ABSTRACT. The original Kepler mission achieved high photometric precision thanks to ultrastable pointing enabled by use of four reaction wheels. The loss of two of these reaction wheels reduced the telescope's ability to point precisely for extended periods of time, and as a result, the photometric precision has suffered. We present a technique for generating photometric light curves from pixel-level data obtained with the two-wheeled extended Kepler mission, K2. Our photometric technique accounts for the nonuniform pixel response function of the Kepler detectors by correlating flux measurements with the spacecraft's pointing and removing the dependence. When we apply our technique to the ensemble of stars observed during the Kepler Two-Wheel Concept Engineering Test, we find improvements over raw K2 photometry by factors of 2-5, with noise properties qualitatively similar to Kepler targets at the same magnitudes. We find evidence that the improvement in photometric precision depends on each target's position in the Kepler field of view, with worst precision near the edges of the field. Overall, this technique restores the median-attainable photometric precision within a factor of two of the original Kepler photometric precision for targets ranging from 10th to 15th magnitude in the Kepler bandpass, peaking with a median precision within 35% to that of Kepler for stars between 12th and 13th magnitude in the Kepler bandpass.

Most stars become white dwarfs after they have exhausted their nuclear fuel (the Sun will be one such). Between one-quarter and one-half of white dwarfs have elements heavier than helium in their atmospheres, even though these elements ought to sink rapidly into the stellar interiors (unless they are occasionally replenished). The abundance ratios of heavy elements in the atmospheres of white dwarfs are similar to the ratios in rocky bodies in the Solar System. This fact, together with the existence of warm, dusty debris disks surrounding about four per cent of white dwarfs, suggests that rocky debris from the planetary systems of white-dwarf progenitors occasionally pollutes the atmospheres of the stars. The total accreted mass of this debris is sometimes comparable to the mass of large asteroids in the Solar System. However, rocky, disintegrating bodies around a white dwarf have not yet been observed. Here we report observations of a white dwarf--WD 1145+017--being transited by at least one, and probably several, disintegrating planetesimals, with periods ranging from 4.5 hours to 4.9 hours. The strongest transit signals occur every 4.5 hours and exhibit varying depths (blocking up to 40 per cent of the star's brightness) and asymmetric profiles, indicative of a small object with a cometary tail of dusty effluent material. The star has a dusty debris disk, and the star's spectrum shows prominent lines from heavy elements such as magnesium, aluminium, silicon, calcium, iron, and nickel. This system provides further evidence that the pollution of white dwarfs by heavy elements might originate from disrupted rocky bodies such as asteroids and minor planets.

Context. Transiting super-Earths orbiting bright stars in short orbital periods are interesting targets for the study of planetary atmospheres. Aims. While selecting super-Earths suitable for further characterization from the ground among a list of confirmed and validated exoplanets detected by K2, we found some suspicious cases that led to us reassessing the nature of the detected transiting signal. Methods. We did a photometric analysis of the K2 light curves and centroid motions of the photometric barycenters. Results. Our study shows that the validated planets K2-78b, K2-82b, and K2-92b are actually not planets but background eclipsing binaries. The eclipsing binaries are inside the Kepler photometric aperture, but outside the ground-based high resolution images used for validation. Conclusions. We advise extreme care on the validation of candidate planets discovered by space missions. It is important that all the assumptions in the validation process are carefully checked. An independent confirmation is mandatory in order to avoid wasting valuable resources on further characterization of non-existent targets.

The radii and orbital periods of 4000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. Yet an important question about the composition of planets ranging from 2 to 4 Earth radii (RÅ) still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multi-component, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 MÅ, if half-ice and half-rock by mass, have radii of 2.5 RÅ, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2-4 RÅ range requires a gas envelope of at most a few mass%, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are "water worlds". Keywords: exoplanets / bimodal distribution / ices / water worlds / planet formation Significance Statement: The discovery of numerous exoplanet systems containing diverse populations of planets orbiting very close to their host stars challenges the planet formation theories based on the Solar system. Here we focus on the planets with radii of 2-4 RÅ, whose compositions are debated. They are thought to be either gas dwarfs consisting of rocky cores embedded in H2-rich gas envelopes or water worlds containing significant amounts of H2Odominated fluid/ice in addition to rock and gas. We argue that these planets are water worlds.

NASA's Kepler Space Telescope was designed to determine the frequency of Earth-sized planets orbiting Sun-like stars, but these planets are on the very edge of the mission's detection sensitivity. Accurately determining the occurrence rate of these planets will require automatically and accurately assessing the likelihood that individual candidates are indeed planets, even at low signal-to-noise ratios. We present a method for classifying potential planet signals using deep learning, a class of machine learning algorithms that have recently become state-of-theart in a wide variety of tasks. We train a deep convolutional neural network to predict whether a given signal is a transiting exoplanet or a false positive caused by astrophysical or instrumental phenomena. Our model is highly effective at ranking individual candidates by the likelihood that they are indeed planets: 98.8% of the time it ranks plausible planet signals higher than false-positive signals in our test set. We apply our model to a new set of candidate signals that we identified in a search of known Kepler multi-planet systems. We statistically validate two new planets that are identified with high confidence by our model. One of these planets is part of a five-planet resonant chain around Kepler-80, with an orbital period closely matching the prediction by three-body Laplace relations. The other planet orbits Kepler-90, a star that was previously known to host seven transiting planets. Our discovery of an eighth planet brings Kepler-90 into a tie with our Sun as the star known to host the most planets.