arXiv subjects

Daniel Fabrycky

Publications and source records attributed to Daniel Fabrycky.

At least 37 records · Page 2Linked to original sources

arXiv2019

The Gemini Planet Imager Exoplanet Survey: Giant Planet and Brown Dwarf Demographics From 10-100 AU

We present a statistical analysis of the first 300 stars observed by the Gemini Planet Imager Exoplanet Survey (GPIES). This subsample includes six detected planets and three brown dwarfs; from these detections and our contrast curves we infer the underlying distributions of substellar companions with respect to their mass, semi-major axis, and host stellar mass. We uncover a strong correlation between planet occurrence rate and host star mass, with stars M $>$ 1.5 $M_\odot$ more likely to host planets with masses between 2-13 M$_{\rm Jup}$ and semi-major axes of 3-100 au at 99.92% confidence. We fit a double power-law model in planet mass (m) and semi-major axis (a) for planet populations around high-mass stars (M $>$ 1.5M$_\odot$) of the form $\frac{d^2 N}{dm da} \propto m^αa^β$, finding $α$ = -2.4 $\pm$ 0.8 and $β$ = -2.0 $\pm$ 0.5, and an integrated occurrence rate of $9^{+5}_{-4}$% between 5-13 M$_{\rm Jup}$ and 10-100 au. A significantly lower occurrence rate is obtained for brown dwarfs around all stars, with 0.8$^{+0.8}_{-0.5}$% of stars hosting a brown dwarf companion between 13-80 M$_{\rm Jup}$ and 10-100 au. Brown dwarfs also appear to be distributed differently in mass and semi-major axis compared to giant planets; whereas giant planets follow a bottom-heavy mass distribution and favor smaller semi-major axes, brown dwarfs exhibit just the opposite behaviors. Comparing to studies of short-period giant planets from the RV method, our results are consistent with a peak in occurrence of giant planets between ~1-10 au. We discuss how these trends, including the preference of giant planets for high-mass host stars, point to formation of giant planets by core/pebble accretion, and formation of brown dwarfs by gravitational instability.

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arXiv2018

Dynamical Constraints on the HR 8799 Planets with GPI

The HR 8799 system uniquely harbors four young super-Jupiters whose orbits can provide insights into the system's dynamical history and constrain the masses of the planets themselves. Using the Gemini Planet Imager (GPI), we obtained down to one milliarcsecond precision on the astrometry of these planets. We assessed four-planet orbit models with different levels of constraints and found that assuming the planets are near 1:2:4:8 period commensurabilities, or are coplanar, does not worsen the fit. We added the prior that the planets must have been stable for the age of the system (40 Myr) by running orbit configurations from our posteriors through $N$-body simulations and varying the masses of the planets. We found that only assuming the planets are both coplanar and near 1:2:4:8 period commensurabilities produces dynamically stable orbits in large quantities. Our posterior of stable coplanar orbits tightly constrains the planets' orbits, and we discuss implications for the outermost planet b shaping the debris disk. A four-planet resonance lock is not necessary for stability up to now. However, planet pairs d and e, and c and d, are each likely locked in two-body resonances for stability if their component masses are above $6~M_{\rm{Jup}}$ and $7~M_{\rm{Jup}}$, respectively. Combining the dynamical and luminosity constraints on the masses using hot-start evolutionary models and a system age of $42 \pm 5$~Myr, we found the mass of planet b to be $5.8 \pm 0.5~M_{\rm{Jup}}$, and the masses of planets c, d, and e to be $7.2_{-0.7}^{+0.6}~M_{\rm{Jup}}$ each.

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arXiv2018

The nature of the TRAPPIST-1 exoplanets

Context. The TRAPPIST-1 system hosts seven Earth-sized, temperate exoplanets orbiting an ultra-cool dwarf star. As such, it represents a remarkable setting to study the formation and evolution of terrestrial planets that formed in the same protoplanetary disk. While the sizes of the TRAPPIST-1 planets are all known to better than 5% precision, their densities have significant uncertainties (between 28% and 95%) because of poor constraints on the planet's masses. Aims.The goal of this paper is to improve our knowledge of the TRAPPIST-1 planetary masses and densities using transit-timing variations (TTV). The complexity of the TTV inversion problem is known to be particularly acute in multi-planetary systems (convergence issues, degeneracies and size of the parameter space), especially for resonant chain systems such as TRAPPIST-1. Methods. To overcome these challenges, we have used a novel method that employs a genetic algorithm coupled to a full N-body integrator that we applied to a set of 284 individual transit timings. This approach enables us to efficiently explore the parameter space and to derive reliable masses and densities from TTVs for all seven planets. Results. Our new masses result in a five- to eight-fold improvement on the planetary density uncertainties, with precisions ranging from 5% to 12%. These updated values provide new insights into the bulk structure of the TRAPPIST-1 planets. We find that TRAPPIST-1\,c and e likely have largely rocky interiors, while planets b, d, f, g, and h require envelopes of volatiles in the form of thick atmospheres, oceans, or ice, in most cases with water mass fractions less than 5%.

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arXiv2017

Evidence that the Directly-Imaged Planet HD 131399 Ab is a Background Star

We present evidence that the recently discovered, directly-imaged planet HD 131399 Ab is a background star with non-zero proper motion. From new JHK1L' photometry and spectroscopy obtained with the Gemini Planet Imager, VLT/SPHERE, and Keck/NIRC2, and a reanalysis of the discovery data obtained with VLT/SPHERE, we derive colors, spectra, and astrometry for HD 131399 Ab. The broader wavelength coverage and higher data quality allow us to re-investigate its status. Its near-infrared spectral energy distribution excludes spectral types later than L0 and is consistent with a K or M dwarf, which are the most likely candidates for a background object in this direction at the apparent magnitude observed. If it were a physically associated object, the projected velocity of HD 131399 Ab would exceed escape velocity given the mass and distance to HD 131399 A. We show that HD 131399 Ab is also not following the expected track for a stationary background star at infinite distance. Solving for the proper motion and parallax required to explain the relative motion of HD 131399 Ab, we find a proper motion of 12.3 mas/yr. When compared to predicted background objects drawn from a galactic model, we find this proper motion to be high, but consistent with the top 4% fastest-moving background stars. From our analysis we conclude that HD 131399 Ab is a background K or M dwarf.

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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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arXiv2016

Outer-planet scattering can gently tilt an inner planetary system

Chaotic dynamics are expected during and after planet formation, and a leading mechanism to explain large eccentricities of gas giant exoplanets is planet-planet gravitational scattering. The same scattering has been invoked to explain misalignments of planetary orbital planes with respect to their host star's spin. However, an observational puzzle is presented by Kepler-56, which has two inner planets (b and c) that are nearly coplanar with each other, yet are more than 45 degrees inclined to their star's equator. Thus the spin-orbit misalignment might be primordial. Instead, we further develop the hypothesis in the discovery paper, that planets on wider orbits generated misalignment through scattering, and as a result gently torqued the inner planets away from the equator plane of the star. We integrated the equations of motion for Kepler-56 b and c along with an unstable outer system initialized with either two or three Jupiter-mass planets. We address here whether the violent scattering that generates large mutual inclinations can leave the inner system intact, tilting it gently. In almost all of the cases initially with two outer planets, either the inner planets remain nearly coplanar with each other in the star's equator plane, or they are scattered violently to high mutual inclination and high spin-orbit misalignment. On the contrary, of the systems with three unstable outer planets, a spin-orbit misalignment large enough to explain the observations is generated 28% of the time for coplanar inner planets, which is consistent with the observed frequency of this phenomenon reported so far. We conclude that multiple-planet scattering in the outer parts of the system may account for this new population of coplanar planets hosted by oblique stars.

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arXiv2016

Transit Timing Observations from Kepler. IX. Catalog of the Full Long-Cadence Data Set

We present a new transit timing catalog of 2599 Kepler Objects of Interest (=KOIs), using the PDC-MAP long-cadence light curves that include the full seventeen quarters of the mission (ftp://wise- ftp.tau.ac.il/pub/tauttv/TTV/ver_112). The goal is to produce an easy-to-use catalog that can stimulate further analyses of interesting systems. For 779 KOIs with high enough SNRs, we derived the timing, duration and depth of 69,914 transits. For 1820 KOIs with lower SNR, we derived only the timing of 225,273 transits. After removal of outlier timings, we derived various statistics for each KOI that were used to indicate significant variations. Including systems found by previous works, we have detected 260 KOIs which showed significant TTVs with long-term variations (>100 day), and another fourteen KOIs with periodic modulations shorter than 100 day and small amplitudes. For five of those, the periodicity is probably due to the crossing of rotating stellar spots by the transiting planets.

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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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arXiv2014

A Hubble Space Telescope Search for a Sub-Earth-Sized Exoplanet in the GJ 436 System

The detection of small planets orbiting nearby stars is an important step towards the identification of Earth twins. In previous work using the Spitzer Space Telescope, we found evidence to support at least one sub-Earth-sized exoplanet orbiting the nearby mid-M dwarf star GJ 436. As a follow up, here we used the Hubble Space Telescope to investigate the existence of one of these candidate planets, UCF-1.01, by searching for two transit signals as it passed in front of its host star. Interpretation of the data hinges critically on correctly modeling and removing the WFC3 instrument systematics from the light curves. Building on previous HST work, we demonstrate that WFC3 analyses need to explore the use of a quadratic function to fit a visit-long time-dependent systematic. This is important for establishing absolute transit and eclipse depths in the white light curves of all transiting systems. The work presented here exemplifies this point by putatively detecting the primary transit of UCF-1.01 with the use of a linear trend. However, using a quadratic trend, we achieve a better fit to the white light curves and a reduced transit depth that is inconsistent with previous Spitzer measurements. Furthermore, quadratic trends with or without a transit model component produce comparable fits to the available data. Using extant WFC3 transit light curves for GJ436b, we further validate the quadratic model component by achieving photon-limited model fit residuals and consistent transit depths over multiple epochs. We conclude that, when we fit for a quadratic trend, our new data contradict the prediction of a sub-Earth-sized planet orbiting GJ 436 with the size, period, and ephemeris posited from the Spitzer data by a margin of 3.1σ.

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arXiv2014

Gemini Planet Imager Observational Calibrations V: Astrometry and Distortion

We present the results of both laboratory and on sky astrometric characterization of the Gemini Planet Imager (GPI). This characterization includes measurement of the pixel scale of the integral field spectrograph (IFS), the position of the detector with respect to north, and optical distortion. Two of these three quantities (pixel scale and distortion) were measured in the laboratory using two transparent grids of spots, one with a square pattern and the other with a random pattern. The pixel scale in the laboratory was also estimate using small movements of the artificial star unit (ASU) in the GPI adaptive optics system. On sky, the pixel scale and the north angle are determined using a number of known binary or multiple systems and Solar System objects, a subsample of which had concurrent measurements at Keck Observatory. Our current estimate of the GPI pixel scale is 14.14 $\pm$ 0.01 millarcseconds/pixel, and the north angle is -1.00 $\pm$ 0.03$°$. Distortion is shown to be small, with an average positional residual of 0.26 pixels over the field of view, and is corrected using a 5th order polynomial. We also present results from Monte Carlo simulations of the GPI Exoplanet Survey (GPIES) assuming GPI achieves ~1 milliarcsecond relative astrometric precision. We find that with this precision, we will be able to constrain the eccentricities of all detected planets, and possibly determine the underlying eccentricity distribution of widely separated Jovians.

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arXiv2014

Compact planetary systems perturbed by an inclined companion: I. Vectorial representation of the secular model

The non-resonant secular dynamics of compact planetary systems are modeled by a perturbing function which is usually expanded in eccentricity and absolute inclination with respect to the invariant plane. Here, the expressions are given in a vectorial form which naturally leads to an expansion in eccentricity and mutual inclination. The two approaches are equivalent in most cases, but the vectorial one is specially designed for those where a quasi-coplanar system tilts as a whole by a large amount. Moreover, the vectorial expressions of the Hamiltonian and of the equations of motion are slightly simpler than those given in terms of the usual elliptical elements. We also provide the secular perturbing function in vectorial form expanded in semimajor axis ratio allowing for arbitrary eccentricities and inclinations. The interaction between the equatorial bulge of a central star and its planets is also provided, as is the relativistic periapse precession of any planet induced by the central star. We illustrate the use of this representation for following the secular oscillations of the terrestrial planets of the solar system, and for Kozai cycles as may take place in exoplanetary systems.

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arXiv2014

Compact planetary systems perturbed by an inclined companion: II. Stellar spin-orbit evolution

The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an inclined outer companion. Our study is based on classical secular theory, using a vectorial approach developed in a separate paper. When planet-planet perturbations are truncated at the second order in eccentricity and mutual inclination, and the planet-companion perturbations are developed at the quadrupole order, the problem becomes integrable. The motion is composed of a uniform precession of the whole system around the total angular momentum, and in the rotating frame, the evolution is periodic. Here, we focus on the relative motion associated to the oscillations of the inclination between the planet system and the outer orbit, and of the obliquities of the star with respect to the two orbital planes. The solution is obtained using a powerful geometric method. With this technique, we identify four different regimes characterized by the nutation amplitude of the stellar spin-axis relative to the orbital plane of the planets. In particular, the obliquity of the star reaches its maximum when the system is in the Cassini regime where planets have more angular momentum than the star, and where the precession rate of the star is similar to that of the planets induced by the companion. In that case, spin-orbit oscillations exceed twice the inclination between the planets and the companion. Even if mutual inclination is only ~ 20 deg, this resonant case can cause the spin-orbit angle to oscillate between perfectly aligned and retrograde values.

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arXiv2013

NEOKepler: Discovering Near-Earth Objects Using the Kepler Spacecraft

We propose a new Kepler mission, called NEOKepler, that would survey near Earth's orbit to identify potentially hazardous objects (PHOs). To understand its surveying power, Kepler's large field of view produces an 'etendue' (A*Omega) that is 4.5 times larger than the best survey telescope currently in operation. In this paper, we investigate the feasibility of NEOKepler using a double "fence post" survey pattern that efficiently detects PHOs. In a simulated 12-month survey, we estimate that NEOKepler would detect ~150 new NEOs with absolute magnitudes of less than 21.5, ~50 of which would be new PHOs. This would increase the annual PHO discovery rate by at least 50% and improve upon our goal of discovering 90% of PHOs by the end of 2020. Due to its heliocentric orbit, Kepler would also be sensitive to objects inside Earth's orbit, discovering more objects in its first year than are currently known to exist. Understanding this undersampled sub-population of NEOs will reveal new insights into the actual PHO distribution by further constraining current NEO models. As an alternative science goal, NEOKepler could employ a different observing strategy to discover suitable targets for NASA's Asteroid Redirect Mission.

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arXiv2012

Observational constraints on tidal effects using orbital eccentricities

We have analysed radial velocity measurements for known transiting exoplanets to study the empirical signature of tidal orbital evolution for close-in planets. Compared to standard eccentricity determination, our approach is modified to focus on the rejection of the null hypothesis of a circular orbit. We are using a MCMC analysis of radial velocity measurements and photometric constraints, including a component of correlated noise, as well as Bayesian model selection to check if the data justifies the additional complexity of an eccentric orbit. We find that among planets with non-zero eccentricity values quoted in the literature, there is no evidence for an eccentricity detection for the 7 planets CoRoT-5b, WASP-5b, WASP-6b, WASP-10b, WASP-12b, WASP-17b, and WASP-18b. In contrast, we confirm the eccentricity of HAT-P-16b, e=0.034\pm0.003, the smallest eccentricity that is reliably measured so far for an exoplanet as well as that of WASP-14b, which is the planet at the shortest period (P=2.24 d), with a confirmed eccentricity, e= 0.088\pm0.003. As part of the study, we present new radial velocity data using the HARPS spectrograph for CoRoT-1, CoRoT-3, WASP-2, WASP-4, WASP-5 and WASP-7 as well as the SOPHIE spectrograph for HAT-P-4, HAT-P-7, TrES-2 and XO-2. We show that the dissipative effect of tides raised in the planet by the star and vice-versa explain all the eccentricity and spin-orbit alignment measurements available for transiting planets. We revisit the mass-period relation (Mazeh et al. 2005, Pont 2011) and consider its relation to the stopping mechanism of orbital migration for hot Jupiters. In addition to CoRoT-2 and HD 189733 (Pont 2009), we find evidence for excess rotation of the star in the systems CoRoT-18, HAT-P-20, WASP-19 and WASP-43.

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arXiv2011

Kepler-22b: A 2.4 Earth-radius Planet in the Habitable Zone of a Sun-like Star

A search of the time-series photometry from NASA's Kepler spacecraft reveals a transiting planet candidate orbiting the 11th magnitude G5 dwarf KIC 10593626 with a period of 290 days. The characteristics of the host star are well constrained by high-resolution spectroscopy combined with an asteroseismic analysis of the Kepler photometry, leading to an estimated mass and radius of 0.970 +/- 0.060 MSun and 0.979 +/- 0.020 RSun. The depth of 492 +/- 10ppm for the three observed transits yields a radius of 2.38 +/- 0.13 REarth for the planet. The system passes a battery of tests for false positives, including reconnaissance spectroscopy, high-resolution imaging, and centroid motion. A full BLENDER analysis provides further validation of the planet interpretation by showing that contamination of the target by an eclipsing system would rarely mimic the observed shape of the transits. The final validation of the planet is provided by 16 radial velocities obtained with HIRES on Keck 1 over a one year span. Although the velocities do not lead to a reliable orbit and mass determination, they are able to constrain the mass to a 3σ upper limit of 124 MEarth, safely in the regime of planetary masses, thus earning the designation Kepler-22b. The radiative equilibrium temperature is 262K for a planet in Kepler-22b's orbit. Although there is no evidence that Kepler-22b is a rocky planet, it is the first confirmed planet with a measured radius to orbit in the Habitable Zone of any star other than the Sun.

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arXiv2011

The Kepler-19 System: A Transiting 2.2 R_Earth Planet and a Second Planet Detected via Transit Timing Variations

We present the discovery of the Kepler-19 planetary system, which we first identified from a 9.3-day periodic transit signal in the Kepler photometry. From high-resolution spectroscopy of the star, we find a stellar effective temperature Teff=5541 \pm 60 K, a metallicity [Fe/H]=-0.13 \pm 0.06, and a surface gravity log(g)=4.59 \pm 0.10. We combine the estimate of Teff and [Fe/H] with an estimate of the stellar density derived from the photometric light curve to deduce a stellar mass of M_star = 0.936 \pm 0.040 M_Sun and a stellar radius of R_star = 0.850 \pm 0.018 R_Sun. We rule out the possibility that the transits result from an astrophysical false positive by first identifying the subset of stellar blends that reproduce the precise shape of the light curve. We conclude that the planetary scenario is more than three orders of magnitude more likely than a blend. The blend scenario is independently disfavored by the achromaticity of the transit: we measure a transit depth with Spitzer at 4.5 μm of 547+113-110 ppm, consistent with the depth measured in the Kepler optical bandpass of 567\pm6 ppm. We determine a physical radius of the planet Kepler-19b of R_p = 2.209 \pm 0.048 R_Earth. From radial-velocity observations of the star, we find an upper limit on the planet mass of 20.3 M_Earth, corresponding to a maximum density of 10.4 g cm^-3. We report a significant sinusoidal deviation of the transit times from a predicted linear ephemeris, which we conclude is due to an additional perturbing body in the system. We cannot uniquely determine the orbital parameters of the perturber, as various dynamical mechanisms match the amplitude, period, and shape of the transit timing signal and satisfy the host star's radial velocity limits. However, the perturber in these mechanisms has period <160 days and mass <6 M_Jup, confirming its planetary nature as Kepler-19c. [Abridged]

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arXiv2011

A Super-Earth Transiting a Naked-Eye Star

We have detected transits of the innermost planet "e" orbiting 55 Cnc (V=6.0), based on two weeks of nearly continuous photometric monitoring with the MOST space telescope. The transits occur with the period (0.74 d) and phase that had been predicted by Dawson & Fabrycky, and with the expected duration and depth for the crossing of a Sun-like star by a hot super-Earth. Assuming the star's mass and radius to be 0.963_{-0.029}^{+0.051} M_sun and 0.943 +/- 0.010 R_sun, the planet's mass, radius, and mean density are 8.63 +/- 0.35 Mearth, 2.00 +/- 0.14 Rearth, and 5.9_{-1.1}^{+1.5} g/cm^3. The mean density is comparable to that of Earth, despite the greater mass and consequently greater compression of the interior of 55 Cnc e. This suggests a rock-iron composition supplemented by a significant mass of water, gas, or other light elements. Outside of transits, we detected a sinusoidal signal resembling the expected signal due to the changing illuminated phase of the planet, but with a full range (168 +/- 70 ppm) too large to be reflected light or thermal emission. This signal has no straightforward interpretation and should be checked with further observations. The host star of 55 Cnc e is brighter than that of any other known transiting planet, which will facilitate future investigations.

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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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