1. Introduction
The molecular composition of early terrestrial atmospheres is extremely important for understanding climatic conditions and prebiotic chemistry, especially at the time life was born on Earth and perhaps on Mars. For example, a CH4-rich atmosphere on early terrestrial planets has been invoked as a solution for the faint young Sun problem (Sagan and Mullen, 1972, Kiehl and Dickinson, 1987, Pavlov et al., 2000 and Haqq-Misra et al., 2008). Thus, the possibility of the abiotic formation of CH4-containing atmospheres on early terrestrial planets has been investigated rather extensively (Kress and McKay, 2004, Kasting, 2005, Hashimoto et al., 2007 and Schaefer and Fegley, 2010). However, the presence of such an atmosphere during the prebiotic stage is still highly controversial.

The estimation of the molecular composition of early terrestrial planetary atmospheres requires knowledge on both the source of volatiles and outgassing processes. The bulk elemental abundance of the volatile sources largely determines the overall redox states of early terrestrial atmospheres. Thus, the elemental abundance of a planetary atmosphere varies greatly depending on its volatile sources. Previous studies have discussed mainly the oxidation state of early atmospheres based on that of possible volatile sources (e.g., Hashimoto et al., 2007, Schaefer and Fegley, 2010 and Hirschmann, 2012).

In contrast, the influence of the thermodynamic paths of outgassing processes on the molecular composition of the degassing vapor has not been investigated extensively. However, cooling paths of the vapor should affect the thermodynamic stability of the molecular composition, especially in impact degassing. In fact, the above studies based on chemical equilibrium calculations indicate that the molecular composition of the vapor with a given elemental abundance could vary greatly depending on temperature and/or pressure (Hashimoto et al., 2007 and Schaefer and Fegley, 2010). For instance, the CH4/CO ratio of chondritic vapor may vary greatly as a function of pressure and temperature. Because pressure and temperature in expanding impact-degassed plume would change with time, its molecular composition would vary as a function of time. Furthermore, its terminal molecular composition also change depending on their cooling rate. In order to address these issues, one must consider the dynamic aspect of impact degassing process, such as adiabatic expansion and radiative cooling. However, such dynamic aspects of chondritic vapor has not been investigated extensively. These species have different chemical properties, and thus, the climates and nonequilibrium-reaction processes would also be different, strongly depending on molecular compositions, even if the bulk oxidation states of the atmosphere are the same (e.g., Zahnle, 1986 and McKay and Borucki, 1997).

Based on theoretical predictions, the source of volatiles for terrestrial planets could have varied with time evolution. During the main accretion phase, terrestrial planetary atmospheres are thought to have been generated by the capture of the solar nebula (e.g., Hayashi et al., 1979) and volatiles degassed from the magma ocean (e.g., Abe and Matsui, 1985). Such hybrid atmospheres from solar nebula/accreting materials would have been very reducing, rich in H2 and CO (Hashimoto et al., 2007). However, both theoretical and geochemical studies indicate that such very reducing primordial atmospheres may have been efficiently lost by a giant impact during the terminal phase of planetary accretion (Genda and Abe, 2005, Stewart and Mukhopadhyay, 2013 and Tucker and Mukhopadhyay, 2014). If this is the case, degassing by subsequent volcanic activity is thought to be the dominant source for the terrestrial atmosphere. However, the isotopic composition of volatiles in the terrestrial mantle cannot explain the characteristics of the present Earth’s atmosphere as we discuss in the following section. Therefore, other sources would be required as a part of the present atmosphere, such as the late accretion of volatiles with meteoritic impact after magma ocean solidification (e.g., Chyba, 1990 and Albarède, 2009).

In this study, we focus on impact degassing of volatiles from chondritic materials based on a consideration of the cooling path of impact-generated vapor plumes, and we discuss the implications of the results for the molecular composition of early atmospheres on terrestrial planets during the post-accretion phase. In Section 2, we discuss the importance of the late-impact delivery of volatiles for terrestrial planetary atmospheres, in Sections 3 and 4 we describe our models, in Section 5 we show the calculation results, in Section 6 we discuss the implications of our results for the earliest atmosphere of terrestrial planets, and in Section 7 we summarize our study.

2. Impact delivery of volatiles after magma ocean solidification
An efficient atmospheric loss during the giant impact stage and geochemical constraints on isotopic composition of noble gases supports that the impact degassing from late-accreting materials after magma ocean solidification have greatly contributed to the formation of the early terrestrial atmosphere than previously thought, as we discuss in the following.

In comparison with the solar abundance, noble gases in the volatile inventory of terrestrial planets are much more depleted than H, C, and N (e.g., Halliday, 2013). If all terrestrial volatiles were of solar nebula origin, the currently observed noble gas abundance in the present terrestrial atmosphere would require selective loss in noble gases to the space. This is because incorporation of noble gases into core is highly unlikely. However, such a simple view is not possible as the origin of the present terrestrial atmosphere as discussed in previous studies (e.g., Zahnle et al., 2010 and references therein). For example, Ne and N, which have similar atomic mass, are equally abundant in the solar composition. Thus, the Ne/N ratio of the terrestrial atmosphere would be close to unity if the origin of terrestrial volatiles is mainly the solar nebula because the mass fractionation by atmospheric escape between Ne and N would be limited. However, Ne is depleted relative to N on terrestrial planets by more than several orders of magnitude. Consequently, it is now widely believed that the solar nebula captured by the gravity of a protoplanet cannot be the only source for the terrestrial atmosphere and that other sources, such as degassing from meteoritic materials, must have made a major contribution (e.g., Brown, 1949). In fact, the abundance pattern of volatiles on terrestrial planets are approximately chondritic (e.g., Marty, 2012 and Halliday, 2013).

If major atmospheric erosion occurred during the accretion phase, the degassing of volatiles after the formation of planets would have largely controlled the composition of post-accretion terrestrial atmospheres. A recent theoretical study shows that giant impacts during the late accretion phase may have efficiently blown off pre-existing atmospheres if protoplanets were covered with oceans (Genda and Abe, 2005). Calculations on the thermal evolution of magma oceans overlaid with a steam atmosphere show that the timescales of water condensation for Mars (i.e., 0.1 Myr) and Earth (i.e., 1.5 Myr) may have been shorter than a typical interval between giant impacts (i.e., 5 Myr), whereas the timescale of water condensation for Venus (i.e., 10 Myr) may not have been shorter than the average interval (Lebrun et al., 2013). Consequently, most of the pre-existing atmospheres may have been lost during the stage of giant impacts for at least Mars and Earth. Nevertheless, it is also noted that most of primordial oceans are estimated to survive atmosphere-stripping giant impacts (Genda and Abe, 2005). Such selective loss of an atmosphere compared to an ocean is actually consistent with the geological observations that the H/N and H2O/Xe ratios of terrestrial planets are higher than any types of primitive materials (Halliday, 2013; Tucker and Mukhopadhyay, 2014; Dauphas and Morbidelli, 2014). If the efficiency of atmospheric loss during the main-accretion phase was very high, the contribution of late-impact delivery of volatiles to the terrestrial atmosphere is most likely significant.

The high abundances of highly siderophile elements (HSEs) in silicate mantles of many terrestrial planets (i.e., Vesta, the Moon, Mars, Earth) suggest that late accretion of chondritic materials, the so-called late veneer, on terrestrial planets after core formation may have been a common phenomenon in the inner Solar System (Dale et al., 2012 and Day et al., 2012). Thus, terrestrial planetary atmospheres during the post-accretion stage would have been mainly generated by outgassing from magmas and late-impact delivery of volatiles. Furthermore, the isotopic composition of nitrogen on the Earth surface is similar to carbonaceous chondrites, but that of mantles are lighter and more solar-like (e.g., Marty, 2012 and Cartigny and Marty, 2013). Such isotopic compositions of terrestrial nitrogen may reflect the overprint of the late veneer. Although these isotopic heterogeneity can also be achieved by the mass fractionation of gas molecules in primordial atmospheres, such as hydrodynamic escape, such processes cannot explain the abundance patterns of noble gases (Marty, 2012 and Cartigny and Marty, 2013). Moreover, the heavier isotopic compositions of Kr derived from the Earth’s mantle relative to those observed in the present atmosphere suggest that noble gases in the present terrestrial atmosphere is not residual of mantle degassing (Holland et al., 2009). These geochemical constraints on the terrestrial atmosphere, suggest that the late addition of volatiles by meteoritic impacts after magma ocean solidification may have greatly contributed to the formation of the atmosphere on a terrestrial planet after its formation than previously thought.

2.1. The chemical difference in degassed volatiles between differentiated magmas and primitive meteorites
The bulk oxidation states of differentiated magmas and late-accreting materials are likely to be different, suggesting that outgassing compositions of volatiles would also have been different. Subsequent to metal–silicate segregation, the near-surface portion in a magma ocean with a deep core-mantle boundary is likely to be relatively oxidized (Hirschmann, 2012). For Earth, Ce anomalies in Hadean zircons indicate that the oxidation state of magma was already close to the FMQ buffer at least 4.35 billion years ago (Trail et al., 2011). Because magma equilibrated with the FMQ buffer yields CO2-rich and CO–CH4-poor gases (e.g., Zolotov and Shock, 2000), early terrestrial atmospheres dominated by the degassing of volatiles from magma would have been oxidizing.

In contrast, because even the most oxidizing chondrites are more reducing than magmas with oxygen fugacity close to the FMQ buffer, early atmospheres dominated by impact degassing from chondrites would have been more reducing than atmosphere degassed from post core-segregation silicate magma, at least for Earth (Hashimoto et al., 2007 and Schaefer and Fegley, 2010). Thermodynamic equilibrium calculations suggest that the vapor of chondritic materials may have been rich in H2, CO and/or CH4 (Hashimoto et al., 2007, Schaefer and Fegley, 2007 and Schaefer and Fegley, 2010).

Given such chemical differences between differentiated magmas and accreting materials, the assessment of impact degassing from late-accreting chondrites is a key for the occurrence of a CH4-rich atmosphere on early terrestrial planets.

3. Cooling dynamics of impact-induced vapor
Because the direction of chemical reactions depends largely on both the pressure and temperature of the system, the next question on impact degassing components focuses on the thermodynamic conditions of the impact-induced vapor during cooling. Previous studies have discussed equilibrium compositions as a function of temperature under a constant pressure (Kress and McKay, 2004, Hashimoto et al., 2007 and Schaefer and Fegley, 2010). This approach would be appropriate if chemical reactions in impact-induced vapor are controlled by radiative cooling, which decreases temperature while pressure is kept approximately constant. During cooling, however, pressure in impact-induced vapor dynamically changes due to expansion. If chemical reactions in impact-induced vapor are kinetically prohibited due to rapid cooling and subsequently quenched during expansion, the approach taken by previous studies may not be appropriate; another approach would be necessary to accurately calculate the molecular composition of impact-generated atmospheres.

3.1. The key factors for cooling dynamics of impact-induced vapor
During the shock compression phase of hypervelocity meteoritic impacts, high pressure–temperature (P–T) conditions are generated by shock waves via the conversion of impact kinetic energy to internal energy. Subsequently, when rarefaction waves from rear free surfaces arrive, the shock-compressed target and projectile materials start to expand as impact plumes. This decompression process can be approximated as adiabatic because the timescale for pressure heterogeneities within an impact plume to equilibrate is typically much shorter than that for temperature heterogeneities (e.g., Sugita and Schultz, 2002). Consequently, the entropy gain during the shock-compression phase would strongly regulate the P–T pathway of the decompression phase. In other words, the impact condition (e.g., impact velocity and the shock impedance of surface material) would control the molecular compositions of the impact-induced vapor. Then, the molecular composition of the impact-derived atmospheres on different planets may have been different because the impact-induced entropy gain would be substantially different even for the same composition of impactors.

(taken from here)