We investigate the origin and loss of captured hydrogen envelopes from protoplanets having masses in a range between 'sub-Earth'-like bodies of 0.1M ⊕ and 'super-Earths' with 5M ⊕ 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 0.1-1M ⊕ we obtain hydrogen envelopes with masses between ∼ 2.5 × 10 19 -1.5 × 10 26 g. For 'super-Earths' with masses between 2-5M ⊕ more massive hydrogen envelopes within the mass range of ∼ 7.5 × 10 23 -1.5 × 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 ∼ 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, more massive 'super-Earths' that 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.

Terrestrial planets formed within gaseous protoplanetary disks can accumulate significant hydrogen envelopes. The evolution of such an atmosphere due to XUV driven evaporation depends on the activity evolution of the host star, which itself depends sensitively on its rotational evolution, and therefore on its initial rotation rate. In this Letter, we derive an easily applicable method for calculating planetary atmosphere evaporation that combines models for a hydrostatic lower atmosphere and a hydrodynamic upper atmosphere. We show that the initial rotation rate of the central star is of critical importance for the evolution of planetary atmospheres and can determine if a planet keeps or loses its primordial hydrogen envelope. Our results highlight the need for a detailed treatment of stellar activity evolution when studying the evolution of planetary atmospheres.

Latest research in planet formation indicates that Mars formed within a few million years (Myr) and remained as a planetary embryo that never grew to a more massive planet. It can also be expected from dynamical models that most of Mars' building blocks consisted of material that formed in orbital locations just beyond the ice line which could have contained ~0.1–0.20.25emwt.% of H2O. By using these constraints, we estimate the nebula-captured and catastrophically outgassed volatile contents during the solidification of Mars' magma ocean and apply a hydrodynamic upper atmosphere model for the study of the soft X-ray and extreme ultraviolet (XUV) driven thermal escape of the martian protoatmosphere during the early active epoch of the young Sun. The amount of gas that has been captured from the protoplanetary disk into the planetary atmosphere is calculated by solving the hydrostatic structure equations in the protoplanetary nebula. Depending on nebular properties such as the dust grain depletion factor, planetesimal accretion rates and luminosities, hydrogen envelopes with masses ≥3×10190.25emnormalg to ≤6.5×10220.25emnormalg could have been captured from the nebula around early Mars. Depending on the before mentioned parameters, due to the planets low gravity and a solar XUV flux that was ~100 times stronger compared to the present value, our results indicate that early Mars would have lost its nebular captured hydrogen envelope after the nebula gas evaporated, during a fast period of ~0.1–7.50.25emMyr. After the solidification of early Mars' magma ocean, catastrophically outgassed volatiles with the amount of ~50–2500.25embar H2O and ~10–550.25embar CO2 could have been lost during ~0.4–120.25emMyr, if the impact related energy flux of large planetesimals and small embryos to the planet's surface lasted long enough, that the steam atmosphere could have been prevented from condensing. If this was not the case, then our results suggest that the timescales for H2O condensation and ocean formation may have been shorter compared to the atmosphere evaporation timescale, so that one can speculate that sporadically periods, where some amount of liquid water may have been present on the planet's surface. However, depending on the amount of the outgassed volatiles, because of impacts and the high XUV-driven atmospheric escape rates, such sporadically wet surface conditions may have also not lasted much longer than ~0.4–120.25emMyr. After the loss of the captured hydrogen envelope and outgassed volatiles during the first 100 Myr period of the young Sun, a warmer and probably wetter period may have evolved by a combination of volcanic outgassing and impact delivered volatiles ~4.0±0.20.25emGyr ago, when the solar XUV flux decreased to values that have been <10 times that of today's Sun.

Context. Young terrestrial planets, when they are still embedded in a circumstellar disk, accumulate an atmosphere of nebula gas. The evolution and eventual evaporation of the protoplanetary disk affect the structure and dynamics of the planetary atmosphere. These processes, combined with other mass loss mechanisms, such as thermal escape driven by extreme ultraviolet and soft X-ray radiation from the young host star, determine how much of the primary atmosphere, if anything at all, survives into later stages of planetary evolution. Aims. Our aim is to explore the structure and the dynamic outflow processes of nebula-accreted atmospheres in dependency on changes in the planetary environment. Methods. We integrate stationary hydrostatic models and perform time-dependent dynamical simulations to investigate the effect of a changing nebula environment on the atmospheric structure and the timescales on which the protoatmosphere reacts to these changes. Results. We find that the behavior of the atmospheres strongly depends on the mass of the planetary core. For planets of about Marsmass the atmospheric structure, and in particular the atmospheric mass, changes drastically and on very short timescales whereas atmospheres around higher mass planets are much more robust and inert.

In the early, disk-embedded phase of evolution of terrestrial planets, a protoplanetary core can accumulate gas from the circumstellar disk into a planetary envelope. In order to relate the accumulation and structure of this primordial atmosphere to the thermal evolution of the planetary core, we calculated atmosphere models characterized by the surface temperature of the core. We considered cores with masses between 0.1 and 5 M ⊕ situated in the habitable zone around a solar-like star. The time-dependent simulations in 1D-spherical symmetry include the hydrodynamics equations, gray radiative transport, and convective energy transport. Using an implicit time integration scheme, we can use large time steps and and thus efficiently cover evolutionary timescales. Our results show that planetary atmospheres, when considered with reference to a fixed core temperature, are not necessarily stable, and multiple solutions may exist for one core temperature. As the structure and properties of nebulaembedded planetary atmospheres are an inherently time-dependent problem, we calculated estimates for the amount of primordial atmosphere by simulating the accretion process of disk gas onto planetary cores and the subsequent evolution of the embedded atmospheres. The temperature of the planetary core is thereby determined from the computation of the internal energy budget of the core. For cores more massive than about one Earth mass, we obtain that a comparatively short duration of the disk-embedded phase (∼10 5 years) is sufficient for the accumulation of significant amounts of hydrogen atmosphere that are unlikely to be removed by later atmospheric escape processes.