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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Formation Of the Giant Planets By Concurrent Accretion Of Solids And Gas

New numerical simulations of the formation of the giant planets are presented, in which for the first time both the gas and planetesimal accretion rates are calculated in a self-consistent, interactive fashion. The simulations combine three elements: 1) three-body accretion cross-sections of solids onto an isolated planetary embryo, 2) a stellar evolution code for the planet's gaseous envelope, and 3) a planetesimal dissolution code within the envelope, used to evaluate the planet's effective capture radius and the energy deposition profile of accreted material. Major assumptions include: The planet is embedded in a disk of gas and small planetesimals with locally uniform initial surface mass density, and planetesimals are not allowed to migrate into or out of the planet's feeding zone. All simulations are characterized by three major phases. During the first phase, the planet's mass consists primarily of solid material. The planetesimal accretion rate, which dominates that of gas, rapidly increases owing to runaway accretion, then decreases as the planet's feeding zone is depleted. During the second phase, both solid and gas accretion rates are small and nearly independent of time. The third phase, marked by runaway gas accretion, starts when the solid and gas masses are about equal. It is engendered by a strong positive feedback on the gas accretion rates, driven by the rapid contraction of the gaseous envelope and the rapid expansion of the outer boundary, which depends on the planet's total mass. The overall evolutionary time scale is generally determined by the length of the second phase. The actual rates at which the giant planets accreted small planetesimals is probably intermediate between the constant rates assumed in most previous studies and the highly variable rates that we have used. Within the context, of the adopted model of planetesimal accretion, the joint constraints of the time scale for dissipation of the solar nebula and the current high-Z masses of the giant planets lead to estimates of the initial surface density (sigma(sub init)) of planetesimals in the outer region of the solar nebula. The results show sigma(sub init) approx. = 10 g/sq cm near Jupiter's orbit and that sigma(sub init) proportional to alpha(sup -2), where alpha is the distance from the Sun. These values are a factor of 3 - 4 times as high as that of the "minimum mass" solar nebula at Jupiter's distance and a factor of 2 - 3 times as high it Saturn's distance. Our estimates for the formation time of Jupiter and Saturn are 1 - 10 million years while those for Uranus fall in the range of 2 - 16 million years. These estimates follow from the properties of our Solar System and do not necessarily apply to giant planets in other planetary systems.

Pollack, James B.↗
NASA NTRS1996

Biases In A Magnitude Limited Versus A Distant Limited Planet Search

All methods utilized to conduct a search or survey inevitably have some built-in biases. These biases are often traced to some limitation of the instrument used or some inherent character of the signal being recorded. We address these limitations for various methods used or proposed for planet detection: spectroscopy, astrometry, interferometry, and photometry. For spectroscopy, the turbulence in the photosphere limits the minimum measurable dossier velocity to 3 m/s and hence the minimum planet to star mass ratio, thereby favoring massive close-in planets. Limited available observing time will necessarily introduce additional selection biases in the targets observed and telescope aperture will limit the faintest magnitude stars to be measured; For astrometry, the angular resolution of the instrument along with motions in the photometric center of the star limit the furthest distance for which giant planets can be detected to about 10 pc and favor massive outer orbit planets around low mass non-solar like stars; For imaging interferometry, the minimum angular size of the central null limits both the distance to the star and closeness of the planet to the host star to about 1 AU at 10 pc and thus to the very few solar-like stars within 10 pc. Solar and extra-solar zodiacal emission will limit the minimum size of the detectable planet. For photometry, the inherent variability of the star does not limit the minimum planet size until earth-sized or smaller planets are considered around solar-like stars. The telescope aperture limits the faintest stars that can be monitored. As with spectroscopy, there is no inherent distant limit to the method. After addressing the limiting factors of each method, an estimate is made of the number of planets of various sizes that could be found for each stellar type based on the detection probability and the number of stars that can be searched for planets.

Koch, David↗
NASA NTRS2002

Kepler Mission: A Discovery-Class Mission Designed to Determine the Frequency of Earth-Size and Larger Planets Around Solar-Like Stars

The first step in discovering the extent of life in our galaxy is to determine the number of terrestrial planets in the habitable zone (HZ). The Kepler Mission is designed around a 0.95 in aperture Schmidt-type telescope with an array of 42 CCDs designed to continuously monitor the brightness of 100,000 solar-like stars to detect the transits of Earth-size and larger planets. The photometer is scheduled to be launched into heliocentric orbit in 2007. Measurements of the depth and repetition time of transits provide the size of the planet relative to the star and its orbital period. When combined with ground-based spectroscopy of these stars to fix the stellar parameters, the true planet radius and orbit scale, hence the position relative to the HZ are determined. These spectra are also used to discover the relationships between the characteristics of planets and the stars they orbit. In particular, the association of planet size and occurrence frequency with stellar mass and metallicity will be investigated. At the end of the four year mission, hundreds of terrestrial planets should be discovered in and near the HZ of their stars if such planets are common. Extending the mission to six years doubles the expected number of Earth-size planets in the HZ. A null result would imply that terrestrial planets in the HZ occur in less than 1% of the stars and that life might be quite rare. Based on the results of the current Doppler-velocity discoveries, detection of a thousand giant planets is expected. Information on their albedos and densities of those giants showing transits will be obtained.

William Borucki↗
NASA NTRS2006

Terrestrial Planet Formation in Binary Star Systems

Most stars reside in binary/multiple star systems; however, previous models of planet formation have studied growth of bodies orbiting an isolated single star. Disk material has been observed around one or both components of various young close binary star systems. If planets form at the right places within such disks, they can remain dynamically stable for very long times. We have simulated the late stages of growth of terrestrial planets in both circumbinary disks around 'close' binary star systems with stellar separations ($a_B$) in the range 0.05 AU $\le a_B \le$ 0.4 AU and binary eccentricities in the range $0 \le e \le 0.8$ and circumstellar disks around individual stars with binary separations of tens of AU. The initial disk of planetary embryos is the same as that used for simulating the late stages of terrestrial planet growth within our Solar System and around individual stars in the Alpha Centauri system (Quintana et al. 2002, A.J., 576, 982); giant planets analogous to Jupiter and Saturn are included if their orbits are stable. The planetary systems formed around close binaries with stellar apastron distances less than or equal to 0.2 AU with small stellar eccentricities are very similar to those formed in the Sun-Jupiter-Saturn, whereas planetary systems formed around binaries with larger maximum separations tend to be sparser, with fewer planets, especially interior to 1 AU. Likewise, when the binary periastron exceeds 10 AU, terrestrial planets can form over essentially the entire range of orbits allowed for single stars with Jupiter-like planets, although fewer terrestrial planets tend to form within high eccentricity binary systems. As the binary periastron decreases, the radial extent of the terrestrial planet systems is reduced accordingly. When the periastron is 5 AU, the formation of Earth-like planets near 1 AU is compromised.

Lissauer, J. J.↗
NASA NTRS2003

Formation of Giant Planets and Brown Dwarves

According to the prevailing core instability model, giant planets begin their growth by the accumulation of small solid bodies, as do terrestrial planets. However, unlike terrestrial planets, the growing giant planet cores become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Models predict that rocky planets should form in orbit about most stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large enough to gravitationally trap substantial quantities of gas. Ongoing theoretical modeling of accretion of giant planet atmospheres, as well as observations of protoplanetary disks, will help decide this issue. Observations of extrasolar planets around main sequence stars can only provide a lower limit on giant planet formation frequency . This is because after giant planets form, gravitational interactions with material within the protoplanetary disk may cause them to migrat~ inwards and be lost to the central star. The core instability model can only produce planets greater than a few jovian masses within protoplanetary disks that are more viscous than most such disks are believed to be. Thus, few brown dwarves (objects massive enough to undergo substantial deuterium fusion, estimated to occur above approximately 13 jovian masses) are likely to be formed in this manner. Most brown dwarves, as well as an unknown number of free-floating objects of planetary mass, are probably formed as are stars, by the collapse of extended gas/dust clouds into more compact objects.

Lissauer, Jack J.↗
NASA NTRS2012

Masses, Radii, and Cloud Properties of the HR 8799 Planets

The near-infrared colors of the planets directly imaged around the A star HR 8799 are much redder than most field brown dwarfs of the same effective temperature. Previous theoretical studies of these objects have compared the photometric and limited spectral data of the planets to the predictions of various atmosphere and evolution models and concluded that the atmospheres of planets b, c, and d are unusually cloudy or have unusual cloud properties. Most studies have also found that the inferred radii of some or all of the planets disagree with expectations of standard giant planet evolution models. Here we compare the available data to the predictions of our own set of atmospheric and evolution models that have been extensively tested against field L and T dwarfs, including the reddest L dwarfs. Unlike almost all previous studies we specify mutually self-consistent choices for effective temperature, gravity, cloud properties, and planetary radius. This procedure yields plausible and self-consistent values for the masses, effective temperatures, and cloud properties of all three planets. We find that the cloud properties of the HR 8799 planets are in fact not unusual but rather follow previously recognized trends including a gravity dependence on the temperature of the L to T spectral transition, some reasons for which we discuss. We find that the inferred mass of planet b is highly sensitive to the H and K band spectrum. Solutions for planets c and particularly d are less certain but are consistent with the generally accepted constraints on the age of the primary star and orbital dynamics. We also confirm that as for L and T dwarfs and solar system giant planets, non-equilibrium chemistry driven by atmospheric mixing is also important for these objects. Given the preponderance of data suggesting that the L to T spectral type transition is gravity dependent, we present a new evolution calculation that predicts cooling tracks on the near-infrared color-magnitude diagram. Finally we argue that the range of uncertainty conventionally quoted for the bolometric luminosity of all three planets is too small.

Marley, Mark S.↗
NASA NTRS2017

Habitable Moist Atmospheres on Terrestrial Planets near the Inner Edge of the Habitable Zone Around M Dwarfs

Terrestrial planets in the habitable zones (HZs) of low-mass stars and cool dwarfs have received significant scrutiny recently. Transit spectroscopy of such planets with the James Webb Space Telescope (JWST) represents our best shot at obtaining the spectrum of a habitable planet within the next decade. As these planets are likely tidally locked, improved 3D numerical simulations of such planetary atmospheres are needed to guide target selection. Here we use a 3D climate system model, updated with new water-vapor absorption coefficients derived from the HITRAN 2012 database, to study ocean-covered planets at the inner edge of the HZ around late M to mid- K stars (2600 K less than or equal to T(sub eff) less than or equal to 4500 K). Our results indicate that these updated water-vapor coefficients result in significant warming compared to previous studies, so the inner HZ around M dwarfs is not as close as suggested by earlier work. Assuming synchronously rotating Earth-sized and Earth-mass planets with background 1 bar N2 atmospheres, we find that planets at the inner HZ of stars with T(sub eff) greater than 3000 K undergo the classical ''moist greenhouse'' (H2O mixing ratio greater than 10(exp -3) in the stratosphere) at significantly lower surface temperature (approx. 280 K) in our 3D model compared with 1D climate models (approx. 340 K). This implies that some planets around low-mass stars can simultaneously undergo water loss and remain habitable. However, for stars with T(sub eff) less than or equal to 3000 K, planets at the inner HZ may directly transition to a runaway state, while bypassing the moist greenhouse water loss entirely. We analyze transmission spectra of planets in a moist greenhouse regime and find that there are several prominent H2O features, including a broad feature between 5 and 8 micron, within JWST MIRI instrument range. Thus, relying only on standard Earth-analog spectra with 24 hr rotation period around M dwarfs for habitability studies will miss the strong H2O features that one would expect to see on synchronously rotating planets around M dwarf stars, with JWST.

Kopparapu, Ravi kumar↗
DOE OSTI2012

THE LAST STAGES OF TERRESTRIAL PLANET FORMATION: DYNAMICAL FRICTION AND THE LATE VENEER

The final stage of terrestrial planet formation consists of the clean-up of residual planetesimals after the giant impact phase. Dynamically, a residual planetesimal population is needed to damp the high eccentricities and inclinations of the terrestrial planets to circular and coplanar orbits after the giant impact stage. Geochemically, highly siderophile element (HSE) abundance patterns inferred for the terrestrial planets and the Moon suggest that a total of about 0.01 M{sub Circled-Plus} of chondritic material was delivered as 'late veneer' by planetesimals to the terrestrial planets after the end of giant impacts. Here, we combine these two independent lines of evidence for a leftover population of planetesimals and show that: (1) a residual population of small planetesimals containing 0.01 M{sub Circled-Plus} is able to damp the high eccentricities and inclinations of the terrestrial planets after giant impacts to their observed values. (2) At the same time, this planetesimal population can account for the observed relative amounts of late veneer added to the Earth, Moon, and Mars provided that the majority of the accreted late veneer was delivered by small planetesimals with radii {approx}< 10 m. These small planetesimal sizes are required to ensure efficient damping of the planetesimal's velocity dispersion by mutual collisions, which in turn ensures sufficiently low relative velocities between the terrestrial planets and the planetesimals such that the planets' accretion cross sections are significantly enhanced by gravitational focusing above their geometric values. Specifically, we find that, in the limit that the relative velocity between the terrestrial planets and the planetesimals is significantly less than the terrestrial planets' escape velocities, gravitational focusing yields a mass accretion ratio of Earth/Mars {approx}({rho}{sub Circled-Plus }/{rho}{sub mars})(R{sub Circled-Plus }/R{sub mars}){sup 4} {approx} 17, which agrees well with the mass accretion ratio inferred from HSEs of 12-23. For the Earth-Moon system, we find a mass accretion ratio of {approx}200, which, as we show, is consistent with estimates of 150-700 derived from HSE abundances that include the lunar crust as well as the mantle component. We conclude that small residual planetesimals containing about {approx}1% of the mass of the Earth could provide the dynamical friction needed to relax the terrestrial planet's eccentricities and inclinations after giant impacts, and also may have been the dominant source for the late veneer added to Earth, Moon, and Mars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Planetary populations in the mass-period diagram: A statistical treatment of exoplanet formation and the role of planet traps

The rapid growth of observed exoplanets has revealed the existence of several distinct planetary populations in the mass-period diagram. Two of the most surprising are (1) the concentration of gas giants around 1 AU and (2) the accumulation of a large number of low-mass planets with tight orbits, also known as super-Earths and hot Neptunes. We have recently shown that protoplanetary disks have multiple planet traps that are characterized by orbital radii in the disks and halt rapid type I planetary migration. By coupling planet traps with the standard core accretion scenario, we showed that one can account for the positions of planets in the mass-period diagram. In this paper, we demonstrate quantitatively that most gas giants formed at planet traps tend to end up around 1 AU, with most of these being contributed by dead zones and ice lines. We also show that a large fraction of super-Earths and hot Neptunes are formed as 'failed' cores of gas giants—this population being constituted by comparable contributions from dead zone and heat transition traps. Our results are based on the evolution of forming planets in an ensemble of disks where we vary only the lifetimes of disks and their mass accretion rates onto the host star. We show that a statistical treatment of the evolution of a large population of planetary cores caught in planet traps accounts for the existence of three distinct exoplanetary populations—the hot Jupiters, the more massive planets around r = 1 AU, and the short-period super-Earths and hot Neptunes. There are very few populations that feed into the large orbital radii characteristic of the imaged Jovian planet, which agrees with recent surveys. Finally, we find that low-mass planets in tight orbits become the dominant planetary population for low-mass stars (M {sub *} ≤ 0.7 M {sub ☉}).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Absence of a Metallicity Effect for Ultra-short-period Planets

Ultra-short-period (USP) planets are a newly recognized class of planets with periods shorter than one day and radii smaller than about 2 R {sub ⊕}. It has been proposed that USP planets are the solid cores of hot Jupiters that have lost their gaseous envelopes due to photo-evaporation or Roche lobe overflow. We test this hypothesis by asking whether USP planets are associated with metal-rich stars, as has long been observed for hot Jupiters. We find the metallicity distributions of USP-planet and hot-Jupiter hosts to be significantly different ( p = 3 × 10{sup −4}) based on Keck spectroscopy of Kepler stars. Evidently, the sample of USP planets is not dominated by the evaporated cores of hot Jupiters. The metallicity distribution of stars with USP planets is indistinguishable from that of stars with short-period planets with sizes between 2 and 4 R {sub ⊕}. Thus, it remains possible that the USP planets are the solid cores of formerly gaseous planets that are smaller than Neptune.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The Separation and Hα Contrasts of Massive Accreting Planets in the Gaps of Transitional Disks: Predicted Hα Protoplanet Yields for Adaptive Optics Surveys

We present a massive accreting gap planet model that ensures large gaps in transitional disks are kept dust free by the scattering action of three coplanar quasi-circular planets in a 1:2:4 mean motion resonance (MMR). This model uses the constraint of the observed gap size, and the dust-free nature of the gap, to determine within ∼10% the possible orbits for three massive planets in an MMR. Calculated orbits are consistent with the observed orbits and Hα emission (the brightest line to observe these planets) for LkCa 15 b, PDS 70 b, and PDS 70 c within observational errors. Moreover, the model suggests that the scarcity of detected Hα planets is likely a selection effect of the current limitations of non-coronagraphic, low (<10%) Strehl, Hα imaging with adaptive optics (AO) systems used in past Hα surveys. We predict that as higher Strehl AO systems (with high-performance custom coronagraphs; like the 6.5 m Magellan Telescope MagAO-X system) are utilized at Hα, the number of detected gap planets will substantially increase by more than tenfold. For example, we show that >25 ± 5 new Hα “gap planets” are potentially discoverable by a survey of the best 19 transitional disks with MagAO-X. Detections of these accreting protoplanets will significantly improve our understanding of planet formation, planet growth and accretion, solar system architectures, and planet–disk interactions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

High-resolution multi-band imaging for validation and characterization of small Kepler planets

High-resolution ground-based optical speckle and near-infrared adaptive optics images are taken to search for stars in close angular proximity to host stars of candidate planets identified by the NASA Kepler Mission. Neighboring stars are a potential source of false positive signals. These stars also blend into Kepler light curves, affecting estimated planet properties, and are important for an understanding of planets in multiple star systems. Deep images with high angular resolution help to validate candidate planets by excluding potential background eclipsing binaries as the source of the transit signals. A study of 18 Kepler Object of Interest stars hosting a total of 28 candidate and validated planets is presented. Validation levels are determined for 18 planets against the likelihood of a false positive from a background eclipsing binary. Most of these are validated at the 99% level or higher, including five newly validated planets in two systems: Kepler-430 and Kepler-431. The stellar properties of the candidate host stars are determined by supplementing existing literature values with new spectroscopic characterizations. Close neighbors of seven of these stars are examined using multi-wavelength photometry to determine their nature and influence on the candidate planet properties. Most of the close neighbors appear to be gravitationally bound secondaries, while a few are best explained as closely co-aligned field stars. Revised planet properties are derived for each candidate and validated planet, including cases where the close neighbors are the potential host stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

ON THE NATURE OF SMALL PLANETS AROUND THE COOLEST KEPLER STARS

We constrain the densities of Earth- to Neptune-size planets around very cool (T{sub e} = 3660-4660 K) Kepler stars by comparing 1202 Keck/HIRES radial velocity measurements of 150 nearby stars to a model based on Kepler candidate planet radii and a power-law mass-radius relation. Our analysis is based on the presumption that the planet populations around the two sets of stars are the same. The model can reproduce the observed distribution of radial velocity variation over a range of parameter values, but, for the expected level of Doppler systematic error, the highest Kolmogorov-Smirnov probabilities occur for a power-law index {alpha} Almost-Equal-To 4, indicating that rocky-metal planets dominate the planet population in this size range. A single population of gas-rich, low-density planets with {alpha} = 2 is ruled out unless our Doppler errors are {>=}5 m s{sup -1}, i.e., much larger than expected based on observations and stellar chromospheric emission. If small planets are a mix of {gamma} rocky planets ({alpha} = 3.85) and 1 - {gamma} gas-rich planets ({alpha} = 2), then {gamma} > 0.5 unless Doppler errors are {>=}4 m s{sup -1}. Our comparison also suggests that Kepler's detection efficiency relative to ideal calculations is less than unity. One possible source of incompleteness is target stars that are misclassified subgiants or giants, for which the transits of small planets would be impossible to detect. Our results are robust to systematic effects, and plausible errors in the estimated radii of Kepler stars have only moderate impact.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

STAR HOPPERS: PLANET INSTABILITY AND CAPTURE IN EVOLVING BINARY SYSTEMS

Many planets are observed in stellar binary systems, and their frequency may be comparable to that of planetary systems around single stars. Binary stellar evolution in such systems influences the dynamical evolution of the resident planets. Here, we study the evolution of a single planet orbiting one star in an evolving binary system. We find that stellar evolution can trigger dynamical instabilities that drive planets into chaotic orbits. This instability leads to planet-star collisions, exchange of the planet between the binary stars ('star hoppers'), and ejection of the planet from the system. The means by which planets can be recaptured is similar to the pull-down capture mechanism for irregular solar system satellites. Because planets often suffer close encounters with the primary on the asymptotic giant branch, captures during a collision with the stellar envelope are also possible for more massive planets. Such capture could populate the habitable zone around white dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

INTERACTIONS BETWEEN MODERATE- AND LONG-PERIOD GIANT PLANETS: SCATTERING EXPERIMENTS FOR SYSTEMS IN ISOLATION AND WITH STELLAR FLYBYS

The chance that a planetary system will interact with another member of its host star's nascent cluster would be greatly increased if gas giant planets form in situ on wide orbits. In this paper, we explore the outcomes of planet-planet scattering for a distribution of multi-planet systems that all have one of the planets on an initial orbit of 100 AU. The scattering experiments are run with and without stellar flybys. We convolve the outcomes with distributions for protoplanetary disk and stellar cluster sizes to generalize the results where possible. We find that the frequencies of large mutual inclinations and high eccentricities are sensitive to the number of planets in a system, but not strongly to stellar flybys. However, flybys do play a role in changing the low and moderate portions of the mutual inclination distributions, and erase dynamically cold initial conditions on average. Wide-orbit planets can be mixed throughout the planetary system, and in some cases, can potentially become hot Jupiters, which we demonstrate using scattering experiments that include a tidal damping model. If planets form in situ on wide orbits, then there will be discernible differences in the proper-motion distributions of a sample of wide-orbit planets compared with a pure scattering formation mechanism. Stellar flybys can enhance the frequency of ejections in planetary systems, but autoionization is likely to remain the dominant source of free-floating planets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

MASSES, RADII, AND CLOUD PROPERTIES OF THE HR 8799 PLANETS

The near-infrared colors of the planets directly imaged around the A star HR 8799 are much redder than most field brown dwarfs of the same effective temperature. Previous theoretical studies of these objects have concluded that the atmospheres of planets b, c, and d are unusually cloudy or have unusual cloud properties. Some studies have also found that the inferred radii of some or all of the planets disagree with expectations of standard giant planet evolution models. Here, we compare the available data to the predictions of our own set of atmospheric and evolution models that have been extensively tested against observations of field L and T dwarfs, including the reddest L dwarfs. Unlike some previous studies, we require mutually consistent choices for effective temperature, gravity, cloud properties, and planetary radius. This procedure thus yields plausible values for the masses, effective temperatures, and cloud properties of all three planets. We find that the cloud properties of the HR 8799 planets are not unusual but rather follow previously recognized trends, including a gravity dependence on the temperature of the L to T spectral transition-some reasons for which we discuss. We find that the inferred mass of planet b is highly sensitive to whether or not we include the H- and the K-band spectrum in our analysis. Solutions for planets c and d are consistent with the generally accepted constraints on the age of the primary star and orbital dynamics. We also confirm that, like in L and T dwarfs and solar system giant planets, non-equilibrium chemistry driven by atmospheric mixing is also important for these objects. Given the preponderance of data suggesting that the L to T spectral type transition is gravity dependent, we present an exploratory evolution calculation that accounts for this effect. Finally we recompute the bolometric luminosity of all three planets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

EXTRACTING PLANET MASS AND ECCENTRICITY FROM TTV DATA

Most planet pairs in the Kepler data that have measured transit time variations (TTVs) are near first-order mean-motion resonances. We derive analytical formulae for their TTV signals. We separate planet eccentricity into free and forced parts, where the forced part is purely due to the planets' proximity to resonance. This separation yields simple analytical formulae. The phase of the TTV depends sensitively on the presence of free eccentricity: if the free eccentricity vanishes, the TTV will be in phase with the longitude of conjunctions. This effect is easily detectable in current TTV data. The amplitude of the TTV depends on planet mass and free eccentricity, and it determines planet mass uniquely only when the free eccentricity is sufficiently small. We analyze the TTV signals of six short-period Kepler pairs. We find that three of these pairs (Kepler 18, 24, 25) have a TTV phase consistent with zero. The other three (Kepler 23, 28, 32) have small TTV phases, but ones that are distinctly non-zero. We deduce that the free eccentricities of the planets are small, {approx}< 0.01, but not always vanishing. Furthermore, as a consequence of this, we deduce that the true masses of the planets are fairly accurately determined by the TTV amplitudes, within a factor of {approx}< 2. The smallness of the free eccentricities suggests that the planets have experienced substantial dissipation. This is consistent with the hypothesis that the observed pile-up of Kepler pairs near mean-motion resonances is caused by resonant repulsion. But the fact that some of the planets have non-vanishing free eccentricity suggests that after resonant repulsion occurred there was a subsequent phase in the planets' evolution when their eccentricities were modestly excited, perhaps by interplanetary interactions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

OBJECTS IN KEPLER'S MIRROR MAY BE LARGER THAN THEY APPEAR: BIAS AND SELECTION EFFECTS IN TRANSITING PLANET SURVEYS

Statistical analyses of large surveys for transiting planets such as the Kepler mission must account for systematic errors and biases. Transit detection depends not only on the planet's radius and orbital period, but also on host star properties. Thus, a sample of stars with transiting planets may not accurately represent the target population. Moreover, targets are selected using criteria such as a limiting apparent magnitude. These selection effects, combined with uncertainties in stellar radius, lead to biases in the properties of transiting planets and their host stars. We quantify possible biases in the Kepler survey. First, Eddington bias produced by a steep planet radius distribution and uncertainties in stellar radius results in a 15%-20% overestimate of planet occurrence. Second, the magnitude limit of the Kepler target catalog induces Malmquist bias toward large, more luminous stars and underestimation of the radii of about one-third of candidate planets, especially those larger than Neptune. Third, because metal-poor stars are smaller, stars with detected planets will be very slightly (<0.02 dex) more metal-poor than the target average. Fourth, uncertainties in stellar radii produce correlated errors in planet radius and stellar irradiation. A previous finding, that highly irradiated giants are more likely to have 'inflated' radii, remains significant, even accounting for this effect. In contrast, transit depth is negatively correlated with stellar metallicity even in the absence of any intrinsic correlation, and a previous claim of a negative correlation between giant planet transit depth and stellar metallicity is probably an artifact.

79 ASTRONOMY AND ASTROPHYSICS↗