The internal activity and thermal evolution of Earth-like planets

We model the internal thermal evolution of planets with Earth-like composition and masses ranging from 0.1 to 10 Earth masses over a period of 10 billion years. We also characterize the internal activity of the planets by the velocity of putative tectonic plates, the rate at which mantle material is processed through melting zones, and the time taken to process one mantle mass. The more massive the planet the larger its processing rate (?), which scales approximately as ?∝M0.8-1.0. The processing times for all the planets increase with time as they cool and become less active. As would be expected, the surface heat flow scales with planet mass. All planets have similar declines in mantle temperature except for the largest, in which pressure effects cause a larger decline. The larger planets have higher mantle temperatures over all times. The less massive the planet, the larger the decrease in core temperature with time. The core heat flow is also found to decrease more rapidly for smaller planet masses. Finally, rough predictions are made for the time required to generate an atmosphere from estimates of the time to degas water and carbon dioxide in mantle melting zones. The degassing times depend strongly on the initial temperature of the planet, but for the temperatures used in our model all the planets degas within ∼32 Ma after their formation.     

Internal structure of massive terrestrial planets

Planetary formation models predict the existence of massive terrestrial planets and experiments are now being designed that should succeed in discovering them and measuring their masses and radii. We calculate internal structures of planets with one to ten times the mass of the Earth (Super-Earths) to obtain scaling laws for total radius, mantle thickness, core size and average density as a function of mass. We explore different compositions and obtain a scaling law of R∝M0.267-0.272 for Super-Earths. We also study a second family of planets, Super-Mercuries with masses ranging from one mercury-mass to ten mercury-masses with similar composition to the Earth's but with a larger core mass fraction. We explore the effect of surface temperature and core mass fraction on the scaling laws for these planets. The scaling law obtained for the Super-Mercuries is R∝M∼0.3.     

Building the terrestrial planets: Constrained accretion in the inner Solar System

To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include: (1) the orbits, in particular the small eccentricities, and (2) the masses of the terrestrial planets - Mars’ relatively small mass in particular has not been adequately reproduced in previous simulations; (3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; (4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and (5) Earth’s relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N = 1000-2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury. We assume that Jupiter and Saturn are fully-formed at the start of each simulation, and test orbital configurations that are both consistent with and contrary to the “Nice model”. We find that a configuration with Jupiter and Saturn on circular orbits forms low-eccentricity terrestrial planets and a water-rich Earth on the correct timescale, but Mars’ mass is too large by a factor of 5-10 and embryos are often stranded in the asteroid belt. A configuration with Jupiter and Saturn in their current locations but with slightly higher initial eccentricities (e = 0.07-0.1) produces a small Mars, an embryo-free asteroid belt, and a reasonable Earth analog but rarely allows water delivery to Earth. None of the configurations we tested reproduced all the observed constraints. Our simulations leave us with a problem: we can reasonably satisfy the observed constraints (except for Earth’s water) with a configuration of Jupiter and Saturn that is at best marginally consistent with models of the outer Solar System, as it does not allow for any outer planet migration after a few Myr. Alternately, giant planet configurations which are consistent with the Nice model fail to reproduce Mars’ small size.     

Atmospheric circulations of terrestrial planets orbiting low-mass stars

Circulations and habitable zones of planets orbiting low-mass stars are investigated. Many of these planets are expected to rotate synchronously relative to their parent stars, thereby raising questions about their surface temperature distributions and habitability. We use a global circulation model to study idealized, synchronously rotating (tidally locked) planets of various rotation periods, with surfaces of all land or all water, but with an Earth-like atmosphere and solar insolation. The dry planets exhibit wide variations in surface temperature: >80 °C on the dayside to <−110 °C on the nightside for the 240-h rotator, for example. The water-covered aquaplanets are warmer and exhibit narrower ranges of surface temperatures, e.g., ∼40 °C to >−60 °C for the 240-h orbiter. They also have a larger habitable area, defined here as the region where average surface temperatures are between 0 °C and 50 °C. This concept has little relevance for either dry or aquaplanets, but might become relevant on a planet with both land area and oceans.The circulations on these tidally locked planets exhibit systematic changes as the rotation period is varied. However, they also reveal abrupt transitions between two different circulation regimes and multiple equilibria. For the dry planet, the transition occurs between a 4-day and a 5-day period, while for the aquaplanet, it occurs between a 3-day and a 4-day period. For both dry and aqua planets, this transition occurs when the Rossby deformation radius exceeds half the planetary radius. Further investigation on the dry planet reveals that multiple equilibria exist between 100- and 221-h periods. These multiple equilibria may be relevant for real planets within the habitable zones of late K and M stars, because these planets are expected to have rotation periods between 8 and 100 Earth days.     

The extreme physical properties of the CoRoT-7b super-Earth

The search for rocky exoplanets plays an important role in our quest for extra-terrestrial life. Here, we discuss the extreme physical properties possible for the first characterised rocky super-Earth, CoRoT-7b (R_pl = 1.58 ± 0.10 R_Earth, M_pl = 6.9 ± 1.2 M_Earth). It is extremely close to its star (a = 0.0171 AU = 4.48 R_st), with its spin and orbital rotation likely synchronised. The comparison of its location in the (M_pl, R_pl) plane with the predictions of planetary models for different compositions points to an Earth-like composition, even if the error bars of the measured quantities and the partial degeneracy of the models prevent a definitive conclusion. The proximity to its star provides an additional constraint on the model. It implies a high extreme-UV flux and particle wind, and the corresponding efficient erosion of the planetary atmosphere especially for volatile species including water. Consequently, we make the working hypothesis that the planet is rocky with no volatiles in its atmosphere, and derive the physical properties that result. As a consequence, the atmosphere is made of rocky vapours with a very low pressure (P ? 1.5 Pa), no cloud can be sustained, and no thermalisation of the planet is expected. The dayside is very hot (2474 ± 71 K at the sub-stellar point) while the nightside is very cold (50-75 K). The sub-stellar point is as hot as the tungsten filament of an incandescent bulb, resulting in the melting and distillation of silicate rocks and the formation of a lava ocean. These possible features of CoRoT-7b could be common to many small and hot planets, including the recently discovered Kepler-10b. They define a new class of objects that we propose to name “Lava-ocean planets”.     

Accretion of terrestrial planets from oligarchs in a turbulent disk

We have investigated the final accretion stage of terrestrial planets from Mars-mass protoplanets that formed through oligarchic growth in a disk comparable to the minimum mass solar nebula (MMSN), through N-body simulation including random torques exerted by disk turbulence due to Magneto-Rotational Instability. For the torques, we used the semi-analytical formula developed by Laughlin et al. [Laughlin, G., Steinacker, A., Adams, F.C., 2004. Astrophys. J. 608, 489-496]. The damping of orbital eccentricities (in all runs) and type-I migration (in some runs) due to the tidal interactions with disk gas is also included. Without any effect of disk gas, Earth-mass planets are formed in terrestrial planet regions in a disk comparable to MMSN but with too large orbital eccentricities to be consistent with the present eccentricities of Earth and Venus in our Solar System. With the eccentricity damping caused by the tidal interaction with a remnant gas disk, Earth-mass planets with eccentricities consistent with those of Earth and Venus are formed in a limited range of disk gas surface density (∼10⁻⁴ times MMSN). However, in this case, on average, too many (?6) planets remain in terrestrial planet regions, because the damping leads to isolation between the planets. We have carried out a series of N-body simulations including the random torques with different disk surface density and strength of turbulence. We found that the orbital eccentricities pumped up by the turbulent torques and associated random walks in semimajor axes tend to delay isolation of planets, resulting in more coagulation of planets. The eccentricities are still damped after planets become isolated. As a result, the number of final planets decreases with increase in strength of the turbulence, while Earth-mass planets with small eccentricities are still formed. In the case of relatively strong turbulence, the number of final planets are 4-5 at 0.5-2 AU, which is more consistent with Solar System, for relatively wide range of disk gas surface density (∼¹⁰⁻⁴-¹⁰⁻² times MMSN).     

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.     

Tidal pattern instabilities on multi-moon planets

The equilibrium tide-generating forces in the lunar orbital plane of a planet of radius R are calculated for the case of N moons of mass Mi orbiting the planet at instantaneous polar coordinates (Di, αi). For the case of a single moon, there are only two high tides. For the case of two moons, it is found that there can exist a critical lunar orbital distance at which two high tides become unstable with respect to formation of three high tides. Bifurcation diagrams are presented which depict how the angular positions of the high and low tides on the planet vary with the lunar distances and lunar separation angle. Tidal stability diagrams, which illustrate the stability regions for various tidal patterns as a function of lunar distances and lunar separation angle, are presented for various values of D₂/D₁ and M₂/M₁. Generally speaking, the aforementioned tidal instability, and hence the propensity for formation of three high tides on a two-moon planet, exists over a significant range of lunar distances and separation angles provided that M₂/M₁∼³(D₂/D₁). For the case of N>2 moons, the tidal stability diagram becomes more complex, revealing a diversity of potential tidal patterns.     

The Effect of Tidal Interaction with a Gas Disk on Formation of Terrestrial Planets

We have performed N-body simulation on final accretion stage of terrestrial planets, including the effect of damping of eccentricity and inclination caused by tidal interaction with a remnant gas disk. As a result of runway and oligarchic accretion, about 20 Mars-sized protoplanets would be formed in nearly circular orbits with orbital separation of several to ten Hill radius. The orbits of the protoplanets would be eventually destabilized by long-term mutual gravity and/or secular resonance of giant gaseous planets. The protoplanets would coalesce with each other to form terrestrial planets through the orbital crossing. Previous N-body simulations, however, showed that the final eccentricities of planets are around 0.1, which are about 10 times higher than the present eccentricities of Earth and Venus. The obtained high eccentricities are the remnant of orbital crossing. We included the effect of eccentricity damping caused by gravitational interaction with disk gas as a drag force (“gravitational drag”) and carried out N-body simulation of accretion of protoplanets. We start with 15 protoplanets with 0.2M⊕ and integrate the orbits for 10⁷ years, which is consistent with the observationally inferred disk lifetime (in some runs, we start with 30 protoplanets with 0.1M⊕). In most runs, the damping time scale, which is equivalent to the strength of the drag force, is kept constant throughout each run in order to clarify the effects of the damping. We found that the planets' final mass, spatial distribution, and eccentricities depend on the damping time scale. If the damping time scale for a 0.2M⊕ mass planet at 1 AU is longer than 10⁸ years, planets grow to Earth's size, but the final eccentricities are too high as in gas-free cases. If it is shorter than 10⁶ years, the eccentricities of the protoplanets cannot be pumped up, resulting in not enough orbital crossing to make Earth-sized planets. Small planets with low eccentricities are formed with small orbital separation. On the other hand, if it is between 10⁶ and 10⁸ years, which may correspond to a mostly depleted disk (0.01-0.1% of surface density of the minimum mass model), some protoplanets can grow to about the size of Earth and Venus, and the eccentricities of such surviving planets can be diminished within the disk lifetime. Furthermore, in innermost and outermost regions in the same system, we often find planets with smaller size and larger eccentricities too, which could be analogous to Mars and Mercury. This is partly because the gravitational drag is less effective for smaller mass planets, and partly due to the “edge effect,” which means the innermost and outermost planets tend to remain without collision. We also carried out several runs with time-dependent drag force according to depletion of a gas disk. In these runs, we used exponential decay model with e-folding time of 3×10⁶ years. The orbits of protoplanets are stablized by the eccentricity damping in the early time. When disk surface density decays to ?1% of the minimum mass disk model, the damping force is no longer strong enough to inhibit the increase of the eccentricity by distant perturbations among protoplanets so that the orbital crossing starts. In this disk decay model, a gas disk with 10⁻⁴-10⁻³ times the minimum mass model still remains after the orbital crossing and accretional events, which is enough to damp the eccentricities of the Earth-sized planets to the order of 0.01. Using these results, we discuss a possible scenario for the last stage of terrestrial planet formation.     

Trapping and dynamical evolution of interplanetary dust particles in Earth’s quasi-satellite resonance

We used numerical simulations to model the orbital evolution of interplanetary dust particles (IDPs) evolving inward past Earth’s orbit under the influence of radiation pressure, Poynting–Robertson light drag (PR drag), solar wind drag, and gravitational perturbations from the planets. A series of β values (where β is the ratio of the force from radiation pressure to that of central gravity) were used ranging from 0.0025 up to 0.02. Assuming a composition consistent with astronomical silicate and a particle density of 2.5 g cm⁻³ these β values correspond to dust particle diameters ranging from 200 μm down to 25 μm. As the dust particle orbits decay past 1 AU between 4% (for β = 0.02, or 25 μm) and 40% (for β = 0.0025, or 200 μm) of the population became trapped in 1:1 co-orbital resonance with Earth. In addition to traditional horseshoe type co-orbitals, we found about a quarter of the co-orbital IDPs became trapped as so-called quasi-satellites. Quasi-satellite IDPs always remain relatively near to Earth (within 0.1–0.3 AU, or 10–30 Hill radii, R_H) and undergo two close-encounters with Earth each year. While resonant perturbations from Earth halt the decay in semi-major axis of quasi-satellite IDPs their orbital eccentricities continue to decrease under the influence of PR drag and solar wind drag, forcing the IDPs onto more Earth-like orbits. This has dramatic consequences for the relative velocity and distance of closest approach between Earth and the quasi-satellite IDPs. After 10⁴–10⁵ years in the quasi-satellite resonance dust particles are typically less than 10R_H from Earth and consistently coming within about 3R_H. In the late stages of evolution, as the dust particles are escaping the 1:1 resonance, quasi-satellite IDPs can have deep close-encounters with Earth significantly below R_H. Removing the effects of Earth’s gravitational acceleration reveals that encounter velocities (i.e., velocities “at infinity”) between quasi-satellite IDPs and Earth during these close-encounters are just a few hundred meters per second or slower, well below the average values of 2–4 km s⁻¹ for non-resonant Earth-crossing IDPs with similar initial orbits. These low encounter velocities lead to a factor of 10–100 increase in Earth’s gravitationally enhanced impact cross-section (σ_grav) for quasi-satellite IDPs compared to similar non-resonant IDPs. The enhancement in σ_grav between quasi-satellite IDPs and cometary Earth-crossing IDPs is even more pronounced, favoring accretion of quasi-satellite dust particles by a factor of 100–3000 over the cometary IDPs. This suggests that quasi-satellite dust particles may dominate the flux of large (25–200 μm) IDPs entering Earth’s atmosphere. Furthermore, because quasi-satellite trapping is known to be directly correlated with the host planet’s orbital eccentricity the accretion of quasi-satellite dust likely ebbs and flows on 10⁵ year time scales synchronized with Earth’s orbital evolution.     

Obliquity evolution of extrasolar terrestrial planets

We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio (m/Mp) and initial obliquity (γ₀), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins (sinγ₀∼1) are more likely to be produced than straight ones (sinγ₀∼0). The ratio m/Mp is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet-satellite systems have focused on a particular case of the Earth-Moon systems in which m/Mp?0.0125 and γ₀∼10° or the two-body planar problem in which γ₀=0° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m/Mp (from 0.0025 to 0.05) and γ₀ (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth-Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼10-20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m/Mp-γ₀ space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet-satellite systems and discussions of surface environments of the planets.     

Oligarchic growth of giant planets

Runaway growth ends when the largest protoplanets dominate the dynamics of the planetesimal disk; the subsequent self-limiting accretion mode is referred to as “oligarchic growth.” Here, we begin by expanding on the existing analytic model of the oligarchic growth regime. From this, we derive global estimates of the planet formation rate throughout a protoplanetary disk. We find that a relatively high-mass protoplanetary disk (∼10 × minimum-mass) is required to produce giant planet core-sized bodies (∼10 M_⊕) within the lifetime of the nebular gas (?10 million years). However, an implausibly massive disk is needed to produce even an Earth mass at the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational effect of gas is even slower and less efficient. In the limit of noninteracting planetesimals, a reasonable-mass disk is unable to produce bodies the size of the Solar System’s two outer giant planets at their current locations on any timescale; if collisional damping of planetesimal random velocities is sufficiently effective, though, it may be possible for a Uranus/Neptune to form in situ in less than the age of the Solar System. We perform numerical simulations of oligarchic growth with gas and find that protoplanet growth rates agree reasonably well with the analytic model as long as protoplanet masses are well below their estimated final masses. However, accretion stalls earlier than predicted, so that the largest final protoplanet masses are smaller than those given by the model. Thus the oligarchic growth model, in the form developed here, appears to provide an upper limit for the efficiency of giant planet formation.     

Terrestrial planet formation surrounding close binary stars

Most stars reside in binary/multiple star systems; however, previous models of planet formation have studied growth of bodies orbiting an isolated single star. Disk material has been observed around both components of some young close binary star systems. Additionally, it has been shown that if planets form at the right places within such disks, they can remain dynamically stable for very long times. Herein, we numerically simulate the late stages of terrestrial planet growth in circumbinary disks around ‘close’ binary star systems with stellar separations 0.05 AU?aB?0.4 AU and binary eccentricities 0?eB?0.8. In each simulation, the sum of the masses of the two stars is 1 M_⊙, and giant planets are included. The initial disk of planetary embryos is the same as that used for simulating the late stages of terrestrial planet formation within our Solar System by Chambers [Chambers, J.E., 2001. Icarus 152, 205-224], and around each individual component of the α Centauri AB binary star system by Quintana et al. [Quintana, E.V., Lissauer, J.J., Chambers, J.E., Duncan, M.J., 2002. Astrophys. J. 576, 982-996]. Multiple simulations are performed for each binary star system under study, and our results are statistically compared to a set of planet formation simulations in the Sun-Jupiter-Saturn system that begin with essentially the same initial disk of protoplanets. The planetary systems formed around binaries with apastron distances QB≡aB(1+eB)?0.2 AU are very similar to those around single stars, whereas those with larger maximum separations tend to be sparcer, with fewer planets, especially interior to 1 AU. We also provide formulae that can be used to scale results of planetary accretion simulations to various systems with different total stellar mass, disk sizes, and planetesimal masses and densities.     

Delivery of icy planetesimals to inner planets in the Proxima Centauri planetary system

The estimates of the delivery of icy planetesimals from the feeding zone of Proxima Centauri c (with mass equal to 7m_E, m_E is the mass of the Earth) to inner planets b and d were made. They included the studies of the total mass of planetesimals in the feeding zone of planet c and the probabilities of collisions of such planetesimals with inner planets. This total mass could be about 10–15m_E. It was estimated based on studies of the ratio of the mass of planetesimals ejected into hyperbolic orbits to the mass of planetesimals collided with forming planet c. At integration of the motion of planetesimals, the gravitational influence of planets c and b and the star was taken into account. In most series of calculations, planetesimals collided with planets were excluded from integrations. Based on estimates of the mass of planetesimals ejected into hyperbolic orbits, it was concluded that during the growth of the mass of planet c the semi-major axis of its orbit could decrease by at least a factor of 1.5. Depending on possible gravitational scattering due to mutual encounters of planetesimals, the total mass of material delivered by planetesimals from the feeding zone of planet c to planet b was estimated to be between 0.002m_E and 0.015m_E. Probably, the amount of water delivered to Proxima Centauri b exceeded the mass of water in Earth's oceans. The amount of material delivered to planet d could be a little less than that delivered to planet b.     

Orbital stability of systems of closely-spaced planets

An investigation of the stability of systems of 1 M_⊕ (Earth-mass) bodies orbiting a Sun-like star has been conducted for virtual times reaching 10 billion years. For the majority of the tests, a symplectic integrator with a fixed timestep of between 1 and 10 days was employed; however, smaller timesteps and a Bulirsch-Stoer integrator were also selectively utilized to increase confidence in the results. In most cases, the planets were started on initially coplanar, circular orbits, and the longitudinal initial positions of neighboring planets were widely separated. The ratio of the semimajor axes of consecutive planets in each system was approximately uniform (so the spacing between consecutive planets increased slowly in terms of distance from the star). The stability time for a system was taken to be the time at which the orbits of two or more planets crossed. Our results show that, for a given class of system (e.g., three 1 M_⊕ planets), orbit crossing times vary with planetary spacing approximately as a power law over a wide range of separation in semimajor axis. Chaos tests indicate that deviations from this power law persist for changed initial longitudes and also for small but non-trivial changes in orbital spacing. We find that the stability time increases more rapidly at large initial orbital separations than the power-law dependence predicted from moderate initial orbital separations. Systems of five planets are less stable than systems of three planets for a specified semimajor axis spacing. Furthermore, systems of less massive planets can be packed more closely, being about as stable as 1 M_⊕ planets when the radial separation between planets is scaled using the mutual Hill radius. Finally, systems with retrograde planets can be packed substantially more closely than prograde systems with equal numbers of planets.     

Life-bearing primordial planets in the solar vicinity

The space density of life-bearing primordial planets in the solar vicinity may amount to ～8.1×10⁴?pc^?3 giving total of ～10¹⁴ throughout the entire galactic disk. Initially dominated by H₂ these planets are stripped of their hydrogen mantles when the ambient radiation temperature exceeds 3?K as they fall from the galactic halo to the mid-plane of the galaxy. The zodiacal cloud in our solar system encounters a primordial planet once every 26 My (on our estimate) thus intercepting an average mass of 10³ tonnes of interplanetary dust on each occasion. If the dust included microbial material that originated on Earth and was scattered via impacts or cometary sublimation into the zodiacal cloud, this process offers a way by which evolved genes from Earth life could become dispersed through the galaxy.     

Formation of terrestrial planets in a dissipating gas disk with Jupiter and Saturn

We have performed N-body simulations on final accretion stage of terrestrial planets, including the eccentricity and inclination damping effect due to tidal interaction with a gas disk. We investigated the dependence on a depletion time scale of the disk, and the effect of secular perturbations by Jupiter and Saturn. In the final stage, terrestrial planets are formed through coagulation of protoplanets of about the size of Mars. They would collide and grow in a decaying gas disk. Kominami and Ida [Icarus 157 (2002) 43-56] showed that it is plausible that Earth-sized, low-eccentricity planets are formed in a mostly depleted gas disk. In this paper, we investigate the formation of planets in a decaying gas disk with various depletion time scales, assuming disk surface density of gas component decays exponentially with time scale of τ_gas. Fifteen protoplanets with are initially distributed in the terrestrial planet regions. We found that Earth-sized planets with low eccentricities are formed, independent of initial gas surface density, when the condition (τ_cross+τ_growth)/2?τ_gas?τ_cross is satisfied, where τ_cross is the time scale for initial protoplanets to start orbit crossing in a gas-free case and τ_growth is the time scale for Earth-sized planets to accrete during the orbit crossing stage. In the cases satisfying the above condition, the final masses and eccentricities of the largest planets are consistent with those of Earth and Venus. However, four or five protoplanets with the initial mass remain. In the final stage of terrestrial planetary formation, it is likely that Jupiter and Saturn have already been formed. When Jupiter and Saturn are included, their secular perturbations pump up eccentricities of protoplanets and tend to reduce the number of final planets in the terrestrial planet regions. However, we found that the reduction is not significant. The perturbations also shorten τ_cross. If the eccentricities of Jupiter and Saturn are comparable to or larger than present values (∼0.05), τ_cross become too short to satisfy the above condition. As a result, eccentricities of the planets cannot be damped to the observed value of Earth and Venus. Hence, for the formation of terrestrial planets, it is preferable that the secular perturbations from Jupiter and Saturn do not have significant effect upon the evolution. Such situation may be reproduced by Jupiter and Saturn not being fully grown, or their eccentricities being smaller than the present values during the terrestrial planets' formation. However, in such cases, we need some other mechanism to eliminate the problem that numerous Mars-sized planets remain uncollided.     

The maximal runaway temperature of Earth-like planets

In Simpson’s (Simpson, G.C. [1927]. Mem. R. Meteorol. Soc. II (16), 69–95) classical derivation of the temperature of the Earth in the semi-gray model, the surface temperature diverges as the fourth root of the thermal radiation’s optical depth. No resolution to this apparent paradox was yet obtained under the strict semi-gray approximation. Using this approximation and a simplified approach, we study the saturation of the runaway greenhouse effect.First we generalize the problem of the semi-gray model to cases in which a non-negligible fraction of the stellar radiation falls on the long-wavelength range, and/or that the planetary long-wavelength emission penetrates into the transparent short wavelength domain of the absorption.Second, applying the most general assumptions and independently of any particular properties of an absorber, we show that the greenhouse effect saturates and that any Earth-like planet has a maximal temperature which depends on the type of and distance to its main-sequence star, its albedo and the primary atmospheric components which determine the cutoff frequency below which the atmosphere is optically thick. For example, a hypothetical convection-less planet similar to Venus, that is optically thin in the visible, could have at most a surface temperature of 1200–1300 K irrespective of the nature of the greenhouse gas.We show that two primary mechanisms are responsible for the saturation of the runaway greenhouse effect, depending on the value of λ_cut, the wavelength above which the atmosphere becomes optically thick. Unless λ_cut is small and resides in the optical region, saturation is achieved by radiating the thermal flux of the planet through the short wavelength tail of the thermal distribution. This has an interesting observational implication, the radiation from such a planet should be skewed towards the NIR. Otherwise, saturation takes place by radiating through windows in the FIR.     

Rheological structure of the mantle of a super-Earth: Some insights from mineral physics

The rheological properties of the mantle of super-Earths have important influences on their orbital and thermal evolution. Mineral physics observations are reviewed to obtain some insights into the rheological properties of deep mantles of these planets where pressure can be as high as ∼1 TPa. It is shown that, in contrast to a conventional view that the viscosity of a solid increases with pressure (at a fixed temperature), viscosity will decrease with pressure (and depth) when pressure exceeds ∼0.1 TPa. The causes for pressure-weakening include: (i) the transition in diffusion mechanisms from vacancy to interstitial mechanism (at ∼0.1 TPa), (ii) the phase transition in MgO from B1 to B2 structure (at ∼0.5 TPa), (iii) the dissociation of MgSiO₃ into MgO and SiO₂ (at ∼1 TPa), and (iv) the transition to the metallic state (at ∼1 TPa). Some (or all) of them individually or in combination reduce the effective viscosity of constituent materials in the deep interior of super-Earths. Taken together, super-Earths are likely to have low viscosity deep mantle by at least 2-3 orders of magnitude less than the maximum viscosity in the lower mantle of Earth. Because viscosity likely decreases with pressure above ∼0.1 TPa (in addition to higher temperatures for larger planets), deep mantle viscosity of super-Earths will decrease with increasing planetary mass. The inferred low viscosity of the deep mantle results in high tidal dissipation and resultant rapid orbital evolution, and affects thermal history and hence generation of the magnetic field and the style of mantle convection.     

From planetesimals to terrestrial planets: N-body simulations including the effects of nebular gas and giant planets

We present results from a suite of N-body simulations that follow the formation and accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5 and 4.0 AU and the collisional growth is followed until the completion of planetary accretion (>100 Myr). A total of 64 simulations were carried out to explore sensitivity to the key parameters and initial conditions. All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas (which dissipates uniformly in space and exponentially in time), and orbits of Jupiter and Saturn. We end up with 1-5 planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1-2 Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today’s eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10 Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100 Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts, as long as we include all the above effects of gas and assume initial disks similar to the minimum mass solar nebular.