopes fromprotoplanets 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, assumingtheir rocky cores had formed before the nebula dissipated. We model thegravitational accumulation of nebula gas around a core as a function ofprotoplanetary luminosity during accretion and calculate the resulting surfacetemperature by solving the hydrostatic structure equations for theprotoplanetary nebula. Depending on nebular properties and resultingluminosities, for planetary bodies of 0.1--1$M_{\oplus}$ we obtain hydrogenenvelopes 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 envelopeswithin the mass range of $\sim 7.5\times 10^{23}$--$1.5\times 10^{28}$ g can becaptured. To study the escape of these hydrogen-dominated protoatmospheres, weapply a hydrodynamic upper atmosphere model and calculate the loss rates due tothe heating by the high XUV flux of the young star. Our results indicate thatunder most nebula conditions `sub-Earth' and Earth-mass planets can lose theirenvelopes by thermal escape during the first $100$ Myr after the diskdissipated. However, if a nebula has a low dust depletion factor or lowaccretion rates resulting in low protoplanetary luminosities, it is possiblethat even protoplanets with Earth-mass cores may keep their hydrogen envelopesduring their whole lifetime. In contrast to lower mass protoplanets,`super-Earths' accumulate a huge amount of nebula gas and lose only tinyfractions of their primordial envelopes. Our results agree with the fact thatVenus, Earth, and Mars are not surrounded by dense hydrogen envelopes, as wellas with the recent discoveries of low density `super-Earths' that most likelycould not get rid of their protoatmospheres.

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