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Photoevaporation is thought to play an important role in the early planetary evolution. In this study, we investigate the diffusion limit of X-ray and ultraviolet induced photoevaporation in primordial atmospheres. We find that compositional fractionation resulting from mass loss is more significant than currently recognized because it is controlled by the conditions at the top of the atmosphere, where particle collisions are less frequent. Such fractionation at the top of the atmosphere develops a compositional gradient that extends downward. Mass outflow eventually reaches a steady state in which hydrogen loss is diffusion limited. We derive new analytic expressions for the diffusion-limited mass loss rate and the crossover mass., Comment: Accepted for publication in The Astrophysical Journal

Convection in planetary mantles is in the so-called mixed heating mode; it is driven by heating from below, due to a hotter core, as well as heating from within, due to radiogenic heating and secular cooling. Thus, in order to model the thermal evolution of terrestrial planets, we require the parameterization of heat flux for mixed heated convection in particular. However, deriving such a parameterization from basic principles is an elusive task. While scaling laws for purely internal heating and purely basal heating have been successfully determined using the idea that thermal boundary layers are marginally stable, recent theoretical analyses have questioned the applicability of this idea to convection in the mixed heating mode. Here, we present a scaling approach that is rooted in the physics of convection, including the boundary layer stability criterion. We show that, as long as interactions between thermal boundary layers are properly accounted for, this criterion succeeds in describing relationships between thermal boundary layer properties for mixed heated convection. The surface heat flux of a convecting fluid is locally determined by the properties of the upper thermal boundary layer, as opposed to globally determined. Our foundational scaling approach can be readily extended to nearly any complexity of convection within planetary mantles.

The early evolution of the Earth-Moon system prescribes the tidal environment of the Hadean Earth and holds the key to the formation mechanism of the Moon and its thermal evolution. Estimating its early state by backtracking from the present, however, suffers from substantial uncertainties associated with ocean tides. Tidal evolution during the solidification of Earth's magma ocean, on the other hand, has the potential to provide robust constraints on the Earth-Moon system before the appearance of a water ocean. Here we show that energy dissipation in a solidifying magma ocean results in considerably more limited lunar recession than previously thought, and that the Moon was probably still at the distance of $\sim$7-9 Earth radii at the end of solidification. This limited early recession aggravates the often overlooked difficulty of modeling tidal dissipation in Earth's first billion years, but it also offers a new possibility of resolving the lunar inclination problem by allowing the operation of multiple excitation mechanisms.

A significant fraction of super-Earths and sub-Neptunes are thought to experience an extreme loss of volatiles because of atmospheric evaporation in the early stages of their life. Though the mechanisms behind the extreme mass loss are not fully understood, two contenders have been widely discussed: photoevaporation from X-ray and ultraviolet irradiation and core powered mass loss. Here, it is shown that both mechanisms occur but with different timescales, and that atmospheric loss can take place over three regimes. In the first regime, a planet has very high internal temperatures arising from its high-energy formation processes. These high temperatures give rise to a fully convecting atmosphere that efficiently loses mass without much internal cooling. The second regime applies to planets with lower internal temperatures, so a radiative region forms but the photosphere still remains outside the Bondi radius. Hence, mass loss continues to depend only on the internal temperatures. Planets with the lowest internal temperatures are in the third regime, when the photosphere forms below the Bondi radius and mass is lost primarily because of X-ray and ultraviolet irradiation. This paper provides the first unifying framework for modeling atmospheric evaporation through the lifespan of a planet., Comment: 37 pages, 13 figures, 2023 ApJ 943 11

A sufficient amount of water is required at the surface to develop water oceans. A significant fraction of water, however, remains in the mantle during magma ocean solidification, and thus the existence of water oceans is not guaranteed even for exoplanets located in the habitable zone. To discuss the likelihood of ocean formation, we built two models to predict the rate of mantle degassing during the magma ocean stage and the subsequent solid-state convection stage. We find that planets with low H$_2$O/CO$_2$ ratios would not have a sufficient amount of surface water to develop water oceans immediately after magma ocean solidification, and the majority of the water inventory would be retained in the mantle during their subsequent evolution regardless of planetary size. This is because oceanless planets are likely to operate under stagnant lid convection, and for such planets, dehydration stiffening of the depleted lithospheric mantle would limit the rate of mantle degassing. In contrast, a significant fraction of CO$_2$ would already be degassed during magma ocean solidification. With a strong greenhouse effect, all surface water would exist as vapor, and water oceans may be absent throughout planetary evolution. Volatile concentrations in the bulk silicate Earth are close to the threshold amount for ocean formation, so if Venus shared similar concentrations, small differences in solar radiation may explain the divergent evolutionary paths of Earth and Venus., Comment: 27 pages, 11 figures

Chondrites are the likely building blocks of Earth, and identifying the group of chondrite that best represents Earth is a key to resolving the state of the early Earth. The origin of chondrites, however, remains controversial partly because of their puzzling major element compositions, some exhibiting depletion in Al, Ca, and Mg. Based on a new thermochemical evolution model of protoplanetary disks, we show that planetesimals with depletion patterns similar to ordinary and enstatite chondrites can originate at 1-2 AU just outside where enstatite evaporates. Around the "evaporation front" of enstatite, the large inward flow of refractory minerals, including forsterite, takes place with a high pebble concentration, and the loss of those minerals result in depletion in Al, Ca, and Mg. When evaporated solid grains re-condense onto pebbles, the concentration of pebbles is further enhanced, potentially triggering the streaming instability. Planetesimals with the composition of ordinary and enstatite chondrites can thus be naturally created in the terrestrial region. The preferential loss of forsterite also creates an enhancement of Mg/Si and heavy Si isotopes just inside the potential source region for ordinary and enstatite chondrites. Earth, which shows both features, may originate just inside where ordinary and enstatite chondrites were born., Comment: 16 pages, 6 figures, 1 table

We propose the possibility of a new phenomenon affecting the settling of dust grains at the terrestrial region in early protoplanetary disks. Sinking dust grains evaporate in a hot inner region during the early stage of disk evolution, and the effects of condensation and evaporation on vertical dust settling can be significant. A 1-D dust settling model considering both physical and chemical aspects is presented in this paper. Modeling results show that dust grains evaporate as they descend into the hotter interior and form a "condensation front," above which dust-composing major elements, Mg, Si, and Fe, accumulate, creating a large temperature gradient. Repeated evaporation at the front inhibits grain growth, and small grain sizes elevate the opacity away from the mid-plane. Self-consistent calculations including radiative heat transfer and condensation theory suggest that the mid-disk temperature could be high enough for silicates to remain evaporated longer than previous estimates. The formation of a condensation front leads to contrasting settling behaviors between highly refractory elements, such as Al and Ca, and moderately refractory elements, such as Mg, Si, and Fe, suggesting that elemental abundance in planetesimals may not be a simple function of volatility., Comment: 18 pages, 11 figures

The ongoing discovery of terrestrial exoplanets accentuates the importance of studying planetary evolution for a wide range of initial conditions. We perform thermal evolution simulations for generic terrestrial planets with masses ranging from that of Mars to 10 Earth-masses in the stagnant-lid regime, the most natural mode of convection with strongly temperature- dependent viscosity. Given considerable uncertainty surrounding the dependency of mantle rheology on pressure, we choose to focus on the end-member case of pressure-independent potential viscosity, where viscosity does not change with depth along an adiabatic temperature gradient. We employ principal component analysis and linear regression to capture the first-order systematics of possible evolutionary scenarios from a large number of simulation runs. With increased planetary mass, crustal thickness and the degree of mantle processing are both predicted to decrease, and such size effects can also be derived with simple scaling analyses. The likelihood of plate tectonics is quantified using a mantle rheology that takes into account both ductile and brittle deformation mechanisms. Confirming earlier scaling analyses, the effects of lithosphere hydration dominate the effects of planetary mass. The possibility of basalt-eclogite phase transition in the planetary crust is found to increase with planetary mass, and we suggest that massive terrestrial planets may escape the stagnant-lid regime through the formation of a self-destabilizing dense eclogite layer., Comment: 22 pages, 13 figures, accepted for publication in Icarus

The scaling of plate-tectonic convection is investigated by simulating thermal convection with pseudoplastic rheology and strongly temperature-dependent viscosity. The effect of mantle melting is also explored with additional depth-dependent viscosity. Heat-flow scaling can be constructed with only two parameters, the internal Rayleigh number and the lithospheric viscosity contrast, the latter of which is determined entirely by rheological properties. The critical viscosity contrast for the transition between plate-tectonic and stagnant-lid convection is found to be proportional to the square root of the internal Rayleigh number. The relation between mantle temperature and surface heat flux on Earth is discussed on the basis of these scaling laws, and the inverse relationship between them, as previously suggested from the consideration of global energy balance, is confirmed by this fully dynamic approach. In the presence of surface water to reduce the effective friction coefficient, the operation of plate tectonics is suggested to be plausible throughout the Earth history., Comment: Accepted for publication in Journal of Geophysical Research - Solid Earth