When the core hydrogen is exhausted during stellar evolution, the central region of a star contracts and the outer envelope expands and cools, giving rise to a red giant. Convection takes place over ...much of the star's radius. Conservation of angular momentum requires that the cores of these stars rotate faster than their envelopes; indirect evidence supports this. Information about the angular-momentum distribution is inaccessible to direct observations, but it can be extracted from the effect of rotation on oscillation modes that probe the stellar interior. Here we report an increasing rotation rate from the surface of the star to the stellar core in the interiors of red giants, obtained using the rotational frequency splitting of recently detected 'mixed modes'. By comparison with theoretical stellar models, we conclude that the core must rotate at least ten times faster than the surface. This observational result confirms the theoretical prediction of a steep gradient in the rotation profile towards the deep stellar interior.
ABSTRACT Kepler provides light curves of 156,000 stars with unprecedented precision. However, the raw data as they come from the spacecraft contain significant systematic and stochastic errors. These ...errors, which include discontinuities, systematic trends, and outliers, obscure the astrophysical signals in the light curves. To correct these errors is the task of the Presearch Data Conditioning (PDC) module of the Kepler data analysis pipeline. The original version of PDC in Kepler did not meet the extremely high performance requirements for the detection of miniscule planet transits or highly accurate analysis of stellar activity and rotation. One particular deficiency was that astrophysical features were often removed as a side effect of the removal of errors. In this article we introduce the completely new and significantly improved version of PDC which was implemented in Kepler SOC version 8.0. This new PDC version, which utilizes a Bayesian approach for removal of systematics, reliably corrects errors in the light curves while at the same time preserving planet transits and other astrophysically interesting signals. We describe the architecture and the algorithms of this new PDC module, show typical errors encountered in Kepler data, and illustrate the corrections using real light curve examples.
ABSTRACT With the unprecedented photometric precision of the Kepler spacecraft, significant systematic and stochastic errors on transit signal levels are observable in the Kepler photometric data. ...These errors, which include discontinuities, outliers, systematic trends, and other instrumental signatures, obscure astrophysical signals. The presearch data conditioning (PDC) module of the Kepler data analysis pipeline tries to remove these errors while preserving planet transits and other astrophysically interesting signals. The completely new noise and stellar variability regime observed in Kepler data poses a significant problem to standard cotrending methods. Variable stars are often of particular astrophysical interest, so the preservation of their signals is of significant importance to the astrophysical community. We present a Bayesian maximum a posteriori (MAP) approach, where a subset of highly correlated and quiet stars is used to generate a cotrending basis vector set, which is in turn used to establish a range of "reasonable" robust fit parameters. These robust fit parameters are then used to generate a Bayesian prior and a Bayesian posterior probability distribution function (PDF) which, when maximized, finds the best fit that simultaneously removes systematic effects while reducing the signal distortion and noise injection that commonly afflicts simple least-squares (LS) fitting. A numerical and empirical approach is taken where the Bayesian prior PDFs are generated from fits to the light-curve distributions themselves.
ABSTRACT We present the seventh Kepler planet candidate (PC) catalog, which is the first catalog to be based on the entire, uniformly processed 48-month Kepler data set. This is the first fully ...automated catalog, employing robotic vetting procedures to uniformly evaluate every periodic signal detected by the Q1-Q17 Data Release 24 (DR24) Kepler pipeline. While we prioritize uniform vetting over the absolute correctness of individual objects, we find that our robotic vetting is overall comparable to, and in most cases superior to, the human vetting procedures employed by past catalogs. This catalog is the first to utilize artificial transit injection to evaluate the performance of our vetting procedures and to quantify potential biases, which are essential for accurate computation of planetary occurrence rates. With respect to the cumulative Kepler Object of Interest (KOI) catalog, we designate 1478 new KOIs, of which 402 are dispositioned as PCs. Also, 237 KOIs dispositioned as false positives (FPs) in previous Kepler catalogs have their disposition changed to PC and 118 PCs have their disposition changed to FPs. This brings the total number of known KOIs to 8826 and PCs to 4696. We compare the Q1-Q17 DR24 KOI catalog to previous KOI catalogs, as well as ancillary Kepler catalogs, finding good agreement between them. We highlight new PCs that are both potentially rocky and potentially in the habitable zone of their host stars, many of which orbit solar-type stars. This work represents significant progress in accurately determining the fraction of Earth-size planets in the habitable zone of Sun-like stars. The full catalog is publicly available at the NASA Exoplanet Archive.
ABSTRACT We present results of the final Kepler Data Processing Pipeline search for transiting planet signals in the full 17-quarter primary mission data set. The search includes a total of 198,709 ...stellar targets, of which 112,046 were observed in all 17 quarters and 86,663 in fewer than 17 quarters. We report on 17,230 targets for which at least one transit signature is identified that meets the specified detection criteria: periodicity, minimum of three observed transit events, detection statistic (i.e., signal-to-noise ratio) in excess of the search threshold, and passing grade on three statistical transit consistency tests. Light curves for which a transit signal is identified are iteratively searched for additional signatures after a limb-darkened transiting planet model is fitted to the data and transit events are removed. The search for additional planets adds 16,802 transit signals for a total of 34,032; this far exceeds the number of transit signatures identified in prior pipeline runs. There was a strategic emphasis on completeness over reliability for the final Kepler transit search. A comparison of the transit signals against a set of 3402 well-established, high-quality Kepler Objects of Interest yields a recovery rate of 99.8%. The high recovery rate must be weighed against a large number of false-alarm detections. We examine characteristics of the planet population implied by the transiting planet model fits with an emphasis on detections that would represent small planets orbiting in the habitable zone of their host stars.
The previous presearch data conditioning algorithm, PDC-MAP, for the Kepler data processing pipeline performs very well for the majority of targets in the Kepler field of view. However, for an ...appreciable minority, PDC-MAP has its limitations. To further minimize the number of targets for which PDC-MAP fails to perform admirably, we have developed a new method, called multiscale MAP, or msMAP. Utilizing an overcomplete discrete wavelet transform, the new method divides each light curve into multiple channels, or bands. The light curves in each band are then corrected separately, thereby allowing for a better separation of characteristic signals and improved removal of the systematics.
We present the Kepler Object of Interest (KOI) catalog of transiting exoplanets based on searching 4 yr of Kepler time series photometry (Data Release 25, Q1-Q17). The catalog contains 8054 KOIs, of ...which 4034 are planet candidates with periods between 0.25 and 632 days. Of these candidates, 219 are new, including two in multiplanet systems (KOI-82.06 and KOI-2926.05) and 10 high-reliability, terrestrial-size, habitable zone candidates. This catalog was created using a tool called the Robovetter, which automatically vets the DR25 threshold crossing events (TCEs). The Robovetter also vetted simulated data sets and measured how well it was able to separate TCEs caused by noise from those caused by low signal-to-noise transits. We discuss the Robovetter and the metrics it uses to sort TCEs. For orbital periods less than 100 days the Robovetter completeness (the fraction of simulated transits that are determined to be planet candidates) across all observed stars is greater than 85%. For the same period range, the catalog reliability (the fraction of candidates that are not due to instrumental or stellar noise) is greater than 98%. However, for low signal-to-noise candidates between 200 and 500 days around FGK-dwarf stars, the Robovetter is 76.7% complete and the catalog is 50.5% reliable. The KOI catalog, the transit fits, and all of the simulated data used to characterize this catalog are available at the NASA Exoplanet Archive.
Kepler-16 is an eccentric low-mass eclipsing binary with a circumbinary transiting planet. Here, we investigate the angular momentum of the primary star, based on Kepler photometry and Keck ...spectroscopy. The primary star's rotation period is 35.1 ? 1.0 days, and its projected obliquity with respect to the stellar binary orbit is 16 ? 24. Therefore, the three largest sources of angular momentum--the stellar orbit, the planetary orbit, and the primary's rotation--are all closely aligned. This finding supports a formation scenario involving accretion from a single disk. Alternatively, tides may have realigned the stars despite their relatively wide separation (0.2 AU), a hypothesis that is supported by the agreement between the measured rotation period and the 'pseudosynchronous' period of tidal evolution theory. The rotation period, chromospheric activity level, and fractional light variations suggest a main-sequence age of 2-4 Gyr. Evolutionary models of low-mass stars can match the observed masses and radii of the primary and secondary stars to within about 3%.
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