arXiv subjects

Samuel N. Quinn

Publications and source records attributed to Samuel N. Quinn.

At least 163 records · Page 9Linked to original sources

arXiv2017

Zodiacal Exoplanets in Time (ZEIT) VI: a three-planet system in the Hyades cluster including an Earth-sized planet

Planets in young clusters are powerful probes of the evolution of planetary systems. Here we report the discovery of three planets transiting K2-136 (EPIC 247589423), a late K dwarf in the Hyades (~800 Myr) cluster, and robust detection limits for additional planets in the system. The planets were identified from their K2 light curves, as part of our survey of young clusters and star forming regions. The smallest planet has a radius comparable to Earth (0.99 +/- 0.05 Earth radii), making it one of the few Earth-sized planets with a known, young age. The two larger planets are likely a mini-Neptune and a super-Earth, with radii of 2.91+/-0.11 and 1.45+/-0.10 Earth radii, respectively. The predicted radial velocity signals from these planets are between 0.4 and 2 m/s, achievable with modern precision RV spectrographs. Because the target star is bright (V=11.2) and has relatively low-amplitude stellar variability for a young star (2-6 mmag), EPIC 247589423 hosts the best planets known in a young open cluster for precise radial velocity follow-up, enabling a robust test of earlier claims that young planets are less dense than their older counterparts.

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arXiv2017

KELT-20b: A giant planet with a period of P~ 3.5 days transiting the V~ 7.6 early A star HD 185603

We report the discovery of KELT-20b, a hot Jupiter transiting a V~7.6 early A star with an orbital period of P~3.47 days. We identified the initial transit signal in KELT-North survey data. Archival and follow-up photometry, the Gaia parallax, radial velocities, Doppler tomography, and adaptive optics imaging were used to confirm the planetary nature of the companion and characterize the system. From global modeling we infer that the host star HD 185603 is a rapidly-rotating (VsinI~120 km/s) A2V star with an effective temperature of $T_{eff}$=8730K, mass of $M_{star}=1.76M_{sun}$, radius of $R_{star}=1.561R_{sun}$, surface gravity of logg=4.292, and age of <600 Myr. The planetary companion has a radius of $1.735^{+0.070}_{-0.075}~R_{J}$, a semimajor axis of $a=0.0542^{+0.0014}_{-0.0021}$AU, and a linear ephemeris of $BJD_{TDB}=2457503.120049 \pm 0.000190 + E(3.4741070\pm0.0000019)$. We place a $3σ$ upper limit of ~3.5 $M_{J}$ on the mass of the planet. The Doppler tomographic measurement indicates that the planetary orbit is well aligned with the projected spin-axis of the star ($λ= 3.4\pm {2.1}$ degrees). The inclination of the star is constrained to be $24.4<I_*<155.6$ degrees, implying a true (three-dimensional) spin-orbit alignment of $1.3<ψ<69.8$ degrees. The planet receives an insolation flux of $\sim 8\times 10^9~{\rm erg~s^{-1}~cm^{-2}}$, implying an equilibrium temperature of of ~ 2250 K, assuming zero albedo and complete heat redistribution. Due to the high stellar $T_{eff}$, the planet also receives an ultraviolet (wavelengths $d\le 91.2$~nm) insolation flux of $\sim 9.1\times 10^4~{\rm erg~s^{-1}~cm^{-2}}$, which may lead to significant ablation of the planetary atmosphere. Together with WASP-33, Kepler-13 A, HAT-P-57, KELT-17, and KELT-9, KELT-20 is the sixth A star host of a transiting giant planet, and the third-brightest host (in V) of a transiting planet.

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arXiv2017

A Bright Short Period M-M Eclipsing Binary from the KELT Survey: Magnetic Activity and the Mass-Radius Relationship for M-dwarfs

We report the discovery of KELT J041621-620046, a moderately bright (J$\sim$10.2) M dwarf eclipsing binary system at a distance of 39$\pm$3 pc. KELT J041621-620046 was first identified as an eclipsing binary using observations from the Kilodegree Extremely Little Telescope (KELT) survey. The system has a short orbital period of $\sim$1.11 days and consists of components with M$_1$ = $0.447^{-0.047}_{+0.052}\,M_\odot$ and M$_2$ = $0.399^{-0.042}_{+0.046}\,M_\odot$ in nearly circular orbits. The radii of the two stars are R$_1$ = $0.540^{-0.032}_{+0.034}\,R_\odot$ and R$_2$ = $0.453\pm0.017\,R_\odot$. Full system and orbital properties were determined (to $\sim$10% error) by conducting an EBOP global modeling of the high precision photometric and spectroscopic observations obtained by the KELT Follow-up Network. Each star is larger by 17-28% and cooler by 4-10% than predicted by standard (non-magnetic) stellar models. Strong H$α$ emission indicates chromospheric activity in both stars. The observed radii and temperature discrepancies for both components are more consistent with those predicted by empirical relations that account for convective suppression due to magnetic activity.

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arXiv2016

Obliquities of Exoplanet Host Stars from Precise Distances and Stellar Angular Diameters

The next generation of exoplanet space photometry missions proposed by both NASA and ESA promise to discover small transiting planets around the nearest and brightest main-sequence stars. The physical and rotational properties of these stars, in conjunction with Gaia-precision distances, can be used to determine the inclination of the stellar rotation axis. Given edge-on orbital paths for transiting planets, stellar inclinations can be interpreted as obliquities projected into the line of sight, which can be used to more clearly reveal the system architectures of small planets and the factors that drive their orbital evolution. To demonstrate the method, we use a sample of simulated target stars for the NASA Transiting Exoplanet Survey Satellite (TESS) mission. Based on predicted characteristics of these stars and likely measurement uncertainties, we show that the expected TESS discoveries will allow us to finely differentiate the true underlying obliquity distribution. Under conservative assumptions in our illustrative example--in which the true distribution is assumed to contain systems drawn from both well-aligned and isotropic distributions (e.g., due to multiple migration channels)--the correct fractions can be determined to within $0.15$, thus enabling constraints on the evolutionary processes that shape system architectures. Moreover, because of the excellent astrometric precision expected from Gaia, this technique will also be applicable to the large number of planets already discovered by ${\textit Kepler}$ orbiting much more distant stars.

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arXiv2016

Kepler-1647b: the largest and longest-period Kepler transiting circumbinary planet

We report the discovery of a new Kepler transiting circumbinary planet (CBP). This latest addition to the still-small family of CBPs defies the current trend of known short-period planets orbiting near the stability limit of binary stars. Unlike the previous discoveries, the planet revolving around the eclipsing binary system Kepler-1647 has a very long orbital period (~1100 days) and was at conjunction only twice during the Kepler mission lifetime. Due to the singular configuration of the system, Kepler-1647b is not only the longest-period transiting CBP at the time of writing, but also one of the longest-period transiting planets. With a radius of 1.06+/-0.01 RJup it is also the largest CBP to date. The planet produced three transits in the light-curve of Kepler-1647 (one of them during an eclipse, creating a syzygy) and measurably perturbed the times of the stellar eclipses, allowing us to measure its mass to be 1.52+/-0.65 MJup. The planet revolves around an 11-day period eclipsing binary consisting of two Solar-mass stars on a slightly inclined, mildly eccentric (e_bin = 0.16), spin-synchronized orbit. Despite having an orbital period three times longer than Earth's, Kepler-1647b is in the conservative habitable zone of the binary star throughout its orbit.

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arXiv2015

HST/COS Detection of the Spectrum of the Subdwarf Companion of KOI-81

KOI-81 is a totally eclipsing binary discovered by the Kepler mission that consists of a rapidly rotating B-type star and a small, hot companion. The system was forged through large scale mass transfer that stripped the mass donor of its envelope and spun up the mass gainer star. We present an analysis of UV spectra of KOI-81 that were obtained with the Cosmic Origins Spectrograph on the Hubble Space Telescope that reveal for the first time the spectral features of the faint, hot companion. We present a double-lined spectroscopic orbit for the system that yields mass estimates of 2.92 M_sun and 0.19 M_sun for the B-star and hot subdwarf, respectively. We used a Doppler tomography algorithm to reconstruct the UV spectra of the components, and a comparison of the reconstructed and model spectra yields effective temperatures of 12 kK and 19 - 27 kK for the B-star and hot companion, respectively. The B-star is pulsating, and we identified a number of peaks in the Fourier transform of the light curve, including one that may indicate an equatorial rotation period of 11.5~hours. The B-star has an equatorial velocity that is 74% of the critical velocity where centrifugal and gravitational accelerations balance at the equator, and we fit the transit light curve by calculating a rotationally distorted model for the photosphere of the B-star.

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arXiv2015

Kepler-432: a red giant interacting with one of its two long period giant planets

We report the discovery of Kepler-432b, a giant planet ($M_b = 5.41^{+0.32}_{-0.18} M_{\rm Jup}, R_b = 1.145^{+0.036}_{-0.039} R_{\rm Jup}$) transiting an evolved star $(M_\star = 1.32^{+0.10}_{-0.07} M_\odot, R_\star = 4.06^{+0.12}_{-0.08} R_\odot)$ with an orbital period of $P_b = 52.501129^{+0.000067}_{-0.000053}$ days. Radial velocities (RVs) reveal that Kepler-432b orbits its parent star with an eccentricity of $e = 0.5134^{+0.0098}_{-0.0089}$, which we also measure independently with asterodensity profiling (AP; $e=0.507^{+0.039}_{-0.114}$), thereby confirming the validity of AP on this particular evolved star. The well-determined planetary properties and unusually large mass also make this planet an important benchmark for theoretical models of super-Jupiter formation. Long-term RV monitoring detected the presence of a non-transiting outer planet (Kepler-432c; $M_c \sin{i_c} = 2.43^{+0.22}_{-0.24} M_{\rm Jup}, P_c = 406.2^{+3.9}_{-2.5}$ days), and adaptive optics imaging revealed a nearby (0\farcs87), faint companion (Kepler-432B) that is a physically bound M dwarf. The host star exhibits high signal-to-noise asteroseismic oscillations, which enable precise measurements of the stellar mass, radius and age. Analysis of the rotational splitting of the oscillation modes additionally reveals the stellar spin axis to be nearly edge-on, which suggests that the stellar spin is likely well-aligned with the orbit of the transiting planet. Despite its long period, the obliquity of the 52.5-day orbit may have been shaped by star-planet interaction in a manner similar to hot Jupiter systems, and we present observational and theoretical evidence to support this scenario. Finally, as a short-period outlier among giant planets orbiting giant stars, study of Kepler-432b may help explain the distribution of massive planets orbiting giant stars interior to 1 AU.

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arXiv2015

A 3D Search for Companions to 12 Nearby M-Dwarfs

We present a carefully vetted equatorial ($\pm$ 30$^\circ$ Decl.) sample of all known single (within 4'') mid M-dwarfs (M2.5V-M8.0V) extending out to 10 pc; their proximity and low masses make them ideal targets for planet searches. For this sample of 58 stars, we provide V$_J$, R$_{KC}$, I$_{KC}$ photometry, new low dispersion optical ($6000 - 9000$Å) spectra from which uniform spectral types are determined, multi-epoch H$α$ equivalent widths, and gravity sensitive $Na\,I$ indices. For 12 of these 58 stars, strict limits are placed on the presence of stellar and sub-stellar companions, based on a pioneering program described here that utilizes precise infrared radial velocities and optical astrometric measurements in an effort to search for Jupiter-mass, brown dwarf and stellar-mass companions. Our infrared radial velocity precision using CSHELL at NASA's IRTF is $\sim$90 m s$^{-1}$ over timescales from 13 days to 5 years. With our spectroscopic results the mean companion masses that we rule out of existence are 1.5 M$_{JUP}$ or greater in 10 day orbital periods and 7 M$_{JUP}$ or greater in 100 day orbital periods. We use these spectra to determine rotational velocities and absolute radial velocities of these twelve stars. Our mean astrometric precision using RECONS data from 0.9-m telescope at Cerro Tololo Inter-American Observatory is $\sim$3 milli-arcseconds over baselines ranging from 9 to 13 years. With our astrometric results the mean companion masses that we rule out of existence are greater than 11.5 M$_{JUP}$ with an orbital period of 4 years and greater than 7.5 M$_{JUP}$ with an orbital period of 8 years. Although we do not detect companions around our sub-sample of 12 stars, we demonstrate that our two techniques probe a regime that is commonly missed in other companion searches of late type stars.

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arXiv2014

KIC 9632895 - The 10th Kepler Transiting Circumbinary Planet

We present the discovery of KIC 9632895b, a 6.2 Earth-radius planet in a low-eccentricity, 240.5-day orbit about an eclipsing binary. The binary itself consists of a 0.93 and 0.194 solar mass pair of stars with an orbital period of 27.3 days. The plane of the planet's orbit is rapidly precessing, and its inclination only becomes sufficiently aligned with the primary star in the latter portion of the Kepler data. Thus three transits are present in the latter half of the light curve, but none of the three conjunctions that occurred during the first half of the light curve produced transits. The precession period is ~103 years, and during that cycle, transits are visible only ~8% of the time. This has the important implication that for every system like KIC 9632895 that we detect, there are ~12 circumbinary systems that exist but are not currently exhibiting transits. The planet's mass is too small to noticeably perturb the binary, consequently its mass is not measurable with these data; but our photodynamical model places a 1-sigma upper limit of 16 Earth masses. With a period 8.8 times that of the binary, the planet is well outside the dynamical instability zone. It does, however, lie within the habitable zone of the binary, and making it the third of ten Kepler circumbinary planets to do so.

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arXiv2014

The Solar Neighborhood. XXXIV. A Search for Planets Orbiting Nearby M Dwarfs using Astrometry

Astrometric measurements are presented for seven nearby stars with previously detected planets: six M dwarfs (GJ 317, GJ 667C, GJ 581, GJ 849, GJ 876, and GJ 1214) and one K dwarf (BD $-$10 3166). Measurements are also presented for six additional nearby M dwarfs without known planets, but which are more favorable to astrometric detections of low mass companions, as well as three binary systems for which we provide astrometric orbit solutions. Observations have baselines of three to thirteen years, and were made as part of the RECONS long-term astrometry and photometry program at the CTIO/SMARTS 0.9m telescope. We provide trigonometric parallaxes and proper motions for all 16 systems, and perform an extensive analysis of the astrometric residuals to determine the minimum detectable companion mass for the 12 M dwarfs not having close stellar secondaries. For the six M dwarfs with known planets, we are not sensitive to planets, but can rule out the presence of all but the least massive brown dwarfs at periods of 2 - 12 years. For the six more astrometrically favorable M dwarfs, we conclude that none have brown dwarf companions, and are sensitive to companions with masses as low as 1 $M_{Jup}$ for periods longer than two years. In particular, we conclude that Proxima Centauri has no Jovian companions at orbital periods of 2 - 12 years. These results complement previously published M dwarf planet occurrence rates by providing astrometrically determined upper mass limits on potential super-Jupiter companions at orbits of two years and longer. As part of a continuing survey, these results are consistent with the paucity of super-Jupiter and brown dwarf companions we find among the over 250 red dwarfs within 25 pc observed longer than five years in our astrometric program.

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arXiv2014

Stellar rotational periods in the planet hosting open cluster Praesepe

By using the dense coverage of the extrasolar planet survey project HATNet, we Fourier analyze 381 high-probability members of the nearby open cluster Praesepe (Beehive/M44/NGC 2632). In addition to the detection of 10 variables (of δScuti and other types), we identify 180 rotational variables (including the two known planet hosts). This sample increases the number of known rotational variables in this cluster for spectral classes earlier than M by more than a factor of three. These stars closely follow a color/magnitude -- period relation from early F to late K stars. We approximate this relation by polynomials for an easier reference to the rotational characteristics in different colors. The total (peak-to-peak) amplitudes of the large majority (94%) of these variables span the range of 0.005 to 0.04 mag. The periods cover a range from 2.5 to 15 days. These data strongly confirm that Praesepe and the Hyades have the same gyrochronological ages. Regarding the two planet hosts, Pr0211 (the one with the shorter orbital period) has a rotational period that is ~2 days shorter than the one expected from the main rotational pattern in this cluster. This, together with other examples discussed in the paper, may hint that star-planet interaction via tidal dissipation can be significant in some cases in the rotational evolution of stars hosting Hot Jupiters.

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arXiv2014

Masses, Radii, and Orbits of Small Kepler Planets: The Transition from Gaseous to Rocky Planets

We report on the masses, sizes, and orbits of the planets orbiting 22 Kepler stars. There are 49 planet candidates around these stars, including 42 detected through transits and 7 revealed by precise Doppler measurements of the host stars. Based on an analysis of the Kepler brightness measurements, along with high-resolution imaging and spectroscopy, Doppler spectroscopy, and (for 11 stars) asteroseismology, we establish low false-positive probabilities for all of the transiting planets (41 of 42 have a false-positive probability under 1%), and we constrain their sizes and masses. Most of the transiting planets are smaller than 3X the size of Earth. For 16 planets, the Doppler signal was securely detected, providing a direct measurement of the planet's mass. For the other 26 planets we provide either marginal mass measurements or upper limits to their masses and densities; in many cases we can rule out a rocky composition. We identify 6 planets with densities above 5 g/cc, suggesting a mostly rocky interior for them. Indeed, the only planets that are compatible with a purely rocky composition are smaller than ~2 R_earth. Larger planets evidently contain a larger fraction of low-density material (H, He, and H2O).

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arXiv2013

The Closest M-Dwarf Quadruple System to the Sun

We report new infrared radial velocity measurements obtained with CSHELL at NASA's Infrared Telescope Facility that reveal the M3.5 dwarf GJ 867B to be a single-lined spectroscopic binary with a period of 1.795 $\pm$ 0.017 days. Its velocity semi-amplitude of 21.4 $\pm$ 0.5 km s$^{-1}$ corresponds to a minimum mass of 61 $\pm$ 7 M$_{JUP}$; the new companion, which we call GJ 867D, could be a brown dwarf. Stable astrometric measurements of GJ 867BD obtained with CTIO's 0.9-m telescope over the last decade exclude the presence of any massive planetary companions (7-18 M$_{JUP}$) with longer orbital periods (2-10 years) for the majority of orientations. These complementary observations are also used to determine the trigonometric distance and proper motion of GJ 867BD; the measurements are consistent with the HIPPARCOS measured values of the M2 dwarf GJ 867AC, which is itself a 4.1 day double-lined spectroscopic binary at a projected separation of 24.5" (216 AU) from GJ 867BD. These new measurements strengthen the case that GJ 867AC and GJ 867BD are physically associated, making the GJ 867 system one of only four quadruple systems within 10 pc of the Sun (d$=$ 8.82 $\pm$0.08 pc) and the only among these with all M-dwarf (or cooler) components.

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arXiv2012

Kepler Studies of Low-Mass Eclipsing Binaries I. Parameters of the Long-Period Binary KIC 6131659

KIC 6131659 is a long-period (17.5 days) eclipsing binary discovered by the Kepler mission. We analyzed six quarters of Kepler data along with supporting ground-based photometric and spectroscopic data to obtain accurate values for the mass and radius of both stars, namely M_1=0.922 +/- 0.007 M_sun, R_1=0.8800 +/- 0.0028 R_sun, and M_2=0.685 +/- 0.005 M_sun, R_2=0.6395 +/- 0.0061 R_sun. There is a well-known issue with low mass (M <<0.8 M_sun) stars (in cases where the mass and radius measurement uncertainties are smaller than two or three percent) where the measured radii are almost always 5 to 15 percent larger than expected from evolutionary models, i.e. the measured radii are all above the model isochrones in a mass-radius plane. In contrast, the two stars in KIC 6131659 were found to sit on the same theoretical isochrone in the mass-radius plane. Until recently, all of the well-studied eclipsing binaries with low-mass stars had periods less than about three days. The stars in such systems may have been inflated by high levels of stellar activity induced by tidal effects in these close binaries. KIC 6131659 shows essentially no evidence of enhanced stellar activity, and our measurements support the hypothesis that the unusual mass-radius relationship observed in most low-mass stars is influenced by strong magnetic activity created by the rapid rotation of the stars in tidally-locked, short-period systems. Finally, using short cadence data, we show that KIC 6131657 has one of the smallest measured non-zero eccentricities of a binary with two main sequence stars, where e cos omega=(4.57 +/-0.02)*10^-5.

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arXiv2012

Kepler constraints on planets near hot Jupiters

We present the results of a search for planetary companions orbiting near hot Jupiter planet candidates (Jupiter-size candidates with orbital periods near 3 days) identified in the Kepler data through its sixth quarter of science operations. Special emphasis is given to companions between the 2:1 interior and exterior mean-motion resonances. A photometric transit search excludes companions with sizes ranging from roughly 2/3 to 5 times the size of the Earth, depending upon the noise properties of the target star. A search for dynamically induced deviations from a constant period (transit timing variations or TTVs) also shows no significant signals. In contrast, comparison studies of warm Jupiters (with slightly larger orbits) and hot Neptune-size candidates do exhibit signatures of additional companions with these same tests. These differences between hot Jupiters and other planetary systems denote a distinctly different formation or dynamical history.

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arXiv2012

The Transiting Circumbinary Planets Kepler-34 and Kepler-35

Most Sun-like stars in the Galaxy reside in gravitationally-bound pairs of stars called "binary stars". While long anticipated, the existence of a "circumbinary planet" orbiting such a pair of normal stars was not definitively established until the discovery of Kepler-16. Incontrovertible evidence was provided by the miniature eclipses ("transits") of the stars by the planet. However, questions remain about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we present two additional transiting circumbinary planets, Kepler-34 and Kepler-35. Each is a low-density gas giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 orbits two Sun-like stars every 289 days, while Kepler-35 orbits a pair of smaller stars (89% and 81% of the Sun's mass) every 131 days. Due to the orbital motion of the stars, the planets experience large multi-periodic variations in incident stellar radiation. The observed rate of circumbinary planets implies > ~1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.

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arXiv2012

Kepler-20: A Sun-like Star with Three Sub-Neptune Exoplanets and Two Earth-size Candidates

We present the discovery of the Kepler-20 planetary system, which we initially identified through the detection of five distinct periodic transit signals in the Kepler light curve of the host star 2MASSJ19104752+4220194. We find a stellar effective temperature Teff=5455+-100K, a metallicity of [Fe/H]=0.01+-0.04, and a surface gravity of log(g)=4.4+-0.1. Combined with an estimate of the stellar density from the transit light curves we deduce a stellar mass of Mstar=0.912+-0.034 Msun and a stellar radius of Rstar=0.944^{+0.060}_{-0.095} Rsun. For three of the transit signals, our results strongly disfavor the possibility that these result from astrophysical false positives. We conclude that the planetary scenario is more likely than that of an astrophysical false positive by a factor of 2e5 (Kepler-20b), 1e5 (Kepler-20c), and 1.1e3 (Kepler-20d), sufficient to validate these objects as planetary companions. For Kepler-20c and Kepler-20d, the blend scenario is independently disfavored by the achromaticity of the transit: From Spitzer data gathered at 4.5um, we infer a ratio of the planetary to stellar radii of 0.075+-0.015 (Kepler-20c) and 0.065+-0.011 (Kepler-20d), consistent with each of the depths measured in the Kepler optical bandpass. We determine the orbital periods and physical radii of the three confirmed planets to be 3.70d and 1.91^{+0.12}_{-0.21} Rearth for Kepler-20b, 10.85 d and 3.07^{+0.20}_{-0.31} Rearth for Kepelr-20c, and 77.61 d and 2.75^{+0.17}_{-0.30} Rearth for Kepler-20d. From multi-epoch radial velocities, we determine the masses of Kepler-20b and Kepler-20c to be 8.7\+-2.2 Mearth and 16.1+-3.5 Mearth, respectively, and we place an upper limit on the mass of Kepler-20d of 20.1 Mearth (2 sigma).

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arXiv2012

Transit Timing Observations from Kepler: II. Confirmation of Two Multiplanet Systems via a Non-parametric Correlation Analysis

We present a new method for confirming transiting planets based on the combination of transit timingn variations (TTVs) and dynamical stability. Correlated TTVs provide evidence that the pair of bodies are in the same physical system. Orbital stability provides upper limits for the masses of the transiting companions that are in the planetary regime. This paper describes a non-parametric technique for quantifying the statistical significance of TTVs based on the correlation of two TTV data sets. We apply this method to an analysis of the transit timing variations of two stars with multiple transiting planet candidates identified by Kepler. We confirm four transiting planets in two multiple planet systems based on their TTVs and the constraints imposed by dynamical stability. An additional three candidates in these same systems are not confirmed as planets, but are likely to be validated as real planets once further observations and analyses are possible. If all were confirmed, these systems would be near 4:6:9 and 2:4:6:9 period commensurabilities. Our results demonstrate that TTVs provide a powerful tool for confirming transiting planets, including low-mass planets and planets around faint stars for which Doppler follow-up is not practical with existing facilities. Continued Kepler observations will dramatically improve the constraints on the planet masses and orbits and provide sensitivity for detecting additional non-transiting planets. If Kepler observations were extended to eight years, then a similar analysis could likely confirm systems with multiple closely spaced, small transiting planets in or near the habitable zone of solar-type stars.

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