P14B-01 INVITED
Formation of Terrestrial Planets from Protoplanets
The final stage of terrestrial planet formation is known as the giant impact stage where lunar-to-Mars-sized protoplanets collide with one another to form planets. We investigate this final assemblage of terrestrial planets from protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of protoplanets. We systematically change the initial protoplanet system parameters. For each initial condition, we perform more than 20 runs, and from their results we derive the statistical properties of the assembled planets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We show the dependences of the mass and orbital elements of planets on the initial protoplanet system parameters. The number of planets slowly decreases as the surface density of the initial protoplanets increases, while the mass of individual planets increases almost linearly. We also find that the spin angular velocity of the planets is well expressed by a Gaussian distribution and their obliquity is well expressed by an isotropic distribution. The typical spin angular velocity is given by the critical spin angular velocity for rotational instability under the assumption of perfect accretion in collisions. We also discuss the effect of the accretion condition on the terrestrial planet formation.
P14B-02 INVITED
Size Matters - Lessons from the Interiors of Earth and Mars
Phase transitions at high pressure change material properties and therefore affect the structure and dynamics of the planetary interior. The pressure for current measurements for mantle transitions is generally limited to that of the Earth's core-mantle boundary (CMB). Therefore, transitions at the pressures expected for the mantles (1-10 Mbar) of super-Earths (1-10M⊕) are not well known. However, some lessons can be learned from comparing mantle transitions in Earth (1M⊕, 1.4 Mbar at CMB) and Mars (0.1M⊕, 0.2 Mbar at CMB). Early Earth and Mars may have had deep magma oceans. Our recent study on silicate glasses, frozen forms of melts, shows a series of structural transitions at Earth's mid-mantle pressures. The compositional sensitivity of these transitions may result in compositional stratification in the Earth's magma ocean. However, pressure in the Mars magma ocean is not sufficiently high for this process to occur. This shows that the internal pressure of the planet is an important factor for the initial structure of its mantle. New types of transitions have recently been discovered at pressures within the Earth's deep mantle but beyond the Mars mantle. Iron in mantle phases undergoes changes in electronic configuration (high-spin to low-spin transition) in Earth's deep mantle, leading to changes in optical properties and element partitioning which are important parameters for heat generation and transport. Finally, perovskite undergoes a structural transition (post-perovskite transition) at pressures related to the Earth's CMB region. This transition involves a different type of structural changes compared with the upper-mantle transitions and is responsible for the significant property changes in the CMB region. These examples demonstrate that completely different types of transitions may occur in deep super-Earths. Theory predicts that the energy of an electron becomes comparable or even higher than the binding energy of the electron in an atom as pressure approaches to 10 Mbar, suggesting fundamental changes in chemical bonding of materials at the super-Earth's CMB. A recent computer simulation (Umemoto et al., 2006) suggested a dissociation of MgSiO3 to MgO+SiO2 and metallization of SiO2 at 10 Mbar. The metallic electrical conductivity at the CMB may affect the nutation of super-Earth.
P14B-03 INVITED
Mantle Convection, Stagnant Lids and Plate Tectonics on Super-Earths
The discovery of extra-solar super-Earths has prompted interest in their possible mantle dynamics and evolution, and in whether their lithospheres are most likely to be undergoing plate tectonics like on Earth, or be stagnant lids like on Mars and Venus. The origin of plate tectonics is poorly understood for the Earth, likely involving a complex interplay of rheological, compositional, melting and thermal effects, which makes it impossible to make reliable predictions for other planets. Nevertheless, as a starting point it is common to parameterize the complex processes involved as a simple yield stress that is either constant or has a linear "Byerlee's law" dependence on pressure (e.g., [Tackley, GCubed 2000ab] in 3D cartesian geometry; [van Heck and Tackley, GRL 2008] in 3D spherical geometry). For such a simple description, scaling with planet size is expected to depend on heating mode (internal versus basal) and lithospheric strength profile. Simple "back of the envelope" scaling laws (e.g., following Moresi and Solomatov, GJI 1998) ignoring the pressure- dependence of physical properties such as density and thermal expansivity, suggest that the threshold for plate tectonics (i.e., yield stress or friction coefficient) does not depend strongly on planet size, and plate tectonics is equally likely or more likely for larger planets. Scalings that take into account pressure-related changes in physical properties [Valencia et al., Astrophys. J., 2007] make a similar prediction for predominantly internally-heated convection. Because the simplifying assumptions made in developing analytical scalings may not be valid over all parameter ranges, numerical simulations are needed; the one numerical study on super-Earths to date (O'Neill and Lenardic, GRL 2007) finds that plate tectonics is less likely on a larger planet, in apparent contradiction of analytical results. To try and understand this we here present new calculations of yielding- induced plate tectonics as a function of planet size, focusing on the idealized endmembers of internal heating or basal heating as well as different strength profiles, and compare to analytical scalings. The temperature- dependence of viscosity is based on laboratory values, i.e., stronger than previously modelled. Preliminary results indicate some first order similarity to simple scalings although some differences exist. In Earth, physical properties such as density, thermal expansivity, thermal conductivity and viscosity change strongly with pressure so that their values change substantially between the surface and the CMB, and many modelling studies have shown that this has a strong effect on convection. On super-Earths this will be even more accentuated. Thus, in a second set of calculations, we include reasonable variations of physical properties with pressure for planets up to twice Earth radius, studying their effect on convection with rigid lids or plate tectonics.
P14B-04
Detection of Super-Earth Planets via the Transit Timing Variation Method
Short-period terrestrial-class and Super-Earth objects are predicted to be captured into near mean-motion resonant orbits with migrating giant planets. These objects are potentially detectable via transit photometry of their host stars, or the measurement of the variations of the transit-timing due to their close-in Jovian-mass planetary companions. The latter, also known as the TTV method, is particularly efficient in detecting small close-in planets in resonant orbits. We have carried out an extensive study of the capability of the TTV method in detecting close-in Super-Earth objects, and have identified regions of their parameter-space for which such planets will produce strong TTV signals. We have also studied the effects of interior and exterior mean-motion resonancces on the detectability of Super-Earths, and have been able to show that for a tidally locked Jovian body, a Super-Earth planetary companion has a greater chance of detection if it has a long- term stable orbit with a low eccentricity and a low inclination. Our simulations also indiate that regions may exist in the vicinity of unstable mean-motion resonances, where a Super-Earth object can maintain its orbit for a long time and produce strong signals detectable by the transit-timing variations method. We present the results of our study, and discuss the capability of TTV method in detecting super-Earth objects in more detail. This work has been supported by NASA Astrobiology Institute through cooperative agreement NNA04CC08A with the Institute for Astronomy at the University of Hawaii for NH.