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We present robust planet occurrence rates for Kepler planet candidates around M stars for planet radii Rp  = 0.5–4 R⊕ and orbital periods P  = 0.5–256 d using the approximate Bayesian computation technique. This work incorporates the final Kepler DR25 planet candidate catalogue and data products and augments them with updated stellar properties using Gaia DR2 and 2MASS point source catalogue. We apply a set of selection criteria to select a sample of 1746 Kepler M dwarf targets that host 89 associated planet candidates. These early-type M dwarfs and late K dwarfs were selected from cross-referenced targets using several photometric quality flags from Gaia DR2 and colour–magnitude cuts using 2MASS magnitudes. We estimate a habitable zone occurrence rate of |$f_{\textrm {M,HZ}} = 0.33^{+0.10}_{-0.12}$| for planets with 0.75–1.5 R⊕ size. We caution that occurrence rate estimates for Kepler M stars are sensitive to the choice of prior due to the small sample of target stars and planet candidates. For example, we find an occurrence rate of |$4.2^{+0.6}_{-0.6}$| or |$8.4^{+1.2}_{-1.1}$| planets per M dwarf (integrating over Rp  = 0.5–4 R⊕ and P  = 0.5–256 d) for our two choices of prior. These occurrence rates are greater than those for FGK dwarf target when compared at the same range of orbital periods, but similar to occurrence rates when computed as a function of equivalent stellar insolation. Combining our result with recent studies of exoplanet architectures indicates that most, and potentially all, early-type M dwarfs harbour planetary systems. [ABSTRACT FROM AUTHOR]

Protoplanetary discs are thought to be truncated at orbital periods of around 10 d. Therefore, the origin of rocky short-period planets with P < 10 d is a puzzle. We propose that many of these planets may form through the Type-I migration of planets locked into a chain of mutual mean motion resonances. We ran N -body simulations of planetary embryos embedded in a protoplanetary disc. The embryos experienced gravitational scatterings, collisions, disc torques, and dampening of orbital eccentricity and inclination. We then modelled Kepler observations of these planets using a forward model of both the transit probability and the detection efficiency of the Kepler pipeline. We found that planets become locked into long chains of mean motion resonances that migrate in unison. When the chain reaches the edge of the disc, the inner planets are pushed past the edge due to the disc torques acting on the planets farther out in the chain. Our simulated systems successfully reproduce the observed period distribution of short-period Kepler planets between 1 and 2 R ⊕. However, we obtain fewer closely packed short-period planets than in the Kepler sample. Our results provide valuable insight into the planet formation process, and suggests that resonance locks, migration, and dynamical instabilities play important roles in the formation and evolution of close-in small exoplanets. [ABSTRACT FROM AUTHOR]

Transit timing variations (TTVs) are a valuable tool to determine the masses and orbits of transiting planets in multiplanet systems. TTVs can be readily modelled given knowledge of the interacting planets' orbital configurations and planet–star mass ratios, but such models are highly non-linear and difficult to invert. Markov Chain Monte Carlo (MCMC) methods are often used to explore the posterior distribution for model parameters, but, due to the high correlations between parameters, non-linearity, and potential multimodality in the posterior, many samplers perform very inefficiently. Therefore, we assess the performance of several MCMC samplers that use varying degrees of geometric information about the target distribution. We generate synthetic data sets from multiple models, including the TTVFaster model and a simple sinusoidal model, and test the efficiencies of various MCMC samplers. We find that sampling efficiency can be greatly improved for all models by sampling from a parameter space transformed using an estimate of the covariance and means of the target distribution. No one sampler performs the best for all data sets. For data sets with near Gaussian posteriors, the Hamiltonian Monte Carlo sampler obtains the highest efficiencies when the step size and number of steps are properly tuned. Two samplers – Differential Evolution Monte Carlo and Geometric adaptive Monte Carlo, have consistently efficient performance for each data set. Based on differences in effective sample sizes per time, we show that the right choice of sampler can improve sampling efficiencies by several orders of magnitude. [ABSTRACT FROM AUTHOR]

We discovered an error, in which the orbital elements were incorrectly passed from the transit timing code to the long-term integrator. Erratum: "Secure Mass Measurements from Transit Timing: 10 Kepler Exoplanets between 3 and 8 M with Diverse Densities and Incident Fluxes" (2016, ApJ, 820, 39)". Erratum: "Secure Mass Measurements from Transit Timing: 10 Kepler Exoplanets between 3 and 8M with Diverse Densities and Incident Fluxes" (2016, ApJ, 820, 39)" Daniel Jontof-Hutter 1, Eric B. Ford 1, Jason F. Rowe 2, Jack J. Lissauer 3, Daniel C. Fabrycky 4, Christa Van Laerhoven 5, Eric Agol 6, Katherine M. Deck 7, Tomer Holczer 8, and Tsevi Mazeh 8 1 Department of Astronomy, Pennsylvania State University, University Park, PA 16802, USA; djontofhutter@pacific.edu 2 Département de Physique, Université de Montréal, Montréal, QC H3T 1J4, Canada 3 Space Science and Astrobiology Division, MS 245-3, NASA Ames Research Center, Moffett Field, CA 94035, USA 4 Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA 5 Canadian Institute for Theoretical Astrophysics, 60 St. George Street, Toronto, ON M5S 3H8, Canada 6 Department of Astronomy, University of Washington, Seattle, WA 98195, USA 7 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA 8 School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel Received 2021 March 26; published 2021 April 28 Supporting material: machine-readable table A typographical coding error altered the statistics of libration of the three-body angle in Kepler-60. [Extracted from the article]

ABSTRACT We present a method to confirm the planetary nature of objects in systems with multiple transiting exoplanet candidates. This method involves a Fourier-domain analysis of the deviations in the transit times from a constant period that result from dynamical interactions within the system. The combination of observed anticorrelations in the transit times and mass constraints from dynamical stability allow us to claim the discovery of four planetary systems, Kepler-25, Kepler-26, Kepler-27 and Kepler-28, containing eight planets and one additional planet candidate. [ABSTRACT FROM AUTHOR]

ABSTRACT We report observations of HD 80606 using the 10.4-m Gran Telescopio Canarias and the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) tunable filter imager. We acquired very high precision, narrow-band photometry in four bandpasses around the K i absorption feature during the 2010 January transit of HD 80606b and during out-of-transit observations conducted in 2010 January and April. We obtained differential photometric precisions of ∼2.08 × 10−4 for the in-transit flux ratio measured at 769.91 nm, which probes the K i line core. We find no significant difference in the in-transit flux ratio between observations at 768.76 and 769.91 nm. Yet, we find a difference of ∼8.09 ± 2.88 × 10−4 between these observations and observations at a longer wavelength that probes the K i wing (777.36 nm). While the presence of red noise in the transit data has a non-negligible effect on the uncertainties in the flux ratio, the 777.36-769.91 nm colour during transit shows no effects from red noise and also indicates a significant colour change, with a mean value of ∼8.99 ± 0.62 × 10−4. This large change in the colour is equivalent to a ∼4.2 per cent change in the apparent planetary radius with wavelength, which is much larger than the atmospheric scaleheight. This implies the observations probed the atmosphere at very low pressures as well as a dramatic change in the pressure at which the slant optical depth reaches unity between ∼770 and 777 nm. We hypothesize that the excess absorption may be due to K i in a high-speed wind being driven from the exoplanet's exosphere. We discuss the viability of this and alternative interpretations, including stellar limb darkening, star-spots and effects from Earth's atmosphere. We strongly encourage follow-up observations of HD 80606b to confirm the signal measured here. Finally, we discuss the future prospects for exoplanet characterization using tunable filter spectrophotometry. [ABSTRACT FROM AUTHOR]

ABSTRACT We apply standard Markov chain Monte Carlo (MCMC) analysis techniques to 50 short-period, single-planet systems discovered with radial velocity technique. We develop a new method for accessing the significance of a non-zero orbital eccentricity, namely Γ analysis, which combines the frequentist bootstrap approach with Bayesian analysis of each simulated data set. We find that the eccentricity estimations from the Γ analysis are generally consistent with the results from both the standard MCMC analysis and previous references. The Γ method is particular useful for assessing the significance of small eccentricities. Our results suggest that the current sample size is insufficient to draw robust conclusions about the roles of tidal interaction and perturbations in shaping the eccentricity distribution of short-period single-planet systems. We use a Bayesian population analysis to show that a mixture of analytical distributions is a good approximation of the underlying eccentricity distribution. For short-period planets, we find the most probable values of parameters in the analytical functions given the observed eccentricities. These analytical functions can be used in theoretical investigations or as priors for the eccentricity distribution when analysing short-period planets. As the measurement precision improves and sample size increases, the method can be applied to more complex parametrizations for the underlying distribution of eccentricity for extrasolar planetary systems. [ABSTRACT FROM AUTHOR]

When an extrasolar planet passes in front of (transits) its star, its radius can be measured from the decrease in starlight and its orbital period from the time between transits. Multiple planets transiting the same star reveal much more: period ratios determine stability and dynamics, mutual gravitational interactions reflect planet masses and orbital shapes, and the fraction of transiting planets observed as multiples has implications for the planarity of planetary systems. But few stars have more than one known transiting planet, and none has more than three. Here we report Kepler spacecraft observations of a single Sun-like star, which we call Kepler-11, that reveal six transiting planets, five with orbital periods between 10 and 47 days and a sixth planet with a longer period. The five inner planets are among the smallest for which mass and size have both been measured, and these measurements imply substantial envelopes of light gases. The degree of coplanarity and proximity of the planetary orbits imply energy dissipation near the end of planet formation. [ABSTRACT FROM AUTHOR]

ABSTRACT We investigate potential biases in the measurements of exoplanet orbital parameters obtained from radial velocity observations for single-planet systems. We create a mock catalogue of radial velocity data, choosing input planet masses, periods and observing patterns from actual radial velocity surveys and varying input eccentricities. We apply Markov chain Monte Carlo simulations and compare the resulting orbital parameters to the input values. We find that a combination of the effective signal-to-noise ratio of the data, the maximal gap in phase coverage, and the total number of periods covered by observations is a good predictor of the quality of derived orbit parameters. As eccentricity is positive definite, we find that eccentricities of planets on nearly circular orbits are preferentially overestimated, with typical bias of one to two times the median eccentricity uncertainty in a survey (e.g. 0.04 in the Butler et al. catalogue). When performing population analysis, we recommend using the mode of the marginalized posterior eccentricity distribution to minimize potential biases. While the Butler et al. catalogue reports eccentricities below 0.05 for just 17 per cent of single-planet systems, we estimate that the true fraction of e≤ 0.05 orbits is about f0.05= 38 ± 9 per cent. For planets with P > 10 d, we find f0.05= 28 ± 8 per cent versus 10 per cent from Butler et al. These planets either never acquired a large eccentricity or were circularized following any significant eccentricity excitation. [ABSTRACT FROM AUTHOR]

We report the first extrasolar planet observations from the 10.4-m Gran Telescopio Canarias (GTC), currently the world's largest, fully steerable, single-aperture optical telescope. We used the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) tunable filter imager on the GTC to acquire high-precision, narrow-band photometry of the transits of the giant exoplanets, TrES-2b and TrES-3b. We obtained near-simultaneous observations in two near-infrared wavebands (790.2 and 794.4 ± 2.0 nm) specifically chosen to avoid water vapour absorption and skyglow so as to minimize the atmospheric effects that often limit the precision of ground-based photometry. Our results demonstrate a very-high photometric precision with minimal atmospheric contamination despite relatively poor atmospheric conditions and some technical problems with the telescope. We find the photometric precision for the TrES-2 observations to be 0.343 and 0.412 mmag for the 790.2- and 794.4-nm light curves, and the precision of the TrES-3 observations was found to be 0.470 and 0.424 mmag for the 790.2- and 794.4-nm light curves, respectively. We also discuss how future follow-up observations of transiting planets with this novel technique can contribute to the characterization of Neptune- and super-Earth-size planets to be discovered by space-based missions like CoRoT and Kepler, as well as measure atmospheric properties of giant planets, such as the strength of atmospheric absorption features. [ABSTRACT FROM AUTHOR]

Doppler spectroscopy has detected 152 planets around nearby stars. A major puzzle is why many of their orbits are highly eccentric; all planets in our Solar System are on nearly circular orbits, as is expected if they formed by accretion processes in a protostellar disk. Several mechanisms have been proposed to generate large eccentricities after planet formation, but so far there has been little observational evidence to support any particular model. Here we report that the current orbital configuration of the three giant planets around upsilon Andromedae (?And) probably results from a close dynamical interaction with another planet, now lost from the system. The planets started on nearly circular orbits, but chaotic evolution caused the outer planet (?And d) to be perturbed suddenly into a higher-eccentricity orbit. The coupled evolution of the system then causes slow periodic variations in the eccentricity of the middle planet (?And c). Indeed, we show that?And c periodically returns to a very nearly circular state every 6,700 years. [ABSTRACT FROM AUTHOR]

Extrasolar planets that pass in front of their host star (transit) cause a temporary decrease in the apparent brightness of the star, providing a direct measure of the planet's size and orbital period. In some systems with multiple transiting planets, the times of the transits are measurably affected by the gravitational interactions between neighbouring planets. In favourable cases, the departures from Keplerian orbits (that is, unaffected by gravitational effects) implied by the observed transit times permit the planetary masses to be measured, which is key to determining their bulk densities. Characterizing rocky planets is particularly difficult, because they are generally smaller and less massive than gaseous planets. Therefore, few exoplanets near the size of Earth have had their masses measured. Here we report the sizes and masses of three planets orbiting Kepler-138, a star much fainter and cooler than the Sun. We determine that the mass of the Mars-sized inner planet, Kepler-138 b, is Earth masses. Its density is grams per cubic centimetre. The middle and outer planets are both slightly larger than Earth. The middle planet's density ( grams per cubic centimetre) is similar to that of Earth, and the outer planet is less than half as dense at grams per cubic centimetre, implying that it contains a greater portion of low-density components such as water and hydrogen. [ABSTRACT FROM AUTHOR]

The abundance of heavy elements (metallicity) in the photospheres of stars similar to the Sun provides a 'fossil' record of the chemical composition of the initial protoplanetary disk. Metal-rich stars are much more likely to harbour gas giant planets, supporting the model that planets form by accumulation of dust and ice particles. Recent ground-based surveys suggest that this correlation is weakened for Neptunian-sized planets. However, how the relationship between size and metallicity extends into the regime of terrestrial-sized exoplanets is unknown. Here we report spectroscopic metallicities of the host stars of 226 small exoplanet candidates discovered by NASA's Kepler mission, including objects that are comparable in size to the terrestrial planets in the Solar System. We find that planets with radii less than four Earth radii form around host stars with a wide range of metallicities (but on average a metallicity close to that of the Sun), whereas large planets preferentially form around stars with higher metallicities. This observation suggests that terrestrial planets may be widespread in the disk of the Galaxy, with no special requirement of enhanced metallicity for their formation. [ABSTRACT FROM AUTHOR]

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 (MA = 0.949 ± 0.059 M☼ and RA = 1.757 ± 0.034 R☼) paired with a low-mass star (MB = 0.249 ± 0.010 M☼ and RB = 0.2724 ± 0.0053 R☼) 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⊕, or equivalently 1.12 ± 0.03 RNep. 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⊕ (7.11 MNep or equivalently 0.384 MJup) at 95% confidence. This upper limit should decrease as more Kepler data become available. [ABSTRACT FROM AUTHOR]

The chance that a planetary system will interact with another member of its host star's nascent cluster would be greatly increased if gas giant planets form in situ on wide orbits. In this paper, we explore the outcomes of planet-planet scattering for a distribution of multi-planet systems that all have one of the planets on an initial orbit of 100 AU. The scattering experiments are run with and without stellar flybys. We convolve the outcomes with distributions for protoplanetary disk and stellar cluster sizes to generalize the results where possible. We find that the frequencies of large mutual inclinations and high eccentricities are sensitive to the number of planets in a system, but not strongly to stellar flybys. However, flybys do play a role in changing the low and moderate portions of the mutual inclination distributions, and erase dynamically cold initial conditions on average. Wide-orbit planets can be mixed throughout the planetary system, and in some cases, can potentially become hot Jupiters, which we demonstrate using scattering experiments that include a tidal damping model. If planets form in situ on wide orbits, then there will be discernible differences in the proper-motion distributions of a sample of wide-orbit planets compared with a pure scattering formation mechanism. Stellar flybys can enhance the frequency of ejections in planetary systems, but autoionization is likely to remain the dominant source of free-floating planets. [ABSTRACT FROM AUTHOR]

We report the detection of a planet whose orbit surrounds a pair of low-mass stars. Data from the Kepler spacecraft reveal transits of the planet across both stars, in addition to the mutual eclipses of the stars, giving precise constraints on the absolute dimensions of all three bodies. The planet is comparable to Saturn in mass and size and is on a nearly circular 229-day orbit around its two parent stars. The eclipsing stars are 20 and 69% as massive as the Sun and have an eccentric 41-day orbit. The motions of all three bodies are confined to within 0.5° of a single plane, suggesting that the planet formed within a circumbinary disk. [ABSTRACT FROM AUTHOR]

The Kepler spacecraft is monitoring more than 150,000 stars for evidence of planets transiting those stars. We report the detection of two Saturn-size planets that transit the same Sun-like star, based on 7 months of Kepler observations. Their 19.2- and 38.9-day periods are presently increasing and decreasing at respective average rates of 4 and 39 minutes per orbit; in addition, the transit times of the inner body display an alternating variation of smaller amplitude. These signatures are characteristic of gravitational interaction of two planets near a 2:1 orbital resonance. Six radial-velocity observations show that these two planets are the most massive objects orbiting close to the star and substantially improve the estimates of their masses. After removing the signal of the two confirmed giant planets, we identified an additional transiting super-Earth-size planet candidate with a period of 1.6 days. [ABSTRACT FROM AUTHOR]