Predicting Planets in Known Extra-Solar Planetary Systems II: Testing for Saturn-mass Planets

Recent results have shown that many of the known extrasolar planetary systems contain regions which are stable for massless test particles. We examine the possibility that Saturn-mass planets exist in these systems, just below the detection threshold, and attempt to predict likely orbital parameters for such unseen planets. To do this, we insert a Saturn-mass planet into the stable regions of these systems and integrate its orbit for 100 million years. We conduct 200-600 of these experiments to test parameter space in HD37124, HD38529, 55Cnc, and HD74156. In HD37124 the global maximum of the survival rate of Saturns in parameter space is at semimajor axis a = 1.03 AU, eccentricity e=0.1. In HD38529, only 5% of Saturns are unstable, and the region in which a Saturn could survive is very broad, centered on 0.5<a<0.6, e<0.2. In 55Cnc we find three maxima at (a,e) = (1.0 AU, 0.02), (2.0 AU, 0.08), and (3.0 AU, 0.17). In HD74156 we find a broad maximum with $a$ = 0.9-1.2 AU, e<=0.15. Several of these maxima are located in the habitable zones of their parent stars and are therefore of astrobiological interest. We suggest the possibility that companions may lie in these locations of parameter space, and encourage further observational investigation of these systems.Comment: submitted to ApJ 9 pages, 8 figures, 3 table

Vega's hot dust from icy planetesimals scattered inward by an outward-migrating planetary system

Vega has been shown to host multiple dust populations, including both hot exo-zodiacal dust at sub-AU radii and a cold debris disk extending beyond 100 AU. We use dynamical simulations to show how Vega's hot dust can be created by long-range gravitational scattering of planetesimals from its cold outer regions. Planetesimals are scattered progressively inward by a system of 5-7 planets from 30-60 AU to very close-in. In successful simulations the outermost planets are typically Neptune-mass. The back-reaction of planetesimal scattering causes these planets to migrate outward and continually interact with fresh planetesimals, replenishing the source of scattered bodies. The most favorable cases for producing Vega's exo-zodi have negative radial mass gradients, with sub-Saturn- to Jupiter-mass inner planets at 5-10 AU and outer planets of 2.5 to 20 Earth masses. The mechanism fails if a Jupiter-sized planet exists beyond ~15 AU because the planet preferentially ejects planetesimals before they can reach the inner system. Direct-imaging planet searches can therefore directly test this mechanism.Comment: Updated references. Accepted to MNRAS Letters. 5 pages, 4 figures. Blog post about the paper at http://planetplanet.net/2014/03/31/vega-a-planetary-poem

Orbital Dynamics of Multi-Planet Systems with Eccentricity Diversity

Since exoplanets were detected using the radial velocity method, they have revealed a diverse distribution of orbital configurations. Amongst these are planets in highly eccentric orbits (e > 0.5). Most of these systems consist of a single planet but several have been found to also contain a longer period planet in a near-circular orbit. Here we use the latest Keplerian orbital solutions to investigate four known systems which exhibit this extreme eccentricity diversity; HD 37605, HD 74156, HD 163607, and HD 168443. We place limits on the presence of additional planets in these systems based on the radial velocity residuals. We show that the two known planets in each system exchange angular momentum through secular oscillations of their eccentricities. We calculate the amplitude and timescale for these eccentricity oscillations and associated periastron precession. We further demonstrate the effect of mutual orbital inclinations on the amplitude of high-frequency eccentricity oscillations. Finally, we discuss the implications of these oscillations in the context of possible origin scenarios for unequal eccentricities.Comment: 12 pages, 9 figures, accepted for publication in the Astrophysical Journa

High-resolution simulations of the final assembly of Earth-like planets 2: water delivery and planetary habitability

The water content and habitability of terrestrial planets are determined during their final assembly, from perhaps a hundred 1000-km "planetary embryos" and a swarm of billions of 1-10 km "planetesimals." During this process, we assume that water-rich material is accreted by terrestrial planets via impacts of water-rich bodies that originate in the outer asteroid region. We present analysis of water delivery and planetary habitability in five high-resolution simulations containing about ten times more particles than in previous simulations (Raymond et al 2006a, Icarus, 183, 265-282). These simulations formed 15 terrestrial planets from 0.4 to 2.6 Earth masses, including five planets in the habitable zone. Every planet from each simulation accreted at least the Earth's current water budget; most accreted several times that amount (assuming no impact depletion). Each planet accreted at least five water-rich embryos and planetesimals from past 2.5 AU; most accreted 10-20 water-rich bodies. We present a new model for water delivery to terrestrial planets in dynamically calm systems, with low-eccentricity or low-mass giant planets -- such systems may be very common in the Galaxy. We suggest that water is accreted in comparable amounts from a few planetary embryos in a "hit or miss" way and from millions of planetesimals in a statistically robust process. Variations in water content are likely to be caused by fluctuations in the number of water-rich embryos accreted, as well as from systematic effects such as planetary mass and location, and giant planet properties.Comment: Astrobiology, in pres

Terrestrial Planet Formation Constrained by Mars and the Structure of the Asteroid Belt

Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 AU and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas-drag, as has been proposed to explain the formation of close-in super Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar System. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from disks of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Disks with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogs significantly more massive than the real planet. In contrast, a disk with a surface density gradient proportional to $r^{-5.5}$ reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disk profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.Comment: Accepted for publication in MNRA

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

Predicting Planets in Known Extra-Solar Planetary Systems I: Test Particle Simulations

Recent work has suggested that many planetary systems lie near instability. If all systems are near instability, an additional planet must exist in stable regions of well-separated extra-solar planetary systems to push these systems to the edge of stability. We examine the known systems by placing massless test particles in between the planets and integrating for 1-10 million years. We find that some systems, HD168443 and HD74156, eject nearly all test particles within 2 million years. However we find that HD37124, HD38529, and 55Cnc have large contiguous regions in which particles survive for 10 million years. These three systems, therefore, seem the most likely candidates for additional companions. Furthermore HD74156 and HD168443 must be complete and therefore radial velocity surveys should only focus on detecting more distant companions. We also find that several systems show stable regions that only exist at nonzero eccentricities.Comment: 8 pages, 6 figures, 2 tables, submitted to Ap