Daniel C. Fabrycky

Characteristics of planetary candidates observed by Kepler II : Analysis of the first four months of data

On 2011 February 1 the Kepler mission released data for 156,453 stars observed from the beginning of the science observations on 2009 May 2 through September 16. There are 1235 planetary candidates with transit-like signatures detected in this period. These are associated with 997 host stars. Distributions of the characteristics of the planetary candidates are separated into five class sizes: 68 candidates of approximately Earth-size (R_p < 1.25 R_⊕), 288 super-Earth-size (1.25 R_⊕ ≤ R_p < 2 R_⊕), 662 Neptune-size (2 R_⊕ ≤ R_p < 6 R_⊕), 165 Jupiter-size (6 R_⊕ ≤ R_p < 15 R_⊕), and 19 up to twice the size of Jupiter (15 R_⊕ ≤ R_p < 22 R_⊕). In the temperature range appropriate for the habitable zone, 54 candidates are found with sizes ranging from Earth-size to larger than that of Jupiter. Six are less than twice the size of the Earth. Over 74% of the planetary candidates are smaller than Neptune. The observed number versus size distribution of planetary candidates increases to a peak at two to three times the Earth-size and then declines inversely proportional to the area of the candidate. Our current best estimates of the intrinsic frequencies of planetary candidates, after correcting for geometric and sensitivity biases, are 5% for Earth-size candidates, 8% for super-Earth-size candidates, 18% for Neptune-size candidates, 2% for Jupiter-size candidates, and 0.1% for very large candidates; a total of 0.34 candidates per star. Multi-candidate, transiting systems are frequent; 17% of the host stars have multi-candidate systems, and 34% of all the candidates are part of multi-candidate systems.

Shrinking Binary and Planetary Orbits by Kozai Cycles with Tidal Friction

At least two arguments suggest that the orbits of a large fraction of binary stars and extrasolar planets shrank by 1-2 orders of magnitude after formation: (1) the physical radius of a star shrinks by a large factor from birth to the main sequence, yet many main-sequence stars have companions orbiting only a few stellar radii away, and (2) in current theories of planet formation, the region within ~0.1 AU of a protostar is too hot and rarefied for a Jupiter-mass planet to form, yet many hot Jupiters are observed at such distances. We investigate orbital shrinkage by the combined effects of secular perturbations from a distant companion star (Kozai oscillations) and tidal friction. We integrate the relevant equations of motion to predict the distribution of orbital elements produced by this process. Binary stars with orbital periods of 0.1-10 days, with a median of ~2 days, are produced from binaries with much longer periods (10 to ~105 days), consistent with observations indicating that most or all short-period binaries have distant companions (tertiaries). We also make two new testable predictions: (1) For periods between 3 and 10 days, the distribution of the mutual inclination between the inner binary and the tertiary orbit should peak strongly near 40? and 140?. (2) Extrasolar planets whose host stars have a distant binary companion may also undergo this process, in which case the orbit of the resulting hot Jupiter will typically be misaligned with the equator of its host star.

Planetary Candidates Observed by Kepler III: Analysis of the First 16 Months of Data

New transiting planet candidates are identified in 16 months (2009 May-2010 September) of data from the Kepler spacecraft. Nearly 5000 periodic transit-like signals are vetted against astrophysical and instrumental false positives yielding 1108 viable new planet candidates, bringing the total count up to over 2300. Improved vetting metrics are employed, contributing to higher catalog reliability. Most notable is the noise-weighted robust averaging of multi-quarter photo-center offsets derived from difference image analysis that identifies likely background eclipsing binaries. Twenty-two months of photometry are used for the purpose of characterizing each of the candidates. Ephemerides (transit epoch, T_0, and orbital period, P) are tabulated as well as the products of light curve modeling: reduced radius (R_P/R_★), reduced semimajor axis (d/R_★), and impact parameter (b). The largest fractional increases are seen for the smallest planet candidates (201% for candidates smaller than 2 R_⊕ compared to 53% for candidates larger than 2 R_⊕) and those at longer orbital periods (124% for candidates outside of 50 day orbits versus 86% for candidates inside of 50 day orbits). The gains are larger than expected from increasing the observing window from 13 months (Quarters 1-5) to 16 months (Quarters 1-6) even in regions of parameter space where one would have expected the previous catalogs to be complete. Analyses of planet frequencies based on previous catalogs will be affected by such incompleteness. The fraction of all planet candidate host stars with multiple candidates has grown from 17% to 20%, and the paucity of short-period giant planets in multiple systems is still evident. The progression toward smaller planets at longer orbital periods with each new catalog release suggests that Earth-size planets in the habitable zone are forthcoming if, indeed, such planets are abundant.

A closely packed system of low-mass, low-density planets transiting Kepler-11

When an extrasolar planet passes in front of (transits) its star, its radius can be measured from the decrease in starlight and its orbital period from the time between transits. Multiple planets transiting the same star reveal much more: period ratios determine stability and dynamics, mutual gravitational interactions reflect planet masses and orbital shapes, and the fraction of transiting planets observed as multiples has implications for the planarity of planetary systems. But few stars have more than one known transiting planet, and none has more than three. Here we report Kepler spacecraft observations of a single Sun-like star, which we call Kepler-11, that reveal six transiting planets, five with orbital periods between 10 and 47 days and a sixth planet with a longer period. The five inner planets are among the smallest for which mass and size have both been measured, and these measurements imply substantial envelopes of light gases. The degree of coplanarity and proximity of the planetary orbits imply energy dissipation near the end of planet formation.

KEPLER'S FIRST ROCKY PLANET: KEPLER-10b*

NASAs Kepler Mission uses transit photometry to determine the frequency of Earth-size planets in or near the habitable zone of Sun-like stars. The mission reached a milestone toward meeting that goal: the discovery of its first rocky planet, Kepler-10b. Two distinct sets of transit events were detected: (1) a 152 ± 4 ppm dimming lasting 1.811 ± 0.024 hr with ephemeris T [BJD] = 2454964.57375^(+0.00060)_(–0.00082) + N * 0.837495^(+0.000004)_(–0.000005) days and (2) a 376 ± 9 ppm dimming lasting 6.86 ± 0.07 hr with ephemeris T [BJD] = 2454971.6761^(+0.0020)_(–0.0023) + N * 45.29485^(+0.00065) _(–0.00076) days. Statistical tests on the photometric and pixel flux time series established the viability of the planet candidates triggering ground-based follow-up observations. Forty precision Doppler measurements were used to confirm that the short-period transit event is due to a planetary companion. The parent star is bright enough for asteroseismic analysis. Photometry was collected at 1 minute cadence for >4 months from which we detected 19 distinct pulsation frequencies. Modeling the frequencies resulted in precise knowledge of the fundamental stellar properties. Kepler-10 is a relatively old (11.9 ± 4.5 Gyr) but otherwise Sun-like main-sequence star with T_(eff) = 5627 ± 44 K, M_⋆ = 0.895 ± 0.060 M_⊙ , and R_⋆ = 1.056 ± 0.021 R_⊙. Physical models simultaneously fit to the transit light curves and the precision Doppler measurements yielded tight constraints on the properties of Kepler-10b that speak to its rocky composition: M_P = 4.56^9+1.17)_(–1.29) M_⊕, R_P = 1.416^(+0.033)_(–0.036) R_⊕, and ρ_P = 8.8^(+2.1)_(–2.9) g cm^(–3). Kepler-10b is the smallest transiting exoplanet discovered to date.

Kepler-16: a transiting circumbinary planet.

An exoplanet has been observed, comparable in size and mass to Saturn, that orbits a pair of stars. We report the detection of a planet whose orbit surrounds a pair of low-mass stars. Data from the Kepler spacecraft reveal transits of the planet across both stars, in addition to the mutual eclipses of the stars, giving precise constraints on the absolute dimensions of all three bodies. The planet is comparable to Saturn in mass and size and is on a nearly circular 229-day orbit around its two parent stars. The eclipsing stars are 20 and 69% as massive as the Sun and have an eccentric 41-day orbit. The motions of all three bodies are confined to within 0.5° of a single plane, suggesting that the planet formed within a circumbinary disk.

ARCHITECTURE AND DYNAMICS OF KEPLER'S CANDIDATE MULTIPLE TRANSITING PLANET SYSTEMS

About one-third of the ~1200 transiting planet candidates detected in the first four months of Kepler data are members of multiple candidate systems. There are 115 target stars with two candidate transiting planets, 45 with three, 8 with four, and 1 each with five and six. We characterize the dynamical properties of these candidate multi-planet systems. The distribution of observed period ratios shows that the vast majority of candidate pairs are neither in nor near low-order mean-motion resonances. Nonetheless, there are small but statistically significant excesses of candidate pairs both in resonance and spaced slightly too far apart to be in resonance, particularly near the 2:1 resonance. We find that virtually all candidate systems are stable, as tested by numerical integrations that assume a nominal mass-radius relationship. Several considerations strongly suggest that the vast majority of these multi-candidate systems are true planetary systems. Using the observed multiplicity frequencies, we find that a single population of planetary systems that matches the higher multiplicities underpredicts the number of singly transiting systems. We provide constraints on the true multiplicity and mutual inclination distribution of the multi-candidate systems, revealing a population of systems with multiple super-Earth-size and Neptune-size planets with low to moderate mutual inclinations.

Hot Stars with Hot Jupiters Have High Obliquities

We show that stars with transiting planets for which the stellar obliquity is large are preferentially hot (T_(eff) > 6250 K). This could explain why small obliquities were observed in the earliest measurements, which focused on relatively cool stars drawn from Doppler surveys, as opposed to hotter stars that emerged more recently from transit surveys. The observed trend could be due to differences in planet formation and migration around stars of varying mass. Alternatively, we speculate that hot-Jupiter systems begin with a wide range of obliquities, but the photospheres of cool stars realign with the orbits due to tidal dissipation in their convective zones, while hot stars cannot realign because of their thinner convective zones. This in turn would suggest that hot Jupiters originate from few-body gravitational dynamics and that disk migration plays at most a supporting role.

Architecture of Kepler's Multi-transiting Systems: II. New investigations with twice as many candidates

We report on the orbital architectures of Kepler systems having multiple-planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. (2013). These data show 899 transiting planet candidates in 365 multiple-planet systems and provide a powerful means to study the statistical properties of planetary systems. Using a generic mass–radius relationship, we find that only two pairs of planets in these candidate systems (out of 761 pairs total) appear to be on Hill-unstable orbits, indicating ~96% of the candidate planetary systems are correctly interpreted as true systems. We find that planet pairs show little statistical preference to be near mean-motion resonances. We identify an asymmetry in the distribution of period ratios near first-order resonances (e.g., 2:1, 3:2), with an excess of planet pairs lying wide of resonance and relatively few lying narrow of resonance. Finally, based upon the transit duration ratios of adjacent planets in each system, we find that the interior planet tends to have a smaller transit impact parameter than the exterior planet does. This finding suggests that the mode of the mutual inclinations of planetary orbital planes is in the range 1°.0–2°.2, for the packed systems of small planets probed by these observations.

Transiting circumbinary planets Kepler-34 b and Kepler-35 b

Most Sun-like stars in the Galaxy reside in gravitationally bound pairs of stars (binaries). Although long anticipated, the existence of a ‘circumbinary planet’ orbiting such a pair of normal stars was not definitively established until the discovery of the planet transiting (that is, passing in front of) Kepler-16. Questions remained, however, about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we report two additional transiting circumbinary planets: Kepler-34 (AB)b and Kepler-35 (AB)b, referred to here as Kepler-34 b and Kepler-35 b, respectively. Each is a low-density gas-giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 b orbits two Sun-like stars every 289 days, whereas Kepler-35 b orbits a pair of smaller stars (89% and 81% of the Sun’s mass) every 131 days. The planets experience large multi-periodic variations in incident stellar radiation arising from the orbital motion of the stars. The observed rate of circumbinary planets in our sample implies that more than ∼1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.