Hot Earths Research Articles

Homogeneous Analysis of Hot Earths: Masses, Sizes, and Compositions

Abstract Terrestrial planets have been found orbiting Sun-like stars with extremely short periods—some as short as 4 hr. These “ultra-short-period planets” or “hot Earths” are so strongly irradiated that any initial H/He atmosphere has probably been lost to photoevaporation. As such, the sample of hot Earths may give us a glimpse at the rocky cores that are often enshrouded by thick H/He envelopes on wider-orbiting planets. However, the mass and radius measurements of hot Earths have been derived from a hodgepodge of different modeling approaches, and include several cases of contradictory results. Here, we perform a homogeneous analysis of the complete sample of 11 known hot Earths with an insolation exceeding 650 times that of the Earth. We combine all available data for each planet, incorporate parallax information from Gaia to improve the stellar and planetary parameters, and use Gaussian process regression to account for correlated noise in the radial-velocity data. The homogeneous analysis leads to a smaller dispersion in the apparent composition of hot Earths, although there does still appear to be some intrinsic dispersion. Most of the planets are consistent with an Earth-like composition (35% iron and 65% rock), but two planets (K2-141b and K2-229b) show evidence for a higher iron fraction, and one planet (55 Cnc e) has either a very low iron fraction or an envelope of low-density volatiles. All of the planets are less massive than 8 M ⊕, despite the selection bias toward more massive planets, suggesting that 8 M ⊕ is the critical mass for runaway accretion.

On the Origin of Dynamically Isolated Hot Earths

Abstract A distinct population of planetary systems that contain dynamically isolated, Earth-size planets with orbital periods day was recently identified in an analysis of data from the Kepler planet candidate catalog. We argue that these objects could represent the remnant rocky cores of giant planets that arrived at the stellar vicinity on high-eccentricity orbits and were rapidly stripped of their gaseous envelopes after crossing their respective Roche limits (RLs) . In this picture, objects with day are mostly “early” cores that originated in planets with an initial periastron distance they had high initial eccentricities but their orbits underwent fast tidal circularization after the cores were exposed. Objects with day are, by contrast, mostly “late” cores that originated in planets with these planets underwent orbital circularization to a radius but eventually reached through tidal orbital decay. This picture naturally accounts for the spatial distribution of hot Earths and for the similarity of their inferred occurrence rate to that of hot Jupiters, and it fits well with the interpretation of the so-called sub-Jovian desert in the orbital-period–planetary-mass plane in terms of high-eccentricity planet migration to the vicinity of the RL.

INTERACTION OF CLOSE-IN PLANETS WITH THE MAGNETOSPHERE OF THEIR HOST STARS. II. SUPER-EARTHS AS UNIPOLAR INDUCTORS AND THEIR ORBITAL EVOLUTION

Planets with several Earth masses and a few day orbital periods have been discovered through radial velocity and transit surveys. Regardless of their formation mechanism, a key evolution issue is the efficiency of their retention near their host stars. If these planets attained their present-day orbits during or shortly after the T Tauri phase of their host stars, a large fraction would have encountered intense stellar magnetic field. Since these planets have a higher conductivity than the atmosphere of their stars, the magnetic flux tube connecting the planet and host star would slip though the envelope of the star faster than across the planet. The induced electro-motive force across the planet's diameter leads to a potential drop which propagates along a flux tube away from the planet with an Alfven speed. The foot of the flux tube sweeps across the stellar surface and the potential drop drives a DC current analogous to that proposed for the Io-Jupiter electrodynamic interaction. The ohmic dissipation of this current produces potentially observable hot spots in the star envelope. The current heats the planet and leads to a Lorrentz torque which drives the planet's orbit to evolve toward circularization and synchronization with the star's spin. The net effect is the damping of the planet's orbital eccentricity. Around slowly (rapidly) spinning stars, this process also causes rocky planets with periods less than a few days to undergo orbital decay (expansion/stagnation) within a few Myr. In principle, this effect can determine the retention efficiency of short-period hot Earths. We also estimate the ohmic dissipation in these planets and show that it can lead to severe structure evolution and potential loss of volatile material. However, these effects may be significantly weakened by the reconnection of the induced field [Slightly shortened abstract].

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).

Terrestrial planet formation in extra-solar planetary systems

AbstractTerrestrial planets form in a series of dynamical steps from the solid component of circumstellar disks. First, km-sized planetesimals form likely via a combination of sticky collisions, turbulent concentration of solids, and gravitational collapse from micron-sized dust grains in the thin disk midplane. Second, planetesimals coalesce to form Moon- to Mars-sized protoplanets, also called “planetary embryos”. Finally, full-sized terrestrial planets accrete from protoplanets and planetesimals. This final stage of accretion lasts about 10-100 Myr and is strongly affected by gravitational perturbations from any gas giant planets, which are constrained to form more quickly, during the 1-10 Myr lifetime of the gaseous component of the disk. It is during this final stage that the bulk compositions and volatile (e.g., water) contents of terrestrial planets are set, depending on their feeding zones and the amount of radial mixing that occurs. The main factors that influence terrestrial planet formation are the mass and surface density profile of the disk, and the perturbations from giant planets and binary companions if they exist. Simple accretion models predicts that low-mass stars should form small, dry planets in their habitable zones. The migration of a giant planet through a disk of rocky bodies does not completely impede terrestrial planet growth. Rather, “hot Jupiter” systems are likely to also contain exterior, very water-rich Earth-like planets, and also “hot Earths”, very close-in rocky planets. Roughly one third of the known systems of extra-solar (giant) planets could allow a terrestrial planet to form in the habitable zone.

Baroclinic generation of potential vorticity in an embedded planet-disk system

AbstractWe use a multi-dimensional hydrodynamics code to study the gravitational interaction between an embedded planet and a protoplanetary disk with emphasis on the generation of vortensity (Potential Vorticity or PV) through a Baroclinic Instability. We show that the generation of PV is very common and effective in non-barotropic disks through the Baroclinic Instability, especially within the coorbital region. Our results also complement previous work that non-axisymmetric Rossby-Wave Instabilities (RWIs) are likely to develop at local minima of PV distribution that are generated by the interaction between a planet and an inviscid barotropic disk. The development of RWIs results in non-axisymmetric density blobs, which exert stronger torques onto the planet when they move to the vicinity of the planet. Hence, large amplitude oscillations are introduced to the time behavior of the total torque acted on the planet by the disk. In current simulations, RWIs do not change the overall picture of inward orbital migration but cause a non-monotonic behavior to the migration speed. As a side effect, RWIs also introduce interesting structures into the disk. These structures may help the formation of Earth-like planets in the Habitable Zone or Hot Earths interior to a close-in giant planet.

Disk‐Planet Interaction Simulations. I. Baroclinic Generation of Vortensity and Nonaxisymmetric Rossby Wave Instability

We use a multidimensional hydrodynamics code to study the gravitational interaction between an embedded planet and a protoplanetary disk, with emphasis on the generation of vortensity ( potential vorticity) through a baroclinic instability and subsequent development of Rossby wave instability (RWI). It is found that the generation of potential vorticity is very common and effective in nonbarotropic disks through the baroclinic instability, especially within the co-orbital region. Our results also complement previous studies by Koller and coworkers, which showed that nonaxisymmetric RWIs are likely to develop at local minima of potential vorticity distribution that are generated by the interaction between a planet and an inviscid barotropic disk. This second instability appears to be very common and robust, regardless of the equation of state, initial density distribution, and rotational law of the disk. The development of RWIs results in nonaxisymmetric density blobs, which exert stronger torques on the planet when they travel within its vicinity. As a result of that, large-amplitude oscillations are introduced to the time behavior of the total torque acting on the planet from the disk. In our current simulations, RWIs do not change the overall picture of inward orbital migration, but bring in a nonmonotonic behavior to the migration speed. As a side effect, RWIs also introduce interesting structures into the disk. These structures may help the formation of Earth-like planets in the habitable zone, or hot Earths interior to a close-in giant planet.

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 post-migration planetary systems over 200 million years using models with a single migrating giant planet, one migrating and one non-migrating 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.

Looking for Giant Earths in the HD 209458 System: A Search for Transits inMOSTSpace‐based Photometry

We have made a comprehensive transit search for exoplanets down to about 2 Earth radii in the HD 209458 system, based on nearly uninterrupted broadband optical photometry obtained with the MOST (Microvariability and Oscillations of Stars) satellite, spanning 14 days in 2004 and 44 days in 2005. We have searched these data for limb-darkened transits at periods other than that of the known giant planet, from about 0.5 days to 2 weeks. Monte Carlo statistical tests of the data with synthetic transits inserted allow us to rule out additional close-in exoplanets with sizes ranging from about 0.20-0.36 RJ (Jupiter radii), or 2.2-4.0 RE (Earth radii) on orbits whose planes are near that of HD 209458b. These null results constrain theories that invoke lower mass planets in orbits similar to HD 209458b to explain its anomalously large radius, and those that predict "hot Earths" due to the inward migration of HD 209458b.

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 planet's 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.

Could the 47 Ursae Majoris Planetary System be a Second Solar System? Predicting the Earth‐like Planets

(Abridged)We numerically investigated the dynamical architecture of 47 UMa with the planetary configuration of the best-fit orbital solutions by Fischer et al. We systematically studied the existence of Earth-like planets in the region 0.05 AU $\leq a \leq 2.0$ AU for 47 UMa with numerical simulations, and we also explored the packed planetary geometry and Trojan planets in the system. In the simulations, we found that "hot Earths" at 0.05 AU $\leq a < $ 0.4 AU can dynamically survive at least for 1 Myr. The Earth-like planets can eventually remain in the system for 10 Myr in areas involved in the mean motion resonances (MMR) (e.g., 3:2 MMR) with the inner companion. Moreover, we showed that the 2:1 and 3:1 resonances are on the fringe of stability, while the 5:2 MMR is unstable. Additionally, the 2:1 MMR marks out a remarkable boundary between chaotic and regular motions, inside, most of the orbits can survive, outside, they are mostly lost in the orbital evolution. In a dynamical sense, the most likely candidate for habitable environment is Earth-like planets with orbits in the ranges 0.8 AU $\leq a < 1.0$ AU and 1.0 AU $ < a < 1.30$ AU (except several unstable cases) with relatively low eccentricities. The Trojan planets with low eccentricities and inclinations can secularly last at the triangular equilibrium points of two massive planets. Hence, the 47 UMa planetary system may be a close analog to our solar system.