The atmospheric noble gas isotope and elemental bulk ratios on Venus and Earth provide important information on their origin and evolution. If the protoplanets grew to a certain mass (i.e. > 0.5 MEarth), they could have captured H2-dominated primordial atmospheres by accreting gas from the circumstellar disk during the formation of the Solar System, which were then quickly lost by hydrodynamic escape after the disk dissipated. In such a case, the EUV-driven hydrodynamic flow of H atoms dragged heavier elements with it at different rates, leading to changes in their initial isotope ratios. For reproducing Earth and Venus present atmospheric 36Ar/38Ar, 20Ne/22Ne, 36Ar/22Ne, isotope and bulk K/U ratios we applied hydrodynamic upper atmosphere escape and Smooth Particle Hydrodynamics (SPH) impact models for the loss calculations of captured H2-dominated primordial atmospheres for various protoplanetary masses. We investigated a wide range of possible EUV evolution tracks of the young Sun and initial atmospheric compositions based on mixtures of captured nebula gas, outgassed and delivered material from ureilite, enstatite and carbonaceaous chondrites. Depending on the disk lifetime of ≈ 3–5 Myr (Bollard et al., 2017; Wang et al., 2017) and the composition of accreted material after disk dispersal, we find from the reproduction of the present atmospheric Ar, Ne, and bulk K/U ratios, that early Earth's evolution can be explained if proto-Earth had accreted masses between ≈ 0.53 − 0.58 MEarth by the time the nebula gas dissipated. If proto-Earth would have accreted a higher mass during the disk lifetime the present atmospheric Ar and Ne isotope ratios can not be reproduced with our model approach. For masses > 0.75 MEarth, Earth would have had a problem to get get rid of its primordial atmosphere. If proto-Earth accreted ≈ 0.53 − 0.58MEarth of enstatite-dominated material as suggested by Dauphas (2017) during the disk lifetime, it would have captured a tiny primordial atmosphere that was lost ≈ 3 Myr after the disk dissipated. In such a case we find that the present-day atmospheric Ar and Ne isotope ratios can be best reproduced if the post-nebula impactors contained ≈ 5% weakly depleted carbonaceous chondritic material and ≈ 95% enstatite chondrites that are strongly depleted in Ar, Ne and moderately volatile elements like potassium. If higher amounts of carbonaceous chondrites were involved in early Earth's accretion as recently suggested by Schiller et al. (2018), then the Earth's present atmospheric Ar and Ne ratios can only be reproduced if the involved carbonaceous chondritic post-nebula material was also highly depleted in these noble gases and/or had to be partially be delivered as long as the primordial atmosphere was yet escaping. As long as primordial atmospheres surround the growing protoplanets the abundance of their volatile elements is overwritten by their respective captured solar-like atmospheric abundances. Therefore the initial composition of the protoplanets at the disk dispersal time can not be identified by our method. For masses < 0.5 MEarth atmospheric escape cannot explain the present-day ratios, i.e. if Earth grew slower then these ratios have to be explained differently (Marty, 2012). If proto-Venus captured a primordial atmosphere it should have grown to masses of ≈ 0.85− 1.0 MVenus during the time until the disk dissipated and if early Venus accreted its main mass during the disk lifetime than the present atmospheric Ar and Ne isotope ratios and the observed K/U ratios on Venus surface can also be reproduced by the escape of a captured primordial atmosphere that is lost within ≤ 100 Myr, if the Sun was born as a weakly to moderately active young G star. New precise re-measurements of atmospheric noble gases are necessary by future Venus missions to better constrain the material that was involved in the planet's accretion history and possibly also the EUV activity evolution of the young Sun. In addition, measurements of other moderately volatile element and isotope ratios on the surface such as Rb/U, 64Zn/66Zn, and 39K/41K can give an insight on whether Venus accreted slow or fast, i.e. almost to its final mass within the disk lifetime.
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