arXiv subjects

Eric Agol

Publications and source records attributed to Eric Agol.

At least 91 records · Page 5Linked to original sources

arXiv2017

A seven-planet resonant chain in TRAPPIST-1

The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star. At least seven planets similar to Earth in radius and in mass were previously found to transit this host star. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1h has a radius of 0.727 Earth radii and an equilibrium temperature of 173 K. We have also measured the rotational period of the star at 3.3 d and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf.

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arXiv2017

Mass and Eccentricity Constraints in the WASP-47 Planetary System from a Simultaneous Analysis of Radial Velocities & Transit Timing Variations

Measuring precise planet masses, densities, and orbital dynamics in individual planetary systems is an important pathway toward understanding planet formation. The WASP-47 system has an unusual architecture that motivates a complex formation theory. The system includes a hot Jupiter ("b") neighbored by interior ("e") and exterior ("d") sub-Neptunes, and a long-period eccentric giant planet ("c"). We simultaneously modeled transit times from the Kepler K2 Mission and 118 radial velocities to determine precise masses, densities, and Keplerian orbital elements of the WASP-47 planets. Combining RVs and TTVs provides a better estimate of the mass of planet d (13.6\pm2.0~M_\odot) than obtained with only RVs ($12.75\pm2.70~M_\odot$) or TTVs ($16.1\pm3.8~M_\odot$). Planets e and d have high densities for their size, consistent with a history of photo-evaporation and/or formation in a volatile-poor environment. Through our RV and TTV analysis, we find that the planetary orbits have eccentricities similar to the solar system planets. The WASP-47 system has three similarities to our own solar system: (1) the planetary orbits are nearly circular and coplanar, (2) the planets are not trapped in mean motion resonances, and (3) the planets have diverse compositions. None of the current single-process exoplanet formation theories adequately reproduce these three characteristics of the WASP-47 system (or our solar system). We propose that WASP-47, like the solar system, formed in two stages: first, the giant planets formed in a gas-rich disk and migrated to their present locations, and second, the high-density sub-Neptunes formed in situ in a gas-poor environment.

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arXiv2017

Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1

One focus of modern astronomy is to detect temperate terrestrial exoplanets well-suited for atmospheric characterisation. A milestone was recently achieved with the detection of three Earth-sized planets transiting (i.e. passing in front of) a star just 8% the mass of the Sun 12 parsecs away. Indeed, the transiting configuration of these planets with the Jupiter-like size of their host star - named TRAPPIST-1 - makes possible in-depth studies of their atmospheric properties with current and future astronomical facilities. Here we report the results of an intensive photometric monitoring campaign of that star from the ground and with the Spitzer Space Telescope. Our observations reveal that at least seven planets with sizes and masses similar to the Earth revolve around TRAPPIST-1. The six inner planets form a near-resonant chain such that their orbital periods (1.51, 2.42, 4.04, 6.06, 9.21, 12.35 days) are near ratios of small integers. This architecture suggests that the planets formed farther from the star and migrated inward. The seven planets have equilibrium temperatures low enough to make possible liquid water on their surfaces.

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arXiv2017

An update to the EVEREST K2 pipeline: Short cadence, saturated stars, and Kepler-like photometry down to Kp = 15

We present an update to the EVEREST K2 pipeline that addresses various limitations in the previous version and improves the photometric precision of the de-trended light curves. We develop a fast regularization scheme for third order pixel level decorrelation (PLD) and adapt the algorithm to include the PLD vectors of neighboring stars to enhance the predictive power of the model and minimize overfitting, particularly for faint stars. We also modify PLD to work for saturated stars and improve its performance on extremely variable stars. On average, EVEREST 2.0 light curves have 10-20% higher photometric precision than those in the previous version, yielding the highest precision light curves at all Kp magnitudes of any publicly available K2 catalog. For most K2 campaigns, we recover the original Kepler precision to at least Kp = 14, and to at least Kp = 15 for campaigns 1, 5, and 6. We also de-trend all short cadence targets observed by K2, obtaining even higher photometric precision for these stars. All light curves for campaigns 0-8 are available online in the EVEREST catalog, which will be continuously updated with future campaigns. EVEREST 2.0 is open source and is coded in a general framework that can be applied to other photometric surveys, including Kepler and the upcoming TESS mission.

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arXiv2017

The Pale Green Dot: A Method to Characterize Proxima Centauri b using Exo-Aurorae

We examine the feasibility of detecting auroral emission from the potentially habitable exoplanet Proxima Centauri b. Detection of aurorae would yield an independent confirmation of the planet's existence, constrain the presence and composition of its atmosphere, and determine the planet's eccentricity and inclination, thereby breaking the mass-inclination degeneracy. If Proxima Centauri b is a terrestrial world with an Earth-like atmosphere and magnetic field, we estimate the power at the 5577Å OI auroral line is on the order of 0.1 TW under steady-state stellar wind, or ${\sim} 100 {\times}$ stronger than that on Earth. This corresponds to a planet-star contrast ratio of $10^{-6}-10^{-7}$ in a narrow band about the 5577Å line, although higher contrast ($10^{-4}-10^{-5}$) may be possible during periods of strong magnetospheric disturbance (auroral power $1-10$ TW). We searched the Proxima Centauri b HARPS data for the 5577Å line and for other prominent oxygen and nitrogen lines, but find no signal, indicating that the OI auroral line contrast must be lower than $2\times 10^{-2}$ (with power $\lesssim$ 3,000 TW), consistent with our predictions. We find that observations of 0.1 TW auroral emission lines are likely infeasible with current and planned telescopes. However, future observations with a space-based coronagraphic telescope or a ground-based extremely large telescope (ELT) with a coronagraph could push sensitivity down to terawatt oxygen aurorae (contrast $7\times 10^{-6}$) with exposure times of ${\sim} 1$ day. If a coronagraph design contrast of $10^{-7}$ can be achieved with negligible instrumental noise, a future concept ELT could observe steady-state auroral emission in a few nights.

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arXiv2017

Exploring the Brown Dwarf Desert: New Substellar Companions from the SDSS-III MARVELS Survey

Planet searches using the radial velocity technique show a paucity of companions to solar-type stars within ~5 AU in the mass range of ~10 - 80 M$_{\text{Jup}}$. This deficit, known as the brown dwarf desert, currently has no conclusive explanation. New substellar companions in this region help asses the reality of the desert and provide insight to the formation and evolution of these objects. Here we present 10 new brown dwarf and two low-mass stellar companion candidates around solar-type stars from the Multi-object APO Radial-Velocity Exoplanet Large-Area Survey (MARVELS) of the Sloan Digital Sky Survey III (SDSS-III). These companions were selected from processed MARVELS data using the latest University of Florida Two Dimensional (UF2D) pipeline, which shows significant improvement and reduction of systematic errors over previous pipelines. The 10 brown dwarf companions range in mass from ~13 to 76 M$_{\text{Jup}}$ and have orbital radii of less than 1 AU. The two stellar companions have minimum masses of ~98 and 100 M$_{\text{Jup}}$. The host stars of the MARVELS brown dwarf sample have a mean metallicity of [Fe/H] = 0.03 $\pm$ 0.08 dex. Given our stellar sample we estimate the brown dwarf occurrence rate around solar-type stars with periods less than ~300 days to be ~0.56%.

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arXiv2016

The population of long-period transiting exoplanets

The Kepler Mission has discovered thousands of exoplanets and revolutionized our understanding of their population. This large, homogeneous catalog of discoveries has enabled rigorous studies of the occurrence rate of exoplanets and planetary systems as a function of their physical properties. However, transit surveys like Kepler are most sensitive to planets with orbital periods much shorter than the orbital periods of Jupiter and Saturn, the most massive planets in our Solar System. To address this deficiency, we perform a fully automated search for long-period exoplanets with only one or two transits in the archival Kepler light curves. When applied to the $\sim 40,000$ brightest Sun-like target stars, this search produces 16 long-period exoplanet candidates. Of these candidates, 6 are novel discoveries and 5 are in systems with inner short-period transiting planets. Since our method involves no human intervention, we empirically characterize the detection efficiency of our search. Based on these results, we measure the average occurrence rate of exoplanets smaller than Jupiter with orbital periods in the range 2-25 years to be $2.0\pm0.7$ planets per Sun-like star.

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arXiv2016

Very Low-Mass Stellar and Substellar Companions to Solar-like Stars From MARVELS VI: A Giant Planet and a Brown Dwarf Candidate in a Close Binary System HD 87646

We report the detections of a giant planet (MARVELS-7b) and a brown dwarf candidate (MARVELS-7c) around the primary star in the close binary system, HD 87646. It is the first close binary system with more than one substellar circum-primary companion discovered to the best of our knowledge. The detection of this giant planet was accomplished using the first multi-object Doppler instrument (KeckET) at the Sloan Digital Sky Survey (SDSS) telescope. Subsequent radial velocity observations using ET at Kitt Peak National Observatory, HRS at HET, the "Classic" spectrograph at the Automatic Spectroscopic Telescope at Fairborn Observatory, and MARVELS from SDSS-III confirmed this giant planet discovery and revealed the existence of a long-period brown dwarf in this binary. HD 87646 is a close binary with a separation of $\sim22$ AU between the two stars, estimated using the Hipparcos catalogue and our newly acquired AO image from PALAO on the 200-inch Hale Telescope at Palomar. The primary star in the binary, HD 87646A, has Teff = 5770$\pm$80K, log(g)=4.1$\pm$0.1 and [Fe/H] = $-0.17\pm0.08$. The derived minimum masses of the two substellar companions of HD 87646A are 12.4$\pm$0.7M$_{\rm Jup}$ and 57.0$\pm3.7$M$_{\rm Jup}$. The periods are 13.481$\pm$0.001 days and 674$\pm$4 days and the measured eccentricities are 0.05$\pm$0.02 and 0.50$\pm$0.02 respectively. Our dynamical simulations show the system is stable if the binary orbit has a large semi-major axis and a low eccentricity, which can be verified with future astrometry observations.

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arXiv2016

EVEREST: Pixel Level Decorrelation of K2 Light curves

We present EVEREST, an open-source pipeline for removing instrumental noise from K2 light curves. EVEREST employs a variant of pixel level decorrelation (PLD) to remove systematics introduced by the spacecraft's pointing error and a Gaussian process (GP) to capture astrophysical variability. We apply EVEREST to all K2 targets in campaigns 0-7, yielding light curves with precision comparable to that of the original Kepler mission for stars brighter than $K_p \approx 13$, and within a factor of two of the Kepler precision for fainter targets. We perform cross-validation and transit injection and recovery tests to validate the pipeline, and compare our light curves to the other de-trended light curves available for download at the MAST High Level Science Products archive. We find that EVEREST achieves the highest average precision of any of these pipelines for unsaturated K2 stars. The improved precision of these light curves will aid in exoplanet detection and characterization, investigations of stellar variability, asteroseismology, and other photometric studies. The EVEREST pipeline can also easily be applied to future surveys, such as the TESS mission, to correct for instrumental systematics and enable the detection of low signal-to-noise transiting exoplanets. The EVEREST light curves and the source code used to generate them are freely available online.

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arXiv2016

Predictable patterns in planetary transit timing variations and transit duration variations due to exomoons

We present new ways to identify single and multiple moons around extrasolar planets using planetary transit timing variations (TTVs) and transit duration variations (TDVs). For planets with one moon, measurements from successive transits exhibit a hitherto undescribed pattern in the TTV-TDV diagram, originating from the stroboscopic sampling of the planet's orbit around the planet-moon barycenter. This pattern is fully determined and analytically predictable after three consecutive transits. The more measurements become available, the more the TTV-TDV diagram approaches an ellipse. For planets with multiple moons in orbital mean motion resonance (MMR), like the Galilean moons, the pattern is much more complex and addressed numerically in this report. Exomoons in MMR can also form closed, predictable TTV-TDV figures if the drift of the moons' pericenters is sufficiently slow. We find that MMR exomoons produce loops in the TTV-TDV diagram and that the number of these loops is equal to the order of the MMR, or the largest integer in the MMR ratio. We use a Bayesian model and Monte Carlo simulations to test the discoverability of exomoons using TTV-TDV diagrams with current and near-future technology. In a blind test, two of us (BP, DA) successfully retrieved a large moon from simulated TTV-TDV by co-authors MH and RH, which resembled data from a known Kepler planet candidate. Single exomoons with a 10% moon-to-planet mass ratio, like to Pluto-Charon binary, can be detectable in the archival data of the Kepler primary mission. Multi-exomoon systems, however, require either larger telescopes or brighter target stars. Complementary detection methods invoking a moon's own photometric transit or its orbital sampling effect can be used for validation or falsification. A combination of TESS, CHEOPS, and PLATO data would offer a compelling opportunity for exomoon discoveries around bright stars.

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arXiv2016

3.6 and 4.5 $μ$m ${\it Spitzer}$ Phase Curves of the Highly-Irradiated Hot Jupiters WASP-19b and HAT-P-7b

We analyze full-orbit phase curve observations of the transiting hot Jupiters WASP-19b and HAT-P-7b at 3.6 and 4.5 $μ$m obtained using the Spitzer Space Telescope. For WASP-19b, we measure secondary eclipse depths of $0.485\%\pm 0.024\%$ and $0.584\%\pm 0.029\%$ at 3.6 and 4.5 $μ$m, which are consistent with a single blackbody with effective temperature $2372 \pm 60$ K. The measured 3.6 and 4.5 $μ$m secondary eclipse depths for HAT-P-7b are $0.156\%\pm 0.009\%$ and $0.190\%\pm 0.006\%$, which are well-described by a single blackbody with effective temperature $2667\pm 57$ K. Comparing the phase curves to the predictions of one-dimensional and three-dimensional atmospheric models, we find that WASP-19b's dayside emission is consistent with a model atmosphere with no dayside thermal inversion and moderately efficient day-night circulation. We also detect an eastward-shifted hotspot, suggesting the presence of a superrotating equatorial jet. In contrast, HAT-P-7b's dayside emission suggests a dayside thermal inversion and relatively inefficient day-night circulation; no hotspot shift is detected. For both planets, these same models do not agree with the measured nightside emission. The discrepancies in the model-data comparisons for WASP-19b might be explained by high-altitude silicate clouds on the nightside and/or high atmospheric metallicity, while the very low 3.6 $μ$m nightside planetary brightness for HAT-P-7b may be indicative of an enhanced global C/O ratio. We compute Bond albedos of 0 ($<0.08$ at $1σ$) and $0.38\pm 0.06$ for WASP-19b and HAT-P-7b, respectively. In the context of other planets with thermal phase curve measurements, we show that WASP-19b and HAT-P-7b fit the general trend of decreasing day-night heat recirculation with increasing irradiation.

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arXiv2016

Transit timing variations for planets near eccentricity-type mean motion resonances

We derive the transit timing variations (TTVs) of two planets near a second order mean motion resonance on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of $j n_2-(j-2)n_1$, where $j \ge 3$ is an integer characterizing the resonance and $n_2$ and $n_1$ are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV depends on the mass of the perturbing planet, relative to the mass of the star, and on both the eccentricities and longitudes of pericenter of each planet. The TTVs of the two planets are approximated anti-correlated, with phases of $ϕ$ and $\approx ϕ+π$, where the phase $ϕ$ also depends on the eccentricities and longitudes of pericenter. Therefore, the TTVs caused by proximity to a second order mean motion resonance do not in general uniquely determine both planet masses, eccentricities, and pericenters. This is completely analogous to the case of TTVs induced by two planets near a first order mean motion resonance. We explore how other TTV signals, such as the short-period synodic TTV or a first order resonant TTV, in combination with the second order resonant TTV, can break degeneracies. Lastly, we derive approximate formulae for the TTVs of planets near any order eccentricity-type mean motion resonance; this shows that the same basic sinusoidal TTV structure holds for all eccentricity-type resonances. Our general formula reduces to previously derived results near first order mean motion resonances.

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arXiv2016

Transit timing to first order in eccentricity

Characterization of transiting planets with transit timing variations (TTVs) requires understanding how to translate the observed TTVs into masses and orbital elements of the planets. This can be challenging in multi-planet transiting systems, but fortunately these systems tend to be nearly plane-parallel and low eccentricity. Here we present a novel derivation of analytic formulae for TTVs that are accurate to first order in the planet-star mass ratios and in the orbital eccentricities. These formulae are accurate in proximity to first order resonances, as well as away from resonance, and compare well with more computationally expensive N-body integrations in the low eccentricity, low mass-ratio regime when applied to simulated and to actual multi-transiting Kepler planet systems. We make code available for implementing these formulae.

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arXiv2016

Transiting Exoplanet Studies and Community Targets for JWST's Early Release Science Program

The James Webb Space Telescope will revolutionize transiting exoplanet atmospheric science due to its capability for continuous, long-duration observations and its larger collecting area, spectral coverage, and spectral resolution compared to existing space-based facilities. However, it is unclear precisely how well JWST will perform and which of its myriad instruments and observing modes will be best suited for transiting exoplanet studies. In this article, we describe a prefatory JWST Early Release Science (ERS) program that focuses on testing specific observing modes to quickly give the community the data and experience it needs to plan more efficient and successful future transiting exoplanet characterization programs. We propose a multi-pronged approach wherein one aspect of the program focuses on observing transits of a single target with all of the recommended observing modes to identify and understand potential systematics, compare transmission spectra at overlapping and neighboring wavelength regions, confirm throughputs, and determine overall performances. In our search for transiting exoplanets that are well suited to achieving these goals, we identify 12 objects (dubbed "community targets") that meet our defined criteria. Currently, the most favorable target is WASP-62b because of its large predicted signal size, relatively bright host star, and location in JWST's continuous viewing zone. Since most of the community targets do not have well-characterized atmospheres, we recommend initiating preparatory observing programs to determine the presence of obscuring clouds/hazes within their atmospheres. Measurable spectroscopic features are needed to establish the optimal resolution and wavelength regions for exoplanet characterization. Other initiatives from our proposed ERS program include testing the instrument brightness limits and performing phase-curve observations.(Abridged)

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arXiv2016

Secure TTV Mass Measurements: Ten Kepler Exoplanets between 3 and 8 Earth Masses with Diverse Densities and Incident Fluxes

We infer dynamical masses in eight multi-planet systems using transit times measured from Kepler's complete dataset, including short-cadence data where available. Of the eighteen dynamical masses that we infer, ten pass multiple tests for robustness. These are in systems; Kepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), Kepler-105 (KOI-115), and Kepler-307 (KOI-1576). Kepler-105 c has a density consistent with an Earth-like composition. Strong TTV signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently-measured transit times, including planets at; Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115) and Kepler-177 (KOI-523). Strong upper limits on the mass of Kepler-177 c imply an extremely low density ~0.1 g cm$^{-3}$. In most cases, individual orbital eccentricities were poorly constrained due to degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderate-to-high likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, non-librating solutions also match the transit-timing data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have robust mass measurements. Placing these exoplanets on the mass-radius diagram, we find a wide range of densities is observed among sub-Neptune mass planets and that the range in observed densities is anti-correlated with incident flux.

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arXiv2016

The Effect of Orbital Configuration on the Possible Climates and Habitability of Kepler-62f

As lower-mass stars often host multiple rocky planets, gravitational interactions among planets can have significant effects on climate and habitability over long timescales. Here we explore a specific case, Kepler-62f, a potentially habitable planet in a five-planet system with a K2V host star. N-body integrations reveal the stable range of initial eccentricities for Kepler-62f is $0.00 \leqslant e \leqslant 0.32$, absent the effect of additional, undetected planets. We simulate the tidal evolution of Kepler-62f in this range and find that, for certain assumptions, the planet can be locked in a synchronous rotation state. Simulations using LMD Generic GCM indicate that with 3 bars of CO$_2$ in its atmosphere, Kepler-62f would only be warm enough for surface liquid water at the upper limit of this eccentricity range, providing it has a high planetary obliquity (between 60$^\circ$ and 90$^\circ$). A climate similar to modern-day Earth is possible for the entire range of stable eccentricities if atmospheric CO$_2$ is increased to 5-bar levels. In a low-CO$_2$ case, simulations with CCSM4 and LMD Generic GCM indicate that increases in planetary obliquity and orbital eccentricity coupled with an orbital configuration that places the summer solstice at or near pericenter permit regions of the planet with above-freezing surface temperatures. This may melt ice sheets formed during colder seasons. If Kepler-62f is synchronously rotating and has an ocean, CO$_2$ levels above 3 bars would be required to distribute enough heat to the night side of the planet to avoid atmospheric freeze-out and permit a large enough region of open water at the planet's substellar point to remain stable. Overall, we find multiple plausible combinations of orbital and atmospheric properties that permit surface liquid water on Kepler-62f.

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arXiv2016

Seeing Through the Ring: Near-Infrared Photometry of V582 Mon (KH 15D)

We examine the light and color evolution of the T Tauri binary KH 15D through photometry obtained at wavelengths between 0.55 and 8.0 $μ$m. The data were collected with ANDICAM on the 1.3 m SMARTS telescope at Cerro-Tololo Inter-American Observatory and with IRAC on the Spitzer Space Telescope. We show that the system's circumbinary ring, which acts as a screen that covers and uncovers different portions of the binary orbit as the ring precesses, has reached an orientation where the brighter component (star B) fully or nearly fully emerges during each orbital cycle. The fainter component (star A) remains fully occulted by the screen at all phases. The leading and trailing edges of the screen move across the sky at the same rate of $\sim$15 meters per second, consistent with expectation for a ring with a radius and width of $\sim$4 AU and a precession period of $\sim$6500 years. Light and color variations continue to indicate that the screen is sharp edged and opaque at \emph{VRIJH} wavelengths. However, we find an increasing transparency of the ring edge at 2.2, 3.6, and 4.5 $μ$m. Reddening seen at the beginning of the eclipse that occurred during the CSI 2264 campaign particularly suggests selective extinction by a population of large dust grains. Meanwhile, the gradual bluing observed while star B is setting is indicative of forward scattering effects at the edge of the ring. The SED of the system at its bright phase shows no evidence of infrared excess emission that can be attributed to radiation from the ring or other dust component out to 8 microns.

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arXiv2016

Revised Masses and Densities of the Planets around Kepler-10

Determining which small exoplanets have stony-iron compositions is necessary for quantifying the occurrence of such planets and for understanding the physics of planet formation. Kepler-10 hosts the stony-iron world Kepler-10b (K10b), and also contains what has been reported to be the largest solid silicate-ice planet, Kepler-10c (K10c). Using 220 radial velocities (RVs), including 72 precise RVs from Keck-HIRES of which 20 are new from 2014-2015, and 17 quarters of Kepler photometry, we obtain the most complete picture of the Kepler-10 system to date. We find that K10b (Rp=1.47 Re) has mass 3.72$\pm$0.42 Me and density 6.46$\pm$0.73 g/cc. Modeling the interior of K10b as an iron core overlaid with a silicate mantle, we find that the iron core constitutes 0.17$\pm$0.11 of the planet mass. For K10c (Rp=2.35 Re) we measure Mp=13.98$\pm$1.79 Me and $ρ$=5.94$\pm$0.76 g/cc, significantly lower than the mass computed in Dumusque et al. (2014, 17.2$\pm$1.9 Me). Internal compositional modeling reveals that at least $10\%$ of the radius of Kepler-10c is a volatile envelope composed of hydrogen-helium ($0.2\%$ of the mass, $16\%$ of the radius) or super-ionic water ($28\%$ of the mass, $29\%$ of the radius). Analysis of only HIRES data yields a higher mass for K10b and a lower mass for K10c than does analysis of the HARPS-N data alone, with the mass estimates for K10c formally inconsistent by 3$σ$. Splitting the RVs from each instrument leads to inconsistent measurements for the mass of planet c in each data set. This suggests that time-correlated noise is present and that the uncertainties in the planet masses (especially K10c) exceed our formal estimates. Transit timing variations (TTVs) of K10c indicate the likely presence of a third planet in the system, KOI-72.X. The TTVs and RVs are consistent with KOI-72.X having an orbital period of 24, 71, or 101 days, and a mass from 1-7 Me.

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