The Survival Rate of Ejected Terrestrial Planets with Moons

During planet formation, a gas giant will interact with smaller protoplanets that stray within its sphere of gravitational influence. We investigate the outcome of interactions between gas giants and terrestrial-sized protoplanets with lunar-sized companions. An interaction between a giant planet and a protoplanet binary may have one of several consequences, including the delivery of volatiles to the inner system, the capture of retrograde moons by the giant planet, and the ejection of one or both of the protoplanets. We show that an interesting fraction of terrestrial-sized planets with lunar sized companions will likely be ejected into interstellar space with the companion bound to the planet. The companion provides an additional source of heating for the planet from tidal dissipation of orbital and spin angular momentum. This heat flux typically is larger than the current radiogenic heating of the Earth for up to the first few hundred million years of evolution. In combination with an atmosphere of sufficient thickness and composition, the heating can provide the conditions necesary for liquid water to persist on the surface of the terrestrial mass planet, making it a potential site for life. We also determine the possibility for directly detecting such systems through all-sky infrared surveys or microlensing surveys. Microlensing surveys in particular will directly measure the frequency of this phenomenon.Comment: 4 pages, 2 figures, Accepted to ApJ

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. (abridged)Comment: Accepted to Icarus. 21 pages, 12 figures, 5 tables in emulateapj format. Figures 3 and 4 degraded. For full-resolution see http://casa.colorado.edu/~raymonsn/ms_emulateapj.pd

The Complex History of Trojan Asteroids

The Trojan asteroids provide a unique perspective on the history of Solar System. As a large population of small bodies, they record important gravitational interactions and dynamical evolution of the Solar System. In the past decade, significant advances have been made in understanding physical properties, and there has been a revolution in thinking about the origin of Trojans. The ice and organics generally presumed to be a significant part of Trojan compositions have yet to be detected directly, though low density of the binary system Patroclus (and possibly low density of the binary/moonlet system Hektor) is consistent with an interior ice component. By contrast, fine-grained silicates that appear to be similar to cometary silicates in composition have been detected, and a color bimodality may indicate distinct compositional groups among the Trojans. Whereas Trojans had traditionally been thought to have formed near 5 AU, a new paradigm has developed in which the Trojans formed in the proto-Kuiper Belt, and they were scattered inward and captured in the Trojan swarms as a result of resonant interactions of the giant planets. Whereas the orbital and population distributions of current Trojans are consistent with this origin scenario, there are significant differences between current physical properties of Trojans and those of Kuiper Belt objects. These differences may be indicative of surface modification due to the inward migration of objects that became the Trojans, but understanding of appropriate modification mechanisms is poor and would benefit from additional laboratory studies. Many open questions remain, and the future promises significant strides in our understanding of Trojans. The time is ripe for a spacecraft mission to the Trojans, to turn these objects into geologic worlds that can be studied in detail to unravel their complex history.Comment: Chapter for Asteroids IV book (UA Press), accepted for publication, 33 pages, 10 figure

Water Delivery and Giant Impacts in the 'Grand Tack' Scenario

A new model for terrestrial planet formation (Hansen 2009, Walsh et al. 2011) has explored accretion in a truncated protoplanetary disk, and found that such a configuration is able to reproduce the distribution of mass among the planets in the Solar System, especially the Earth/Mars mass ratio, which earlier simulations have generally not been able to match. Walsh et al. tested a possible mechanism to truncate the disk--a two-stage, inward-then-outward migration of Jupiter and Saturn, as found in numerous hydrodynamical simulations of giant planet formation. In addition to truncating the disk and producing a more realistic Earth/Mars mass ratio, the migration of the giant planets also populates the asteroid belt with two distinct populations of bodies--the inner belt is filled by bodies originating inside of 3 AU, and the outer belt is filled with bodies originating from between and beyond the giant planets (which are hereafter referred to as `primitive' bodies). We find here that the planets will accrete on order 1-2% of their total mass from primitive planetesimals scattered onto planet-crossing orbits during the formation of the planets. For an assumed value of 10% for the water mass fraction of the primitive planetesimals, this model delivers a total amount of water comparable to that estimated to be on the Earth today. While the radial distribution of the planetary masses and the dynamical excitation of their orbits are a good match to the observed system, we find that the last giant impact is typically earlier than 20 Myr, and a substantial amount of mass is accreted after that event. However, 5 of the 27 planets larger than half an Earth mass formed in all simulations do experience large late impacts and subsequent accretion consistent with the dating of the Moon-forming impact and the estimated amount of mass accreted by Earth following that event

Abundances in Evolved Intermediate Mass Stars

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On the connection between the Nekhoroshev theorem and Arnold Diffusion

The analytical techniques of the Nekhoroshev theorem are used to provide estimates on the coefficient of Arnold diffusion along a particular resonance in the Hamiltonian model of Froeschl\'{e} et al. (2000). A resonant normal form is constructed by a computer program and the size of its remainder $||R_{opt}||$ at the optimal order of normalization is calculated as a function of the small parameter $\epsilon$. We find that the diffusion coefficient scales as $D\propto||R_{opt}||^3$, while the size of the optimal remainder scales as $||R_{opt}|| \propto\exp(1/\epsilon^{0.21})$ in the range $10^{-4}\leq\epsilon \leq 10^{-2}$. A comparison is made with the numerical results of Lega et al. (2003) in the same model.Comment: Accepted in Celestial Mechanics and Dynamical Astronom

Gas accretion onto Jupiter mass planets in discs with laminar accretion flows

(Abridged) Studies have shown that a Jovian mass planet embedded in a viscous protoplanetary disc (PPD) can accrete gas efficiently through the gap and doubles its mass in $\sim 0.1$ Myr. The planet also migrates inwards on a timescale of $\sim 0.1$ Myr. These timescales are short compared to PPD lifetimes, and raise questions about the origins of cold giant exoplanets. However, PPDs are unlikely to be globally turbulent, and instead they may launch magnetised winds such that accretion towards the star occurs in laminar accretion flows located in narrow layers near the surfaces of the disc. The aim of this study is to examine the rate at which gas accretes onto Jovian mass planets that are embedded in layered PPDs. We use 3D hydrodynamical simulations of planets embedded in PPDs, in which a constant radial mass flux towards the star of ${\dot m} = 10^{-8}$ M$_{\odot}$ yr$^{-1}$ is sustained. We consider a classical viscous alpha model, and also models in which an external torque is applied in narrow surface layers to mimic the effects of a magnetised wind. The accreting layers are parameterised by their column densities $\Sigma_{\rm A}$, and we consider values in the range 0.1 to 10 g cm$^{-2}$. The viscous model gives results in agreement with previous studies. We find the accretion rate onto the planet in the layered models crucially depends on the planet's ability to block the wind-induced mass flow. For $\Sigma_{\rm A}=10$ g cm$^{-2}$, the planet torque can block the mass flow through the disc, accretion onto the planet is slow, and a mass doubling time of 10 Myr is obtained. For $\Sigma_{\rm A}=0.1$ g cm$^{-2}$, accretion is fast and the mass doubling time is 0.2 Myr. Although the radial mass flow through the layered disc models is always $10^{-8}$ M$_{\odot}$ yr$^{-1}$, adopting different values of $\Sigma_{\rm A}$ leads to very different gas accretion rates onto gas giant planets.Comment: 14 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Massive planet migration: Theoretical predictions and comparison with observations

We quantify the utility of large radial velocity surveys for constraining theoretical models of Type II migration and protoplanetary disk physics. We describe a theoretical model for the expected radial distribution of extrasolar planets that combines an analytic description of migration with an empirically calibrated disk model. The disk model includes viscous evolution and mass loss via photoevaporation. Comparing the predicted distribution to a uniformly selected subsample of planets from the Lick / Keck / AAT planet search programs, we find that a simple model in which planets form in the outer disk at a uniform rate, migrate inward according to a standard Type II prescription, and become stranded when the gas disk is dispersed, is consistent with the radial distribution of planets for orbital radii 0.1 AU < a < 2.5 AU and planet masses greater than 1.65 Jupiter masses. Some variant models are disfavored by existing data, but the significance is limited (~95%) due to the small sample of planets suitable for statistical analysis. We show that the favored model predicts that the planetary mass function should be almost independent of orbital radius at distances where migration dominates the massive planet population. We also study how the radial distribution of planets depends upon the adopted disk model. We find that the distribution can constrain not only changes in the power-law index of the disk viscosity, but also sharp jumps in the efficiency of angular momentum transport that might occur at small radii.Comment: ApJ, in press. References updated to match published versio