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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

New Formation Models for the Kepler-36 System

Formation of the planets in the Kepler-36 system is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. The standard model is updated to include the dissolution of accreting rocky planetesimals in the gaseous envelope of the planet, leading to substantial enrichment of the envelope mass in heavy elements and a non-uniform composition with depth. For Kepler-36 c, models involving in situ formation and models involving orbital migration are considered. The results are compared with standard formation models. The calculations include the formation (accretion) phase, as well as the subsequent cooling phase, up to the age of Kepler-36 (7 Gyr). During the latter phase, mass loss induced by stellar XUV radiation is included. In all cases, the results fit the measured mass, 7.84 M, and radius, 3.68 R, of Kepler-36 c. Two parameters are varied to obtain these fits: the disk solid surface density at the formation location, and the "efficiency" factor in the XUV mass loss rate. The updated models are hotter and therefore less dense in the silicate portion of the planet and in the overlying layers of H/He, as compared with standard models. The lower densities mean that only about half as much H/He is needed to be accreted to fit the present-day mass and radius constraints. For Kepler-36 b, an updated in situ calculation shows that the entire H/He envelope is lost, early in the cooling phase, in agreement with observation.

planets and satellites:formation↗
NASA NTRS2016

Kepler Stellar Properties Catalog Update for Q1-Q17 DR25 Transit Search

Huber et al. (2014) presented revised stellar properties for 196,468 Kepler targets, which were used for the Q1-Q16 TPSDV planet search (Tenenbaum et al. 2014). The catalog was based on atmospheric properties (i.e., temperature (Teff), surface gravity (log(g)), and metallicity ([FeH])) published in the literature using a variety of methods (e.g., asteroseismology, spectroscopy, exoplanet transits, photometry), which were then homogeneously fitted to a grid of Dartmouth (DSEP) isochrones (Dotter et al. 2008). The catalog was updated in early 2015 for the Q1-Q17 Data Release (DR) 24 transit search (Seader et al. 2015) based on the latest classifications of Kepler targets in the literature at that time. The methodology followed Huber et al. (2014). Here we provide updated stellar properties of 197,096 Kepler targets. Like the previous catalog, this update is based on atmospheric properties that were either published in the literature or provided by the Kepler community follow-up program (CFOP). The input values again come from different methods: asteroseismology, spectroscopy, flicker, and photometry. This catalog update was developed to support the SOC 9.3 TPSDV planet search (Twicken et al. 2016), which is expected to be the final search and data release by the Kepler project.In this document, we describe the method and the inputs that were used to build the catalog. The methodology follows Huber et al. (2014) with a few improvements as described in Section 2.

DR25↗
NASA NTRS2017

Synergies Between the Kepler, K2 and TESS Missions with the PLATO Mission (Revised)

Two transit survey missions will have been flown by NASA prior to the launch of ESA's PLATO Mission in 2026, laying the groundwork for exoplanet discovery via the transit method. The Kepler Mission, which launched in 2009, collected data on its 100+ square degree field of view for four years before failure of a reaction wheel ended its primary mission. The results from Kepler include 2300+ confirmed or validated exoplanets, 2200+ planetary candidates, 2100+ eclipsing binaries. Kepler also revolutionized the field of asteroseismology by measuring the pressure mode oscillations of over 15000 solar-like stars spanning the lifecycle of such stars from hydrogen-burning dwarfs to helium-burning red giants. The re-purposed Kepler Mission, dubbed K2, continues to observe fields of view in and near the ecliptic plane for 80 days each, significantly broadening the scope of the astrophysical investigations as well as discovering an additional 156 exoplanets to date. The TESS mission will launch in 2017 to conduct an all-sky survey for small exoplanets orbiting stars 10X closer and 100X brighter than Kepler exoplanet host stars, allowing for far greater follow-up and characterization of their masses as well as their sizes for at least 50 small planets. Future assets such as James Webb Space Telescope, and ground-based assets such as ESOs Very Large Telescope (VLT) array, the Exremely Large Telescope (ELT), and the Thirty Meter Telescope (TMT) will be able to characterize the atmospheric composition and properties of these small planets. TESS will observe each 24 X 96 field of view for 30 days and thereby cover first the southern and then the northern hemisphere over 13 pointings during each year of the primary mission. The pole-most camera will observe the James Webb continuous viewing zone for one year in each hemisphere, permitting much longer period planets to be detected in this region. The PLATO mission will seek to detect habitable Earth-like planets with an instrument composed of 26 small telescopes in several 2232 square deg FOVs with a range of observation durations over a mission lifetime of up to eight years. This paper summarizes the findings of the KeplerK2 missions, previews the likely results from the TESS mission, and explores the lessons learned and to be learned from these prior missions that can be incorporated into the observation and data reduction strategy for the PLATO Mission so as to maximize the science return.

exoplanet detection↗
DOE OSTI2014

Contamination in the Kepler field. Identification of 685 KOIs as false positives via ephemeris matching based ON Q1-Q12 data

The Kepler mission has to date found almost 6000 planetary transit-like signals, utilizing three years of data for over 170,000 stars at extremely high photometric precision. Due to its design, contamination from eclipsing binaries, variable stars, and other transiting planets results in a significant number of these signals being false positives (FPs). This directly affects the determination of the occurrence rate of Earth-like planets in our Galaxy, as well as other planet population statistics. In order to detect as many of these FPs as possible, we perform ephemeris matching among all transiting planet, eclipsing binary, and variable star sources. We find that 685 Kepler Objects of Interest (KOIs)—12% of all those analyzed—are FPs as a result of contamination, due to 409 unique parent sources. Of these, 118 have not previously been identified by other methods. We estimate that ∼35% of KOIs are FPs due to contamination, when performing a first-order correction for observational bias. Comparing single-planet candidate KOIs to multi-planet candidate KOIs, we find an observed FP fraction due to contamination of 16% and 2.4% respectively, bolstering the existing evidence that multi-planet KOIs are significantly less likely to be FPs. We also analyze the parameter distributions of the ephemeris matches and derive a simple model for the most common type of contamination in the Kepler field. We find that the ephemeris matching technique is able to identify low signal-to-noise FPs that are difficult to identify with other vetting techniques. We expect FP KOIs to become more frequent when analyzing more quarters of Kepler data, and note that many of them will not be able to be identified based on Kepler data alone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Adaptive optics images. III. 87 Kepler objects of interest

The Kepler mission has revolutionized our understanding of exoplanets, but some of the planet candidates identified by Kepler may actually be astrophysical false positives or planets whose transit depths are diluted by the presence of another star. Adaptive optics images made with ARIES at the MMT of 87 Kepler Objects of Interest place limits on the presence of fainter stars in or near the Kepler aperture. We detected visual companions within 1'' for 5 stars, between 1'' and 2'' for 7 stars, and between 2'' and 4'' for 15 stars. For those systems, we estimate the brightness of companion stars in the Kepler bandpass and provide approximate corrections to the radii of associated planet candidates due to the extra light in the aperture. For all stars observed, we report detection limits on the presence of nearby stars. ARIES is typically sensitive to stars approximately 5.3 Ks magnitudes fainter than the target star within 1'' and approximately 5.7 Ks magnitudes fainter within 2'', but can detect stars as faint as ΔKs = 7.5 under ideal conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A technique to derive improved proper motions for Kepler objects of interest

We outline an approach yielding proper motions with higher precision than exists in present catalogs for a sample of stars in the Kepler field. To increase proper-motion precision, we combine first-moment centroids of Kepler pixel data from a single season with existing catalog positions and proper motions. We use this astrometry to produce improved reduced-proper-motion diagrams, analogous to a Hertzsprung-Russell (H-R) diagram, for stars identified as Kepler objects of interest. The more precise the relative proper motions, the better the discrimination between stellar luminosity classes. Using UCAC4 and PPMXL epoch 2000 positions (and proper motions from those catalogs as quasi-Bayesian priors), astrometry for a single test Channel (21) and Season (0) spanning 2 yr yields proper motions with an average per-coordinate proper-motion error of 1.0 mas yr{sup –1}, which is over a factor of three better than existing catalogs. We apply a mapping between a reduced-proper-motion diagram and an H-R diagram, both constructed using Hubble Space Telescope parallaxes and proper motions, to estimate Kepler object of interest K-band absolute magnitudes. The techniques discussed apply to any future small-field astrometry as well as to the rest of the Kepler field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

The EB factory project. II. Validation with the Kepler field in preparation for K2 and TESS

Large repositories of high precision light curve data, such as the Kepler data set, provide the opportunity to identify astrophysically important eclipsing binary (EB) systems in large quantities. However, the rate of classical “by eye” human analysis restricts complete and efficient mining of EBs from these data using classical techniques. To prepare for mining EBs from the upcoming K2 mission as well as other current missions, we developed an automated end-to-end computational pipeline—the Eclipsing Binary Factory (EBF)—that automatically identifies EBs and classifies them into morphological types. The EBF has been previously tested on ground-based light curves. To assess the performance of the EBF in the context of space-based data, we apply the EBF to the full set of light curves in the Kepler “Q3” Data Release. We compare the EBs identified from this automated approach against the human generated Kepler EB Catalog of ∼2600 EBs. When we require EB classification with ⩾90% confidence, we find that the EBF correctly identifies and classifies eclipsing contact (EC), eclipsing semi-detached (ESD), and eclipsing detached (ED) systems with a false positive rate of only 4%, 4%, and 8%, while complete to 64%, 46%, and 32%, respectively. When classification confidence is relaxed, the EBF identifies and classifies ECs, ESDs, and EDs with a slightly higher false positive rate of 6%, 16%, and 8%, while much more complete to 86%, 74%, and 62%, respectively. Through our processing of the entire Kepler “Q3” data set, we also identify 68 new candidate EBs that may have been missed by the human generated Kepler EB Catalog. We discuss the EBF's potential application to light curve classification for periodic variable stars more generally for current and upcoming surveys like K2 and the Transiting Exoplanet Survey Satellite.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

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

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

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

ON THE LOW FALSE POSITIVE PROBABILITIES OF KEPLER PLANET CANDIDATES

We present a framework to conservatively estimate the probability that any particular planet-like transit signal observed by the Kepler mission is in fact a planet, prior to any ground-based follow-up efforts. We use Monte Carlo methods based on stellar population synthesis and Galactic structure models, and report false positive probabilities (FPPs) for every Kepler Object of Interest, assuming a 20% intrinsic occurrence rate of close-in planets in the radius range 0.5 R{sub +} < R{sub p} < 20 R{sub +}. Nearly 90% of the 1235 candidates have FPP <10%, and over half have FPP <5%. This probability varies with the magnitude and Galactic latitude of the target star, and with the depth of the transit signal-deeper signals generally have higher FPPs than shallower signals. We establish that a single deep high-resolution image will be an effective follow-up tool for the shallowest (Earth-sized) transits, providing the quickest route toward probabilistically validating the smallest candidates by potentially decreasing the FPP of an Earth-sized transit around a faint star from >10% to <1%. Since Kepler has detected many more planetary signals than can be positively confirmed with ground-based follow-up efforts in the near term, these calculations will be crucial to using the ensemble of Kepler data to determine population characteristics of planetary systems. We also describe how our analysis complements the Kepler team's more detailed BLENDER false positive analysis for planet validation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

KEPLER AND GROUND-BASED TRANSITS OF THE EXO-NEPTUNE HAT-P-11b

We analyze 26 archival Kepler transits of the exo-Neptune HAT-P-11b, supplemented by ground-based transits observed in the blue (B band) and near-IR (J band). Both the planet and host star are smaller than previously believed; our analysis yields R{sub p} = 4.31 R{sub +} {+-} 0.06 R{sub +} and R{sub s} = 0.683 R{sub sun} {+-} 0.009 R{sub sun}, both about 3{sigma} smaller than the discovery values. Our ground-based transit data at wavelengths bracketing the Kepler bandpass serve to check the wavelength dependence of stellar limb darkening, and the J-band transit provides a precise and independent constraint on the transit duration. Both the limb darkening and transit duration from our ground-based data are consistent with the new Kepler values for the system parameters. Our smaller radius for the planet implies that its gaseous envelope can be less extensive than previously believed, being very similar to the H-He envelope of GJ 436b and Kepler-4b. HAT-P-11 is an active star, and signatures of star spot crossings are ubiquitous in the Kepler transit data. We develop and apply a methodology to correct the planetary radius for the presence of both crossed and uncrossed star spots. Star spot crossings are concentrated at phases -0.002 and +0.006. This is consistent with inferences from Rossiter-McLaughlin measurements that the planet transits nearly perpendicular to the stellar equator. We identify the dominant phases of star spot crossings with active latitudes on the star, and infer that the stellar rotational pole is inclined at about 12{sup 0} {+-} 5{sup 0} to the plane of the sky. We point out that precise transit measurements over long durations could in principle allow us to construct a stellar Butterfly diagram to probe the cyclic evolution of magnetic activity on this active K-dwarf star.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

THEY MIGHT BE GIANTS: LUMINOSITY CLASS, PLANET OCCURRENCE, AND PLANET-METALLICITY RELATION OF THE COOLEST KEPLER TARGET STARS

We estimate the stellar parameters of late K- and early M-type Kepler target stars. We obtain medium-resolution visible spectra of 382 stars with K{sub P} - J > 2 ({approx_equal}K5 and later spectral type). We determine luminosity class by comparing the strength of gravity-sensitive indices (CaH, K I, Ca II, and Na I) to their strength in a sample of stars of known luminosity class. We find that giants constitute 96% {+-} 1% of the bright (K{sub P} < 14) Kepler target stars, and 7% {+-} 3% of dim (K{sub P} > 14) stars, significantly higher than fractions based on the stellar parameters quoted in the Kepler Input Catalog (KIC). The KIC effective temperatures are systematically (110{sup +15}{sub -35} K) higher than temperatures we determine from fitting our spectra to PHOENIX stellar models. Through Monte Carlo simulations of the Kepler exoplanet candidate population, we find a planet occurrence of 0.36 {+-} 0.08 when giant stars are properly removed, somewhat higher than when a KIC log g > 4 criterion is used (0.27 {+-} 0.05). Last, we show that there is no significant difference in g - r color (a probe of metallicity) between late-type Kepler stars with transiting Earth-to-Neptune-size exoplanet candidates and dwarf stars with no detected transits. We show that a previous claimed offset between these two populations is most likely an artifact of including a large number of misidentified giants.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

THE NEPTUNE-SIZED CIRCUMBINARY PLANET KEPLER-38b

We discuss the discovery and characterization of the circumbinary planet Kepler-38b. The stellar binary is single-lined, with a period of 18.8 days, and consists of a moderately evolved main-sequence star (M{sub A} = 0.949 {+-} 0.059 M {sub Sun} and R{sub A} = 1.757 {+-} 0.034 R {sub Sun }) paired with a low-mass star (M{sub B} = 0.249 {+-} 0.010 M {sub Sun} and R{sub B} = 0.2724 {+-} 0.0053 R {sub Sun }) in a mildly eccentric (e = 0.103) orbit. A total of eight transits due to a circumbinary planet crossing the primary star were identified in the Kepler light curve (using Kepler Quarters 1-11), from which a planetary period of 105.595 {+-} 0.053 days can be established. A photometric dynamical model fit to the radial velocity curve and Kepler light curve yields a planetary radius of 4.35 {+-} 0.11 R {sub Circled-Plus }, or equivalently 1.12 {+-} 0.03 R {sub Nep}. Since the planet is not sufficiently massive to observably alter the orbit of the binary from Keplerian motion, we can only place an upper limit on the mass of the planet of 122 M {sub Circled-Plus} (7.11 M {sub Nep} or equivalently 0.384 M {sub Jup}) at 95% confidence. This upper limit should decrease as more Kepler data become available.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

ARCHITECTURE OF PLANETARY SYSTEMS BASED ON KEPLER DATA: NUMBER OF PLANETS AND COPLANARITY

We investigated the underlying architecture of planetary systems by deriving the distribution of planet multiplicity (number of planets) and the distribution of orbital inclinations based on the sample of planet candidates discovered by the Kepler mission. The scope of our study included solar-like stars and planets with orbital periods less than 200 days and with radii between 1.5 and 30 Earth radii, and was based on Kepler planet candidates detected during Quarters 1-6. We created models of planetary systems with different distributions of planet multiplicity and inclinations, simulated observations of these systems by Kepler, and compared the properties of the transits of detectable objects to actual Kepler planet detections. Specifically, we compared with both the Kepler sample's transit numbers and normalized transit duration ratios in order to determine each model's goodness of fit. We did not include any constraints from radial velocity surveys. Based on our best-fit models, 75%-80% of planetary systems have one or two planets with orbital periods less than 200 days. In addition, over 85% of planets have orbital inclinations less than 3 Degree-Sign (relative to a common reference plane). This high degree of coplanarity is comparable to that seen in our solar system. These results have implications for planet formation and evolution theories. Low inclinations are consistent with planets forming in a protoplanetary disk, followed by evolution without significant and lasting perturbations from other bodies capable of increasing inclinations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

CANDIDATE PLANETS IN THE HABITABLE ZONES OF KEPLER STARS

A key goal of the Kepler mission is the discovery of Earth-size transiting planets in ''habitable zones'' where stellar irradiance maintains a temperate climate on an Earth-like planet. Robust estimates of planet radius and irradiance require accurate stellar parameters, but most Kepler systems are faint, making spectroscopy difficult and prioritization of targets desirable. The parameters of 2035 host stars were estimated by Bayesian analysis and the probabilities p{sub HZ} that 2738 candidate or confirmed planets orbit in the habitable zone were calculated. Dartmouth Stellar Evolution Program models were compared to photometry from the Kepler Input Catalog, priors for stellar mass, age, metallicity and distance, and planet transit duration. The analysis yielded probability density functions for calculating confidence intervals of planet radius and stellar irradiance, as well as p{sub HZ}. Sixty-two planets have p{sub HZ} > 0.5 and a most probable stellar irradiance within habitable zone limits. Fourteen of these have radii less than twice the Earth; the objects most resembling Earth in terms of radius and irradiance are KOIs 2626.01 and 3010.01, which orbit late K/M-type dwarf stars. The fraction of Kepler dwarf stars with Earth-size planets in the habitable zone ({eta}{sub Circled-Plus }) is 0.46, with a 95% confidence interval of 0.31-0.64. Parallaxes from the Gaia mission will reduce uncertainties by more than a factor of five and permit definitive assignments of transiting planets to the habitable zones of Kepler stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

KEPLER PLANETS: A TALE OF EVAPORATION

Inspired by the Kepler mission's planet discoveries, we consider the thermal contraction of planets close to their parent star, under the influence of evaporation. The mass-loss rates are based on hydrodynamic models of evaporation that include both X-ray and EUV irradiation. We find that only low mass planets with hydrogen envelopes are significantly affected by evaporation, with evaporation being able to remove massive hydrogen envelopes inward of ∼0.1 AU for Neptune-mass objects, while evaporation is negligible for Jupiter-mass objects. Moreover, most of the evaporation occurs in the first 100 Myr of stars' lives when they are more chromospherically active. We construct a theoretical population of planets with varying core masses, envelope masses, orbital separations, and stellar spectral types, and compare this population with the sizes and densities measured for low-mass planets, both in the Kepler mission and from radial velocity surveys. This exercise leads us to conclude that evaporation is the driving force of evolution for close-in Kepler planets. In fact, some 50% of the Kepler planet candidates may have been significantly eroded. Evaporation explains two striking correlations observed in these objects: a lack of large radius/low density planets close to the stars and a possible bimodal distribution in planet sizes with a deficit of planets around 2 R{sub ⊕}. Planets that have experienced high X-ray exposures are generally smaller than this size, and those with lower X-ray exposures are typically larger. A bimodal planet size distribution is naturally predicted by the evaporation model, where, depending on their X-ray exposure, close-in planets can either hold on to hydrogen envelopes ∼0.5%-1% in mass or be stripped entirely. To quantitatively reproduce the observed features, we argue that not only do low-mass Kepler planets need to be made of rocky cores surrounded with hydrogen envelopes, but few of them should have initial masses above 20 M{sub ⊕} and the majority of them should have core masses of a few Earth masses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Phase curves of the Kepler-11 multi-planet system

The Kepler mission has allowed the detection of numerous multi-planet exosystems where the planetary orbits are relatively compact. The first such system detected was Kepler-11 which has six known planets at the present time. These kinds of systems offer unique opportunities to study constraints on planetary albedos by taking advantage of both the precision timing and photometry provided by Kepler data to monitor possible phase variations. Here we present a case study of the Kepler-11 system in which we investigate the phase modulation of the system as the planets orbit the host star. We provide predictions of maximum phase modulation where the planets are simultaneously close to superior conjunction. We use corrected Kepler data for Q1-Q17 to determine the significance of these phase peaks. We find that data quarters where maximum phase peaks occur are better fit by a phase model than a 'null hypothesis' model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A misaligned prograde orbit for Kepler-13 Ab via doppler tomography

Transiting planets around rapidly rotating stars are not amenable to precise radial velocity observations, such as are used for planet candidate validation, as they have wide, rotationally broadened stellar lines. Such planets can, however, be observed using Doppler tomography, wherein stellar absorption line profile distortions during transit are spectroscopically resolved. This allows the validation of transiting planet candidates and the measurement of the stellar spin-planetary orbit (mis)alignment, which is an important statistical probe of planetary migration processes. We present Doppler tomographic observations that provide direct confirmation of the hot Jupiter Kepler-13 Ab and also show that the planet has a prograde, misaligned orbit with λ = 58.°6 ± 2.°0. Our measured value of the spin-orbit misalignment is in significant disagreement with the value of λ = 23° ± 4° previously measured by Barnes et al. (2011) from the gravity-darkened Kepler light curve. We also place an upper limit of 0.75 M{sub ☉} (95% confidence) on the mass of Kepler-13 C, the spectroscopic companion to Kepler-13 B, which is the proper-motion companion of the planet host star Kepler-13 A.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

determining the mass of kepler-78b with nonparametric Gaussian process estimation

Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hr. The mass of Kepler-78b has been independently reported by two teams based on radial velocity (RV) measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in RV data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the RV data sets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV data sets, giving a Doppler amplitude of 1.86 ± 0.25 m s{sup −1} and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87{sub −0.26}{sup +0.27} M{sub ⊕} is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0{sub −1.4}{sup +1.9} g cm{sup −3}. We estimate that Kepler-78b is 32% ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.

79 ASTRONOMY AND ASTROPHYSICS↗