Origin of the atmospheres of the terrestrial planets

The monotonic decrease in the atmospheric abundance of ³⁶Ar per gram of planet in the sequence, Venus, Earth, and Mars has been assumed to reflect some conditions in the primitive solar nebula at the time of formation of the planetary atmospheres, having to do either with the composition of the nebula itself or the composition of the trapped gases in small solid bodies in the nebula. Behind such hypotheses lies the assumption that planetary atmospheres steadily gain components. However, not only can gases enter atmospheres; they may also be lost from atmospheres both by adsorption into the planetary interior and by loss into space as a result of collisions with minor and major planetesimals. In this paper a necessarily qualitative discussion is given of the problem of collisions with minor planetesimals, a process called atmospheric cratering or atmospheric erosion, and a discussion is given of atmospheric loss accompanying collision of a planet with a major planetesimal, such as may have produced the Earth's Moon.     

Geology of terrestrial planets with dynamic atmospheres

Geological exploration of the solar system shows that solid-surfaced planets and satellites are subject to endogenic processes (volcanism and tectonism) and exogenic processes (impact cratering and gradation). The present appearance of planetary suffaces is the result of the complex interplay of these processes and is the linked to the evolution of planets and their environments. Terrestrial planets that have dynamic atmospheres are Earth, Mars, and Venus. Atmospheric interaction with the surfaces of these planets, oraeolian activity, is a form of gradation. The manifestation of aeolian activity is the weathering and erosion of rocks into sediments, transportation of the weathered debris (mostly sand and dust) by the wind, and deposition of windblown material. Wind-eroded features include small-scale ventifacts (wind-sculptured rocks) and large-scale landforms such as yardangs. Wind depositional features include dunes, drifts, and mantles of windblown sediments. These and other aeolian features are observed on Earth, Mars, and Venus.     

Numerical simulation of the final stages of terrestrial planet formation

Three representative numerical simulations of the growth of the terrestrial planets by accretion of large protoplanets are presented. The mass and relative-velocity distributions of the bodies in these simulations are free to evolve simultaneously in response to close gravitational encounters and occasional collisions between bodies. The collisions between bodies, therefore, arise in a natural way and the assumption of expressions for the relative velocity distribution and the gravitational collision cross section is unnecessary. These simulations indicate that the growth of bodies with final masses approaching those of Venus and the Earth is possible, at least for the case of a two-dimensional system. Simulations assuming an initial uniform distribution of orbital eccentricities on the interval from 0 to e_max are found to produce final states containing too many bodies with masses which are too small when e_max < 0.10, while simulations with e_max > 0.20 result in too many catastrophic collisions between bodies thus preventing rapid accretion of planetary-size bodies. The e_max = 0.15 simulation ends with a state surprisingly similar to that of the present terrestrial planets and, therefore, provides a rough estimate of the range of radial sampling to be expected for the terrestrial planets.     

Sulfuric acid aerosols in the atmospheres of the terrestrial planets

Clouds and hazes composed of sulfuric acid are observed to exist or postulated to have once existed on each of the terrestrial planets with atmospheres in our solar system. Venus today maintains a global cover of clouds composed of a sulfuric acid/water solution that extends in altitude from roughly 50 km to roughly 80 km. Terrestrial polar stratospheric clouds (PSCs) form on stratospheric sulfuric acid aerosols, and both PSCs and stratospheric aerosols play a critical role in the formation of the ozone hole. Stratospheric aerosols can modify the climate when they are enhanced following volcanic eruptions, and are a current focus for geoengineering studies. Rain is made more acidic by sulfuric acid originating from sulfur dioxide generated by industry on Earth. Analysis of the sulfur content of Martian rocks has led to the hypothesis that an early Martian atmosphere, rich in SO₂ and H₂O, could support a sulfur-infused hydrological cycle. Here we consider the plausibility of frozen sulfuric acid in the upper clouds of Venus, which could lead to lightning generation, with implications for observations by the European Space Agency's Venus Express and the Japan Aerospace Exploration Agency's Venus Climate Orbiter (also known as Akatsuki). We also present simulations of a sulfur-rich early Martian atmosphere. We find that about 40 cm/yr of precipitation having a pH of about 2.0 could fall in an early Martian atmosphere, assuming a surface temperature of 273 K, and SO₂ generation rates consistent with the formation of Tharsis. This modeled acid rain is a powerful sink for SO₂, quickly removing it and preventing it from having a significant greenhouse effect.     

Migration of protoplanets: Effects on terrestrial planet formation

I review the role of planetary migration on the formation process of terrestrial planets. I first show a simple estimation for growth timescale of solid proto-planets and review a linear theory of disk-planet gravitational interaction to estimate the migration rate of proto-planets in a gas disk, and then discuss the difficulty of the formation of terrestrial planets in terms of comparison between migration timescale and growth timescale. Next I show recent studies which suggest possible mechanisms to solve the problem. I briefly discuss the formation process of Mercury in the context of terrestrial-planet formation.     

The origin and evolution of the atmospheres of the terrestrial planets

The chemical nature of the Earth's atmosphere is determined by its interaction with the biosphere, hydrosphere and lithosphere. Detailed balance is maintained over long time periods by a complex series of cyclical processes. The chemical differences between the atmosphere of the Earth, on the one hand, and the atmospheres of Venus and Mars, on the other, can be understood in terms of the greater complexity of the terrestrial interactions. When this has been taken into account, the origin of all three planetary atmospheres can be explained as resulting from degassing. Despite the similarity of the atmospheres of Venus and Mars, it seems necessary to invoke different mechanisms for the low amount of water vapour on each.     

The formation of the atmospheres of the terrestrial planets by impact

It is generally supposed that the atmospheres of the terrestrial planets were formed by secondary degassing processes. We propose, instead, that they are of primary origin, forming as an immediate and necessary consequence of the final stages of planetary accretion. Once the planetary embryo reached a critical size, the impacting material began to vaporize. The atmosphere, so created, then decelerated other impacting material, thus limiting the rate of atmospheric growth. We show that, given reasonable assumptions concerning the chemical composition of the impacting material, an acceptable model for the early atmosphere of the Earth, and the present atmospheres of Venus and Mars results.A discussion of the noble gas data for the terrestrial atmosphere indicates that these can be readily reconciled with an impact origin.     

Orbital stability of massive protoplanets in the terrestrial planet region of the solar system

A number of theories of the formation of the planets advocate that the terrestrial planets were originally of cosmic composition and that it is only subsequent evolution that has removed their volatile components. This paper shows that such protoplanets could have remained in the terrestrial planet region without significant changes occurring in their orbits for an acceptable time interval.     

Ice clathrate as a possible source of the atmospheres of the terrestrial planets

The presence and compositions of atmospheres on the terrestrial planets do not follow directly from condensation models which would have Earth accreting near 500°K. No single mechanism yet proposed adequately accounts for the abundances of noble gases and carbon and nitrogen in the atmospheres. We show that the composition of clathrates forming at low temperatures in cold regions of the nebula can be predicted. Addition of about 1 ppm clathrate material to the Earth can explain observed abundances of Ar, Kr, and Xe. Condensation and adsorption processes occuring at 400–500°K are necessary to explain the observed abundances of Ne, H₂O, C, and N. Possible sources of clathrates could be cometary bodies formed in the outer solar system.     

On the figure of the planet Mercury

The figure of Mercury is estimated in terms of an isostatic form of equilibrium which tends to be controlled by the situation near perihelion passage at the 32 resonance spin rate. The ratios of the principal moments of inertia for Mercury are: (1)(C–A)/C7×10^–5; (2)(C–B)/C5×10^–5 and (3)(B–A)/C2×10^–5. The thermal effect on Mercury's figure during solidification forces Mercury's rotation to be trapped in the 32 resonance lock as its spin rate is being slowed by tidal effects. It is shown that the process of trapping of Mercury has been naturally affected by the instantaneous solidification of Mercury into a shape with two thermal bulges, and that the two permanent thermal bulges stabilize the planet's rotation.     

Chemistry of atmospheres formed during accretion of the Earth and other terrestrial planets

We used chemical equilibrium and chemical kinetic calculations to model chemistry of the volatiles released by heating different types of carbonaceous, ordinary and enstatite chondritic material as a function of temperature and pressure. Our results predict the composition of atmospheres formed by outgassing during accretion of the Earth and other terrestrial planets. Outgassing of CI and CM carbonaceous chondritic material produces H₂O-rich (steam) atmospheres in agreement with the results of impact experiments. However, outgassing of other types of chondritic material produces atmospheres dominated by other gases. Outgassing of ordinary (H, L, LL) and high iron enstatite (EH) chondritic material yields H₂-rich atmospheres with CO and H₂O being the second and third most abundant gases. Outgassing of low iron enstatite (EL) chondritic material gives a CO-rich atmosphere with H₂, CO₂, and H₂O being the next most abundant gases. Outgassing of CV carbonaceous chondritic material gives a CO₂-rich atmosphere with H₂O being the second most abundant gas. Our results predict that the atmospheres formed during accretion of the Earth and Mars were probably H₂-rich unless the accreted material was dominantly CI and CM carbonaceous chondritic material. We also predict significant amounts of S, P, Cl, F, Na, and K in accretionary atmospheres at high temperatures (1500-2500 K). Finally, our results may be useful for interpreting spectroscopic observations of accreting extrasolar terrestrial planets.     

Synthetic spectra of simulated terrestrial atmospheres containing possible biomarker gases.

NASA's proposed Terrestrial Planet Finder, a space-based interferometer, will eventually allow spectroscopic analyses of the atmospheres of extrasolar planets. Such analyses would provide information about the existence of life on these planets. One strategy in the search for life is to look for evidence of O3 (and hence O2) in a planet's atmosphere; another is to look for gases that might be present in an atmosphere analogous to that of the inhabited early Earth. In order to investigate these possibilities, we have calculated synthetic spectra for several hypothetical terrestrial-type atmospheres. The model atmospheres represent four different scenarios. The first two, representing inhabited terrestrial planets, are an Earth-like atmosphere containing variable amounts of oxygen and an early Earth-type atmosphere containing methane. In addition, two cases representing Mars-like and early Venus-like atmospheres were evaluated, to provide possible "false positive" spectra. The calculated spectra suggest that ozone could be detected by an instrument like Terrestrial Planet Finder if the O2 concentration in the planet's atmosphere is > or = 200 ppm, or 10(-3) times the present atmospheric level. Methane should be observable on an early-Earth type planet if it is present in concentrations of 100 ppm or more. Methane has both biogenic and abiogenic sources, but concentrations exceeding 1000 ppm, or 0.1% by volume, would be difficult to produce from abiogenic sources alone. High methane concentrations in a planet's atmosphere are therefore another potential indicator for extraterrestrial life.     

Observable consequences of planet formation models in systems with close-in terrestrial planets

To date, two planetary systems have been discovered with close-in, terrestrial-mass planets     . Many more such discoveries are anticipated in the coming years with radial velocity and transit searches. Here we investigate the different mechanisms that could form 'hot Earths' and their observable predictions. Models include: (1) in situ accretion; (2) formation at larger orbital distance followed by inward 'type 1' migration; (3) formation from material being 'shepherded' inward by a migrating gas giant planet; (4) formation from material being shepherded by moving secular resonances during dispersal of the protoplanetary disc; (5) tidal circularization of eccentric terrestrial planets with close-in perihelion distances and (6) photoevaporative mass-loss of a close-in giant planet. Models 1–4 have been validated in previous work. We show that tidal circularization can form hot Earths, but only for relatively massive planets     with very close-in perihelion distances (≲0.025 au), and even then the net inward movement in orbital distance is at most only 0.1–0.15 au. For planets of less than     , photoevaporation can remove the planet's envelope and leave behind the solid core on a Gyr time-scale, but only for planets inside 0.025–0.05 au. Using two quantities that are observable by current and upcoming missions, we show that these models each produce unique signatures, and can be observationally distinguished. These observables are the planetary system architecture (detectable with radial velocities, transits and transit timing) and the bulk composition of transiting close-in terrestrial planets (measured by transits via the planet's radius).     

Making other earths: dynamical simulations of terrestrial planet formation and water delivery

We present results from 44 simulations of late stage planetary accretion, focusing on the delivery of volatiles (primarily water) to the terrestrial planets. Our simulations include both planetary “embryos” (defined as Moon to Mars sized protoplanets) and planetesimals, assuming that the embryos formed via oligarchic growth. We investigate volatile delivery as a function of Jupiter's mass, position and eccentricity, the position of the snow line, and the density (in solids) of the solar nebula. In all simulations, we form 1-4 terrestrial planets inside 2 AU, which vary in mass and volatile content. In 44 simulations we have formed 43 planets between 0.8 and 1.5 AU, including 11 “habitable” planets between 0.9 and 1.1 AU. These planets range from dry worlds to “water worlds” with 100+oceans of water (1 ocean=1.5×10²⁴ g), and vary in mass between 0.23M_⊕ and 3.85M_⊕. There is a good deal of stochastic noise in these simulations, but the most important parameter is the planetesimal mass we choose, which reflects the surface density in solids past the snow line. A high density in this region results in the formation of a smaller number of terrestrial planets with larger masses and higher water content, as compared with planets which form in systems with lower densities. We find that an eccentric Jupiter produces drier terrestrial planets with higher eccentricities than a circular one. In cases with Jupiter at 7 AU, we form what we call “super embryos,” 1-2M_⊕ protoplanets which can serve as the accretion seeds for 2+M_⊕ planets with large water contents.     

Can planetesimals left over from terrestrial planet formation produce the lunar Late Heavy Bombardment?

The lunar Late Heavy Bombardment (LHB) defines a time between ∼3.8 to possibly 4.1 Gy ago when the Nectarian and early-Imbrium basins on the Moon with reasonably well-constrained ages were formed. Some have argued that these basins were produced by a terminal cataclysm that caused a spike in the inner Solar System impactor flux during this interval. Others have suggested the basins were formed by the tail end of a monotonically decreasing impactor population originally produced by planet formation processes in the inner Solar System. Here we investigate whether this so-called declining bombardment scenario of the LHB is consistent with constraints provided by planet formation models as well as the inferred ages of Nectaris, Serenitatis, Imbrium, and Orientale. We did this by modeling the collisional and dynamical evolution of the post-planet formation population (PPP) for a range of starting PPP masses. Using a Monte Carlo code, we computed the probability that the aforementioned basins were created at various times after the Moon-forming event approximately 4.54 Ga. Our results indicate that the likelihood that the declining bombardment scenario produced Nectaris, Serenitatis, Imbrium, and Orientale (or even just Imbrium and Orientale) at any of their predicted ages is extremely low and can be ruled out at the 3σ confidence level, regardless of the PPP's starting mass. The reason is that collisional and dynamical evolution quickly depletes the PPP, leaving behind a paucity of large projectiles capable of producing the Moon's youngest basins between 3.8-4.1 Gy ago. If collisions are excluded from our model, we find that the PPP produces numerous South Pole-Aitken-like basins during the pre-Nectarian period. This is inconsistent with our understanding of lunar topography. Accordingly, our results lead us to conclude that the terminal cataclysm scenario is the only existing LHB paradigm at present that is both viable from a dynamical modeling perspective and consistent with existing constraints.     

On the construction of model stellar atmospheres

The construction of model atmospheres by means of differential corrections is discussed. Either flux or flux gradients may be minimized, with arbitrary weighting with depth. For the simple atmospheres studied, no convergence problems were encountered even when very poor first approximations were used; and flux constancy in the radiative case was generally attained in three or four iterations.Quantities computed in one iteration may be re-used, not only in subsequent iterations within the model, but also in the construction of other models with differentT _eff org; and so the method is particularly suited for grid computations.     

Planetesimals to protoplanets – II. Effect of debris on terrestrial planet formation

In this paper, we extend our numerical method for simulating terrestrial planet formation to include dynamical friction from the unresolved debris component. In the previous work, we implemented a rubble pile planetesimal collision model into direct N -body simulations of terrestrial planet formation. The new collision model treated both accretion and erosion of planetesimals but did not include dynamical friction from debris particles smaller than the resolution limit for the simulation. By extending our numerical model to include dynamical friction from the unresolved debris, we can simulate the dynamical effect of debris produced during collisions and can also investigate the effect of initial debris mass on terrestrial planet formation. We find that significant initial debris mass, 10 per cent or more of the total disc mass, changes the mode of planetesimal growth. Specifically, planetesimals in this situation do not go through a runaway growth phase. Instead, they grow concurrently, similar to oligarchic growth. The dynamical friction from the unresolved debris damps the eccentricities of the planetesimals, reducing the mean impact speeds and causing all collisions to result in merging with no mass loss. As a result, there is no debris production. The mass in debris slowly decreases with time. In addition to including the dynamical friction from the unresolved debris, we have implemented particle tracking as a proxy for monitoring compositional mixing. Although there is much less mixing due to collisions and gravitational scattering when dynamical friction of the background debris is included, there is significant inward migration of the largest protoplanets in the most extreme initial conditions (for which the initial mass in unresolved debris is at least equal to the mass in resolved planetesimals).