Evolution of Mercury's Earliest Exosphere

MESSENGER observations suggest a magma ocean formed on proto-Mercury, during which evaporation of metals and outgassing of C- and H-bearing volatiles produced an early atmosphere. Atmosphericescape subsequently occurred by plasma heating, photoevaporation, Jeans escape, and photoionization.To quantify atmospheric loss, we combine constraints on the lifetime of sur cial melt, melt composition, and atmospheric composition. Consideration of two initial Mercury sizes and four magma oceancompositions determine the atmospheric speciation at a given surface temperature. A coupled interior-atmosphere model determines the cooling rate and therefore the lifetime of surficial melt. Combining the melt lifetime and escape flux calculations provide estimates for the total mass loss from earlyMercury. Loss rates by Jeans escape are negligible. Plasma heating and photoionization are limited by homopause diffusion rates of 10^6 kg/s. Loss by photoevaporation depends on the timing of Mercuryformation and assumed heating efficiency and ranges from 10^6.6 to 10^9.6 kg/s. The material for photoevaporation is sourced from below the homopause and is therefore energy-limited rather thandiffusion-limited. The timescale for efficient interior{atmosphere chemical exchange is less than ten thousand years. Therefore, escape processes only account for an equivalent loss of less than 2.3 km of crust (0:3% of Mercury's mass). Accordingly, 0:02% of the total mass of H2O and Na is lost.Therefore, cumulative loss cannot significantly modify Mercury's bulk mantle composition during the magma ocean stage. Mercury's high core:mantle ratio and volatile-rich surface may instead reflect chemical variations in its building blocks resulting from its solar-proximal accretion environment. \section{Introduction} \label{intro}% surface compositionMESSENGER data from X-ray, gamma ray, and neutron spectrometers constrain the composition of Mercury's surface, and motivate theories and models to understand Mercury's bulk composition, formation, and evolution. The surface composition and geology of Mercury is compatible with partial melting of cumulates that were originally formed by magma ocean crystallization \citep{MPM18}. Subsequent impact excavation exposed the cumulates at the surface \citep{MPM18,CGZ13}. The low oxygen fugacity (\emph{f}\ce{O_2}) of the uppermost layer of Mercury's regolith, together with Mercury's large core size, suggest a reduced mantle where nominally lithophile elements such as Ca, Mn, Cr, and Ti are present in sulfides rather than silicates \citep{VKM16}. Relative to basaltic rocks exposed at the surface of other terrestrial planets, a large amount of the moderately volatile element Na (3--5 wt\%) is detected on Mercury's surface \citep{Peplowski2014}. Observations of Na variation in Mercury's exosphere may relate to night-side deposit formation and dawn re-emission \citep[e.g.,][]{CMK16}. Hence, it remains an open question how moderately volatile elements such as Na may have accumulated on the surface---whether from an extant or now extinct process---and how their abundance compares to Mercury's bulk composition. % magma oceansMagma oceans are pivotal in determining the initial conditions and subsequent evolution and chemical differentiation of terrestrial planets in the solar system \citep[e.g.,][]{E12,Chao2021}. Radiometric dating reveals that magmatic iron meteorites, which represent planetesimal cores, formed within 2 Myr of solar system formation \citep{Kruijer2014}. The rocky planet whose mass is most similar to that of Mercury, and for which samples are available, Mars, likely accreted, formed an iron core, and underwent complete solidification of its magma ocean ocean within about 20 Myr of solar system formation \citep{BCC18}. Crucially, rapid core formation in terrestrial planets requires a magma ocean to enable efficient metal segregation \citep{S90}. By analogy, and given its solar-proximal location, extensive melting is therefore expected to have occurred on proto-Mercury \citep{VKM16, BE09}. Following its crystallisation, partial melting of magma ocean cumulates have been invoked to explain Mercury's contemporary surface composition \citep{MPM18}.% Mercury formationEnergy from accretion and radiogenic heat (e.g. from $^{26}$Al) may have driven the differentiation of Mercury if it formed sufficiently early in solar system history \citep{BHS17,Siegfried1974}. Following a phase of rapid growth, the subsequent reduction of impactor flux would have enabled Mercury's magma ocean to cool and crystallize without additional large-scale remelting. During this time, the mantle is expected to have stratified into a basal layer of olivine and a plagioclase and clinopyroxene dominated crust which is now observed on Mercury's surface \citep{BE09}. During the cooling of the magma ocean when the surface remains mostly molten, chemical species readily exchange between the interior, atmosphere, and exosphere---as occurred for other terrestrial planets in the solar system \citep[e.g.,][]{ET08}.% Fegley and Cameron bulk Mercury\cite{Feg87} addressed the hypothesis that the anomalously high bulk density of Mercury (owing to a high core/mantle ratio) is the result of evaporation of silicate melt components from the surface of a Hermean magma ocean. They presumed atmospheric loss was sufficiently slow that the atmosphere remained in equilibrium with the magma ocean. In their model, vapor was removed in a step-wise fashion and the composition of the magma ocean evolved accordingly. In reality, however, evaporated species are transported, mixed, and lost from the atmosphere and exosphere, with the flux at which loss occurs integrated over the magma ocean lifetime ultimately dictating the total mass loss. Therefore, consideration of interior, atmospheric, and exospheric processes are necessary to assess whether significant quantities of rock-derived atmospheres can be lost during the Hermean magma ocean stage.% atmospheric lossBased on observations of solar-mass stars, the early solar extreme ultraviolet (EUV) and X-ray fluxes were likely ~400 times larger than they are today. This would have made photoionization a highly efficient non-thermal, and photoevaporation a highly efficient thermal, atmospheric escape mechanism \citep{Johnstone2015,TCG15}. Other loss mechanisms of potential importance include atmospheric sputtering and kinetic escape (e.g. Jeans escape) that occur over the lifetime of the magma ocean. Non-thermal loss rates can be constrained by known plasma pressures at proto-Mercury due to the incoming solar wind, as well as EUV luminosities of the early Sun estimated from population studies of nearby Sun-like stars \citep{ribas14,TCG15}.% motivationIn this paper we establish the extent of element evaporation and loss from Mercury during its early magma ocean phase. Models are constructed of the (1) coupled evolution of the magma ocean and atmosphere, (2) evaporation of metals and metal-oxide species from the Hermean magma ocean, (3) the mixing ratios and abundances of molecular species throughout the atmosphere and at the exobase, and finally (4) loss rates of these species from the upper atmosphere. We discuss these results in the context of the chemical evolution of Mercury's surface environment, \edit1{bulk composition,} and present-day observations.