arXiv subjects

Sara Seager

Publications and source records attributed to Sara Seager.

At least 325 records · Page 18Linked to original sources

arXiv2011

The Optical and Near-Infrared Transmission Spectrum of the Super-Earth GJ1214b: Further Evidence for a Metal-Rich Atmosphere

We present an investigation of the transmission spectrum of the 6.5 M_earth planet GJ1214b based on new ground-based observations of transits of the planet in the optical and near-infrared, and on previously published data. Observations with the VLT+FORS and Magellan+MMIRS using the technique of multi-object spectroscopy with wide slits yielded new measurements of the planet's transmission spectrum from 0.61 to 0.85 micron, and in the J, H, and K atmospheric windows. We also present a new measurement based on narrow-band photometry centered at 2.09 micron with the VLT+HAWKI. We combined these data with results from a re-analysis of previously published FORS data from 0.78 to 1.00 micron using an improved data reduction algorithm, and previously reported values based on Spitzer data at 3.6 and 4.5 micron. All of the data are consistent with a featureless transmission spectrum for the planet. Our K-band data are inconsistent with the detection of spectral features at these wavelengths reported by Croll and collaborators at the level of 4.1 sigma. The planet's atmosphere must either have at least 70% water by mass or optically thick high-altitude clouds or haze to be consistent with the data.

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arXiv2011

The hot-Jupiter Kepler-17b: discovery, obliquity from stroboscopic starspots, and atmospheric characterization

This paper reports the discovery and characterization of the transiting hot giant exoplanet Kepler-17b. The planet has an orbital period of 1.486 days, and radial velocity measurements from the Hobby-Eberly Telescope (HET) show a Doppler signal of 420+/-15 m.s-1. From a transit-based estimate of the host star's mean density, combined with an estimate of the stellar effective temperature T_eff=5630+/-100 K from high-resolution spectra, we infer a stellar host mass of 1.061+/-0.067 M_sun and a stellar radius of 1.019+/-0.033 R_jup. We estimate the planet mass and radius to be Mp=2.450+/-0.114 M_jup and Rp=1.312+/-0.018 R_jup and a planet density near 1.35 g.cm-3. The host star is active, with dark spots that are frequently occulted by the planet. The continuous monitoring of the star reveals a stellar rotation period of 11.89 days, 8 times the the planet's orbital period; this period ratio produces stroboscopic effects on the occulted starspots. The temporal pattern of these spot-crossing events shows that the planet's orbit is prograde and the star's obliquity is smaller than 15 deg. We detected planetary occultations of Kepler-17b with both the Kepler and Spitzer Space Telescopes. We use these observations to constrain the eccentricity, e, and find that it is consistent with a circular orbit (e<0.0011). The brightness temperatures of the planet the infrared bandpasses are T_3.6um=1880+/-100 K and T4.5um=1770+/-150 K. We measure the optical geometric albedo A_g in the Kepler bandpass and find A_g = 0.10+/-0.02. The observations are best described by atmospheric models for which most of the incident energy is re-radiated away from the day side.

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arXiv2011

Kepler 18-b, c, and d: A System Of Three Planets Confirmed by Transit Timing Variations, Lightcurve Validation, Spitzer Photometry and Radial Velocity Measurements

We report the detection of three transiting planets around a Sunlike star, which we designate Kepler-18. The transit signals were detected in photometric data from the Kepler satellite, and were confirmed to arise from planets using a combination of large transit-timing variations, radial-velocity variations, Warm-Spitzer observations, and statistical analysis of false-positive probabilities. The Kepler-18 star has a mass of 0.97M_sun, radius 1.1R_sun, effective temperature 5345K, and iron abundance [Fe/H]= +0.19. The planets have orbital periods of approximately 3.5, 7.6 and 14.9 days. The innermost planet "b" is a "super-Earth" with mass 6.9 \pm 3.4M_earth, radius 2.00 \pm 0.10R_earth, and mean density 4.9 \pm 2.4 g cm^-3. The two outer planets "c" and "d" are both low-density Neptune-mass planets. Kepler-18c has a mass of 17.3 \pm 1.9M_earth, radius 5.49 \pm 0.26R_earth, and mean density 0.59 \pm 0.07 g cm^-3, while Kepler-18d has a mass of 16.4 \pm 1.4M_earth, radius 6.98 \pm 0.33R_earth, and mean density 0.27 \pm 0.03 g cm^-3. Kepler-18c and Kepler-18d have orbital periods near a 2:1 mean-motion resonance, leading to large and readily detected transit timing variations.

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arXiv2011

Discovery and Atmospheric Characterization of Giant Planet Kepler-12b: An Inflated Radius Outlier

We report the discovery of planet Kepler-12b (KOI-20), which at 1.695\pm0.030 RJ is among the handful of planets with super-inflated radii above 1.65 RJ. Orbiting its slightly evolved G0 host with a 4.438-day period, this 0.431\pm0.041 MJ planet is the least-irradiated within this largest-planet-radius group, which has important implications for planetary physics. The planet's inflated radius and low mass lead to a very low density of 0.111\pm0.010 g cm-3. We detect the occultation of the planet at a significance of 3.7σ in the Kepler bandpass. This yields a geometric albedo of 0.14\pm0.04; the planetary flux is due to a combination of scattered light and emitted thermal flux. We use multiple observations with Warm Spitzer to detect the occultation at 7σ and 4σ in the 3.6 and 4.5 μm bandpasses, respectively. The occultation photometry timing is consistent with a circular orbit, at e < 0.01 (1σ), and e < 0.09 (3σ). The occultation detections across the three bands favor an atmospheric model with no dayside temperature inversion. The Kepler occultation detection provides significant leverage, but conclusions regarding temperature structure are preliminary, given our ignorance of opacity sources at optical wavelengths in hot Jupiter atmospheres. If Kepler-12b and HD 209458b, which intercept similar incident stellar fluxes, have the same heavy element masses, the interior energy source needed to explain the large radius of Kepler-12b is three times larger than that of HD 209458b. This may suggest that more than one radius-inflation mechanism is at work for Kepler-12b, or that it is less heavy-element rich than other transiting planets.

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arXiv2011

Kepler-14b: A massive hot Jupiter transiting an F star in a close visual binary

We present the discovery of a hot Jupiter transiting an F star in a close visual (0.3" sky projected angular separation) binary system. The dilution of the host star's light by the nearly equal magnitude stellar companion (~ 0.5 magnitudes fainter) significantly affects the derived planetary parameters, and if left uncorrected, leads to an underestimate of the radius and mass of the planet by 10% and 60%, respectively. Other published exoplanets, which have not been observed with high-resolution imaging, could similarly have unresolved stellar companions and thus have incorrectly derived planetary parameters. Kepler-14b (KOI-98) has a period of P = 6.790 days and correcting for the dilution, has a mass of Mp = 8.40 +0.19-0.18 MJ and a radius of Rp = 1.136 +0.073-0.054 RJ, yielding a mean density of rho = 7.1 +- 1.1 g cm-3.

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arXiv2011

Formation and Structure of Low Density Exo-Neptunes

Kepler has found hundreds of Neptune-size (2-6 R_Earth) planet candidates within 0.5 AU of their stars. The nature of the vast majority of these planets is not known because their masses have not been measured. Using theoretical models of planet formation, evolution and structure, we explore the range of minimum plausible masses for low-density exo-Neptunes. We focus on highly irradiated planets with T_eq>=500K. We consider two separate formation pathways for low-mass planets with voluminous atmospheres of light gases: core nucleated accretion and outgassing of hydrogen from dissociated ices. We show that Neptune-size planets at T_eq=500K with masses as small as a few times that of Earth can plausibly be formed core nucleated accretion coupled with subsequent inward migration. We also derive a limiting low-density mass-radius relation for rocky planets with outgassed hydrogen envelopes but no surface water. Rocky planets with outgassed hydrogen envelopes typically have computed radii well below 3 R_Earth. For both planets with H/He envelopes from core nucleated accretion and planets with outgassed hydrogen envelopes, we employ planet interior models to map the range of planet mass--envelope mass--equilibrium temperature parameter space that is consistent with Neptune-size planet radii. Atmospheric mass loss mediates which corners of this parameter space are populated by actual planets and ultimately governs the minimum plausible mass at a specified transit radius. We find that Kepler's 2-6 R_Earth planet candidates at T_eq=500--1000K could potentially have masses less than ~4 M_Earth. Although our quantitative results depend on several assumptions, our qualitative finding that warm Neptune-size planets can have masses substantially smaller than those given by interpolating the masses and radii of planets within our Solar System is robust.

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arXiv2011

The high albedo of the hot Jupiter Kepler-7b

Hot Jupiters are expected to be dark from both observations (albedo upper limits) and theory (alkali metals and/or TiO and VO absorption). However, only a handful of hot Jupiters have been observed with high enough photometric precision at visible wavelengths to investigate these expectations. The NASA Kepler mission provides a means to widen the sample and to assess the extent to which hot Jupiter albedos are low. We present a global analysis of Kepler-7b based on Q0-Q4 data, published radial velocities, and asteroseismology constraints. We measure an occultation depth in the Kepler bandpass of 44+-5 ppm. If directly related to the albedo, this translates to a Kepler geometric albedo of 0.32+-0.03, the most precise value measured so far for an exoplanet. We also characterize the planetary orbital phase lightcurve with an amplitude of 42+-4 ppm. Using atmospheric models, we find it unlikely that the high albedo is due to a dominant thermal component and propose two solutions to explain the observed planetary flux. Firstly, we interpret the Kepler-7b albedo as resulting from an excess reflection over what can be explained solely by Rayleigh scattering, along with a nominal thermal component. This excess reflection might indicate the presence of a cloud or haze layer in the atmosphere, motivating new modeling and observational efforts. Alternatively, the albedo can be explained by Rayleigh scattering alone if Na and K are depleted in the atmosphere by a factor of 10-100 below solar abundances.

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arXiv2011

Possible thermochemical disequilibrium in the atmosphere of the exoplanet GJ 436b

The nearby extrasolar planet GJ 436b--which has been labelled as a 'hot Neptune'--reveals itself by the dimming of light as it crosses in front of and behind its parent star as seen from Earth. Respectively known as the primary transit and secondary eclipse, the former constrains the planet's radius and mass, and the latter constrains the planet's temperature and, with measurements at multiple wavelengths, its atmospheric composition. Previous work using transmission spectroscopy failed to detect the 1.4-μm water vapour band, leaving the planet's atmospheric composition poorly constrained. Here we report the detection of planetary thermal emission from the dayside of GJ 436b at multiple infrared wavelengths during the secondary eclipse. The best-fit compositional models contain a high CO abundance and a substantial methane (CH4) deficiency relative to thermochemical equilibrium models for the predicted hydrogen-dominated atmosphere. Moreover, we report the presence of some H2O and traces of CO2. Because CH4 is expected to be the dominant carbon-bearing species, disequilibrium processes such as vertical mixing and polymerization of methane into substances such as ethylene may be required to explain the hot Neptune's small CH4-to-CO ratio, which is at least 10^5 times smaller than predicted.

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arXiv2011

A Spitzer Transmission Spectrum for the Exoplanet GJ 436b, Evidence for Stellar Variability, and Constraints on Dayside Flux Variations

In this paper we describe a uniform analysis of eight transits and eleven secondary eclipses of the extrasolar planet GJ 436b obtained in the 3.6, 4.5, and 8.0 micron bands using the IRAC instrument on the Spitzer Space Telescope between UT 2007 June 29 and UT 2009 Feb 4. We find that the best-fit transit depths for visits in the same bandpass can vary by as much as 8% of the total (4.7 sigma significance) from one epoch to the next. Although we cannot entirely rule out residual detector effects or a time-varying, high-altitude cloud layer in the planet's atmosphere as the cause of these variations, we consider the occultation of active regions on the star in a subset of the transit observations to be the most likely explanation. We reconcile the presence of magnetically active regions with the lack of significant visible or infrared flux variations from the star by proposing that the star's spin axis is tilted with respect to our line of sight, and that the planet's orbit is therefore likely to be misaligned. These observations serve to illustrate the challenges associated with transmission spectroscopy of planets orbiting late-type stars; we expect that other systems, such as GJ 1214, may display comparably variable transit depths. Our measured 8 micron secondary eclipse depths are consistent with a constant value, and we place a 1 sigma upper limit of 17% on changes in the planet's dayside flux in this band. Averaging over the eleven visits gives us an improved estimate of 0.0452% +/- 0.0027% for the secondary eclipse depth. We combine timing information from our observations with previously published data to produce a refined orbital ephemeris, and determine that the best-fit transit and eclipse times are consistent with a constant orbital period. [ABRIDGED]

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arXiv2011

Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler

We report the distribution of planets as a function of planet radius (R_p), orbital period (P), and stellar effective temperature (Teff) for P < 50 day orbits around GK stars. These results are based on the 1,235 planets (formally "planet candidates") from the Kepler mission that include a nearly complete set of detected planets as small as 2 Earth radii (Re). For each of the 156,000 target stars we assess the detectability of planets as a function of R_p and P. We also correct for the geometric probability of transit, R*/a. We consider first stars within the "solar subset" having Teff = 4100-6100 K, logg = 4.0-4.9, and Kepler magnitude Kp < 15 mag. We include only those stars having noise low enough to permit detection of planets down to 2 Re. We count planets in small domains of R_p and P and divide by the included target stars to calculate planet occurrence in each domain. Occurrence of planets varies by more than three orders of magnitude and increases substantially down to the smallest radius (2 Re) and out to the longest orbital period (50 days, ~0.25 AU) in our study. For P < 50 days, the radius distribution is given by a power law, df/dlogR= k R^α. This rapid increase in planet occurrence with decreasing planet size agrees with core-accretion, but disagrees with population synthesis models. We fit occurrence as a function of P to a power law model with an exponential cutoff below a critical period P_0. For smaller planets, P_0 has larger values, suggesting that the "parking distance" for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over Teff = 3600-7100 K, spanning M0 to F2 dwarfs. The occurrence of 2-4 Re planets in the Kepler field increases with decreasing Teff, making these small planets seven times more abundant around cool stars than the hottest stars in our sample. [abridged]

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arXiv2011

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

On 1 February 2011 the Kepler Mission released data for 156,453 stars observed from the beginning of the science observations on 2 May through 16 September 2009. 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 (radius < 1.25 Earth radii), 288 super-Earth size (1.25 Earth radii < radius < 2 Earth radii), 662 Neptune-size (2 Earth radii < radius < 6 Earth radii), 165 Jupiter-size (6 Earth radii < radius < 15 Earth radii), and 19 up to twice the size of Jupiter (15 Earth radii < radius < 22 Earth radii). 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. Five 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 Earth-size and then declines inversely proportional to area of the candidate. Our current best estimates of the intrinsic frequencies of planetary candidates, after correcting for geometric and sensitivity biases, are 6% for Earth-size candidates, 7% for super-Earth size candidates, 17% for Neptune-size candidates, and 4% for Jupiter-size candidates. Multi-candidate, transiting systems are frequent; 17% of the host stars have multi-candidate systems, and 33.9% of all the candidates are part of multi-candidate systems.

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arXiv2011

A Search for Additional Planets in Five of the Exoplanetary Systems Studied by the NASA EPOXI Mission

We present time series photometry and constraints on additional planets in five of the exoplanetary systems studied by the EPOCh (Extrasolar Planet Observation and Characterization) component of the NASA EPOXI mission: HAT-P-4, TrES-3, TrES-2, WASP-3, and HAT-P-7. We conduct a search of the high-precision time series for photometric transits of additional planets. We find no candidate transits with significance higher than our detection limit. From Monte Carlo tests of the time series using putative periods from 0.5 days to 7 days, we demonstrate the sensitivity to detect Neptune-sized companions around TrES-2, sub-Saturn-sized companions in the HAT-P-4, TrES-3, and WASP-3 systems, and Saturn-sized companions around HAT-P-7. We investigate in particular our sensitivity to additional transits in the dynamically favorable 3:2 and 2:1 exterior resonances with the known exoplanets: if we assume coplanar orbits with the known planets, then companions in these resonances with HAT-P-4b, WASP-3b, and HAT-P-7b would be expected to transit, and we can set lower limits on the radii of companions in these systems. In the nearly grazing exoplanetary systems TrES-3 and TrES-2, additional coplanar planets in these resonances are not expected to transit. However, we place lower limits on the radii of companions that would transit if the orbits were misaligned by 2.0 degrees and 1.4 degrees for TrES-3 and TrES-2, respectively.

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arXiv2011

Rotational Variability of Earth's Polar Regions: Implications for Detecting Snowball Planets

We have obtained the first time-resolved, disc-integrated observations of Earth's poles with the Deep Impact spacecraft as part of the EPOXI Mission of Opportunity. These data mimic what we will see when we point next-generation space telescopes at nearby exoplanets. We use principal component analysis (PCA) and rotational lightcurve inversion to characterize color inhomogeneities and map their spatial distribution from these unusual vantage points, as a complement to the equatorial views presented in Cowan et al. (2009). We also perform the same PCA on a suite of simulated rotational multi-band lightcurves from NASA's Virtual Planetary Laboratory 3D spectral Earth model. This numerical experiment allows us to understand what sorts of surface features PCA can robustly identify. We find that the EPOXI polar observations have similar broadband colors as the equatorial Earth, but with 20-30% greater apparent albedo. This is because the polar observations are most sensitive to mid-latitudes, which tend to be more cloudy than the equatorial latitudes emphasized by the original EPOXI Earth observations. The cloudiness of the mid-latitudes also manifests itself in the form of increased variability at short wavelengths in the polar observations, and as a dominant gray eigencolor in the south polar observation. We construct a simple reflectance model for a snowball Earth. By construction, our model has a higher Bond albedo than the modern Earth; its surface albedo is so high that Rayleigh scattering does not noticeably affect its spectrum. The rotational color variations occur at short wavelengths due to the large contrast between glacier ice and bare land in those wavebands. Thus we find that both the broadband colors and diurnal color variations of such a planet would be easily distinguishable from the modern-day Earth, regardless of viewing angle.

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arXiv2011

KEPLER's First Rocky Planet: Kepler-10b

NASA's 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 hours with ephemeris T[BJD]=2454964.57375+N*0.837495 days and 2) a 376 +/- 9 ppm dimming lasting 6.86 +/- 0.07 hours with ephemeris T[BJD]=2454971.6761+N*45.29485 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 Teff=5627 +/- 44 K, Mstar=0.895 +/- 0.060 Msun, and Rstar=1.056 +/- 0.021 Rsun. 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: Mpl=4.56 +/- 1.29 Mearth, Rpl=1.416 +/- 0.036 Rearth, and density=8.8 +/- 2.9 gcc. Kepler-10b is the smallest transiting exoplanet discovered to date.

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arXiv2011

The atmospheres of the hot-Jupiters Kepler-5b and Kepler-6b observed during occultations with Warm-Spitzer and Kepler

This paper reports the detection and the measurements of occultations of the two transiting hot giant exoplanets Kepler-5b and Kepler-6b by their parent stars. The observations are obtained in the near infrared with Spitzer Space Telescope and at optical wavelengths by combining more than a year of Kepler photometry. The investigation consists of constraining the eccentricities of these systems and of obtaining broad band emergent spectra for individual planets. For both targets, the occultations are detected at 3 sigma level at each wavelength with mid-occultation times consistent with circular orbits. The brightness temperatures of these planets are deduced from the infrared observations and reach T=1930+/-100K and T=1660+/-120K for Kepler-5b and Kepler-6b respectively. We measure optical geometric albedos A_g in the Kepler bandpass and find A_g=0.12+/-0.04 for Kepler-5b and A_g=0.11+/-0.04 for Kepler-6b leading to an upper limit for the Bond albedo of A_B < 0.17 in both cases. The observations for both planets are best described by models for which most of the incident energy is redistributed on the dayside, with only less than 10% of the absorbed stellar flux redistributed to the night side of these planets. The data for Kepler-5b favor a model without a temperature inversion, whereas for Kepler-6b they do not allow distinguishing between models with and without inversion.

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arXiv2011

Kepler Eclipsing Binary Stars. I. Catalog and Principal Characterization of 1879 Eclipsing Binaries in the First Data Release

The Kepler space mission is devoted to finding Earth-size planets in habitable zones orbiting other stars. Its large, 105-deg field-of-view features over 156,000 stars that are observed continuously to detect and characterize planet transits. Yet this high-precision instrument holds great promise for other types of objects as well. Here we present a comprehensive catalog of eclipsing binary stars observed by Kepler in the first 44 days of operation, the data which are publicly available through MAST as of 6/15/2010. The catalog contains 1879 unique objects. For each object we provide its Kepler ID (KID), ephemeris (BJD0, P0), morphology type, physical parameters (Teff, log g, E(B-V), crowding), and principal parameters (T2/T1, q, fillout factor and sin i for overcontacts, and T2/T1, (R1+R2)/a, e sin(w), e cos(w), and sin i for detached binaries). We present statistics based on the determined periods and measure an average occurence rate of eclipsing binaries to be ~1.2% across the Kepler field. We further discuss the distribution of binaries as function of galactic latitude, and thoroughly explain the application of artificial intelligence to obtain principal parameters in a matter of seconds for the whole sample. The catalog was envisioned to serve as a bridge between the now public Kepler data and the scientific community interested in eclipsing binary stars.

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arXiv2010

Transit Timing Variation Analysis of OGLE-TR-132b with Seven New Transits

We report the results of the first transit timing variation (TTV) analysis of the very hot Jupiter OGLE-TR-132b, using ten transits collected over a seven-year period. Our analysis combines three previously published transit light curves with seven new transits, which were observed between February 2008 and May 2009 with the new MagIC-e2V instrument on the Magellan Telescopes in Chile. We provide a revised planetary radius of R_p = 1.23+/-0.07 R_J, which is slightly larger than, but consistent within the errors, of the previously published results. Analysis of the planet-to-star radius ratio, orbital separation, inclination and transit duration reveals no apparent variation in any of those parameters during the time span observed. We also find no sign of transit timing variations larger than -108+/-49 s, with most residuals very close to zero. This allows us to place an upper limit of 5-10 M_Earth for a coplanar, low-eccentricity perturber in either the 2:1 or 3:2 mean-motion resonance with OGLE-TR-132b. We similarly find that the data are entirely consistent with a constant orbital period and there is no evidence for orbital decay within the limits of precision of our data.

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arXiv2010

Five Kepler target stars that show multiple transiting exoplanet candidates

We present and discuss five candidate exoplanetary systems identified with the Kepler spacecraft. These five systems show transits from multiple exoplanet candidates. Should these objects prove to be planetary in nature, then these five systems open new opportunities for the field of exoplanets and provide new insights into the formation and dynamical evolution of planetary systems. We discuss the methods used to identify multiple transiting objects from the Kepler photometry as well as the false-positive rejection methods that have been applied to these data. One system shows transits from three distinct objects while the remaining four systems show transits from two objects. Three systems have planet candidates that are near mean motion commensurabilities---two near 2:1 and one just outside 5:2. We discuss the implications that multitransiting systems have on the distribution of orbital inclinations in planetary systems, and hence their dynamical histories; as well as their likely masses and chemical compositions. A Monte Carlo study indicates that, with additional data, most of these systems should exhibit detectable transit timing variations (TTV) due to gravitational interactions---though none are apparent in these data. We also discuss new challenges that arise in TTV analyses due to the presence of more than two planets in a system.

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