Sean N. Raymond

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 × 10 24 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.

Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1

One aim of modern astronomy is to detect temperate, Earth-like exoplanets that are well suited for atmospheric characterization. Recently, three Earth-sized planets were detected that transit (that is, pass in front of) a star with a mass just eight per cent that of the Sun, located 12 parsecs away. The transiting configuration of these planets, combined with the Jupiter-like size of their host star—named TRAPPIST-1—makes possible in-depth studies of their atmospheric properties with present-day and future astronomical facilities. Here we report the results of a photometric monitoring campaign of that star from the ground and space. Our observations reveal that at least seven planets with sizes and masses similar to those of Earth revolve around TRAPPIST-1. The six inner planets form a near-resonant chain, such that their orbital periods (1.51, 2.42, 4.04, 6.06, 9.1 and 12.35 days) are near-ratios of small integers. This architecture suggests that the planets formed farther from the star and migrated inwards. Moreover, the seven planets have equilibrium temperatures low enough to make possible the presence of liquid water on their surfaces.

High-resolution simulations of the final assembly of Earth-like planets I. Terrestrial accretion and dynamics

Abstract The final stage in the formation of terrestrial planets consists of the accumulation of ∼1000-km “planetary embryos” and a swarm of billions of 1–10 km “planetesimals.” During this process, water-rich material is accreted by the terrestrial planets via impacts of water-rich bodies from beyond roughly 2.5 AU. We present results from five high-resolution dynamical simulations. These start from 1000–2000 embryos and planetesimals, roughly 5–10 times more particles than in previous simulations. Each simulation formed 2–4 terrestrial planets with masses between 0.4 and 2.6 Earth masses. The eccentricities of most planets were ∼0.05, lower than in previous simulations, but still higher than for Venus, Earth and Mars. Each planet accreted at least the Earths current water budget. We demonstrate several new aspects of the accretion process: (1) The feeding zones of terrestrial planets change in time, widening and moving outward. Even in the presence of Jupiter, water-rich material from beyond 2.5 AU is not accreted for several millions of years. (2) Even in the absence of secular resonances, the asteroid belt is cleared of >99% of its original mass by self-scattering of bodies into resonances with Jupiter. (3) If planetary embryos form relatively slowly, then the formation of embryos in the asteroid belt may have been stunted by the presence of Jupiter. (4) Self-interacting planetesimals feel dynamical friction from other small bodies, which has important effects on the eccentricity evolution and outcome of a simulation.

Spectroscopic Properties of Cool Stars in the Sloan Digital Sky Survey: An Analysis of Magnetic Activity and a Search for Subdwarfs

We present a spectroscopic analysis of nearly 8000 late-type dwarfs in the Sloan Digital Sky Survey. Using the Hα emission line as an activity indicator, we investigate the fraction of active stars as a function of spectral type and find a peak near type M8, confirming previous results. In contrast to past findings, we find that not all M7–M8 stars are active. We show that this may be a selection effect of the distance distributions of previous samples, since the active stars appear to be concentrated near the Galactic plane. We also examine the activity strength (ratio of the luminosity emitted in Hα to the bolometric luminosity) for each star and find that the mean activity strength is constant over the range M0–M5 and declines at later types. The decline begins at a slightly earlier spectral type than previously found. We explore the effect that activity has on the broadband photometric colors and find no significant differences between active and inactive stars. We also carry out a search for subdwarfs using spectroscopic metallicity indicators and find 60 subdwarf candidates. Several of these candidates are near the extreme subdwarf boundary. The spectroscopic subdwarf candidates are redder by ~0.2 mag in g-r compared with disk dwarfs at the same r-i color.

An earth-sized planet in the habitable zone of a cool star

Starry Brightness The high photometric precision of NASAs Kepler observatory has enabled the detection of many planets because they cause slight dimming of their host stars as they orbit in front of them. From these data, Quintana et al. (p. 277) have spotted a five-planet system around a small star. Here, the outermost planet is only 10% larger than Earth and completes its 130-day orbit entirely within the habitable zone, where liquid water could exist on its surface. Similarly, Kepler can detect faint periodic brightenings, as Kruse and Agol (p. 275) have reported for the binary system KOI-3278. In this system, a white dwarf acts as a gravitational microlens when it passes in front of its Sun-like G-star companion every 88 days. The lensing effect allows the mass of the white dwarf to be estimated, which helps us to understand how similar binary systems may have evolved. NASA’s Kepler mission revealed that the fifth and outermost planet orbiting Kepler-186 is capable of hosting liquid water. The quest for Earth-like planets is a major focus of current exoplanet research. Although planets that are Earth-sized and smaller have been detected, these planets reside in orbits that are too close to their host star to allow liquid water on their surfaces. We present the detection of Kepler-186f, a 1.11 ± 0.14 Earth-radius planet that is the outermost of five planets, all roughly Earth-sized, that transit a 0.47 ± 0.05 solar-radius star. The intensity and spectrum of the star’s radiation place Kepler-186f in the stellar habitable zone, implying that if Kepler-186f has an Earth-like atmosphere and water at its surface, then some of this water is likely to be in liquid form.

Exotic Earths: forming habitable worlds with giant planet migration.

Close-in giant planets (e.g., “hot Jupiters”) are thought to form far from their host stars and migrate inward, through the terrestrial planet zone, via torques with a massive gaseous disk. Here we simulate terrestrial planet growth during and after giant planet migration. Several-Earth-mass planets also form interior to the migrating jovian planet, analogous to recently discovered “hot Earths.” Very-water-rich, Earth-mass planets form from surviving material outside the giant planets orbit, often in the habitable zone and with low orbital eccentricities. More than a third of the known systems of giant planets may harbor Earth-like planets.

Formation of Earth-like Planets During and After Giant Planet Migration

Close-in giant planets are thought to have formed in the cold outer regions of planetary systems and migrated inward, passing through the orbital parameter space occupied by the terrestrial planets in our own solar system. We present dynamical simulations of the effects of a migrating giant planet on a disk of protoplanetary material and the subsequent evolution of the planetary system. We numerically investigate the dynamics of postmigration planetary systems over 200 million years using models with a single migrating giant planet, one migrating and one nonmigrating giant planet, and excluding the effects of a gas disk. Material that is shepherded in front of the migrating giant planet by moving mean motion resonances accretes into hot Earths, but survival of these bodies is strongly dependent on dynamical damping. Furthermore, a significant amount of material scattered outward by the giant planet survives in highly excited orbits; the orbits of these scattered bodies are then damped by gas drag and dynamical friction over the remaining accretion time. In all simulations Earth-mass planets accrete on approximately 100 Myr timescales, often with orbits in the habitable zone. These planets range in mass and water content, with both quantities increasing with the presence of a gas disk and decreasing with the presence of an outer giant planet. We use scaling arguments and previous results to derive a simple recipe that constrains which giant planet systems are able to form and harbor Earth-like planets in the habitable zone, demonstrating that roughly one-third of the known planetary systems are potentially habitable.

A DECREASED PROBABILITY OF HABITABLE PLANET FORMATION AROUND LOW-MASS STARS

Smaller terrestrial planets (P0.3 M⊕) are less likely to retain the substantial atmospheres and ongoing tectonic activity probably required to support life. A key element in determining whether sufficiently massive sustainably habitable planets can form is the availability of solid planet-forming material. We use dynamical simulations of terrestrial planet formation from planetary embryos and simple scaling arguments to explore the implications of correlations between terrestrial planet mass, disk mass, and the mass of the parent star. We assume that the protoplanetary disk mass scales with stellar mass as M-disk ∝ fMh*(h), where f measures the relative disk mass and 1/2 0.3 M⊕ habitable planets decreases for low-mass stars for every realistic combination of parameters. This habitable fraction is small for stellar masses below a mass in the interval 0.5-0.8 M☉, depending on disk parameters, an interval that excludes most M stars. Radial mixing and therefore water delivery are inefficient in the lower mass disks commonly found around low-mass stars, such that terrestrial planets in the habitable zones of most low-mass stars are likely to be small and dry.

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 (� 5‐10 M ⊕ ). 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 (� 5M ⊕) 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 ∼70 M ⊕ , 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).

Highly siderophile elements in Earth’s mantle as a clock for the Moon-forming impact

According to the generally accepted scenario, the last giant impact on Earth formed the Moon and initiated the final phase of core formation by melting Earth’s mantle. A key goal of geochemistry is to date this event, but different ages have been proposed. Some argue for an early Moon-forming event, approximately 30 million years (Myr) after the condensation of the first solids in the Solar System, whereas others claim a date later than 50 Myr (and possibly as late as around 100 Myr) after condensation. Here we show that a Moon-forming event at 40 Myr after condensation, or earlier, is ruled out at a 99.9 per cent confidence level. We use a large number of N-body simulations to demonstrate a relationship between the time of the last giant impact on an Earth-like planet and the amount of mass subsequently added during the era known as Late Accretion. As the last giant impact is delayed, the late-accreted mass decreases in a predictable fashion. This relationship exists within both the classical scenario and the Grand Tack scenario of terrestrial planet formation, and holds across a wide range of disk conditions. The concentration of highly siderophile elements (HSEs) in Earth’s mantle constrains the mass of chondritic material added to Earth during Late Accretion. Using HSE abundance measurements, we determine a Moon-formation age of 95 ± 32 Myr after condensation. The possibility exists that some late projectiles were differentiated and left an incomplete HSE record in Earth’s mantle. Even in this case, various isotopic constraints strongly suggest that the late-accreted mass did not exceed 1 per cent of Earth’s mass, and so the HSE clock still robustly limits the timing of the Moon-forming event to significantly later than 40 Myr after condensation.