Hema Chandrasekaran

Kepler Planet-Detection Mission: Introduction and First Results

Detecting Distant Planets More than 400 planets have been detected outside the solar system, most of which have masses similar to that of the gas giant planet, Jupiter. Borucki et al. (p. 977, published online 7 January) summarize the planetary findings derived from the first six weeks of observations with the Kepler mission whose objective is to search for and determine the frequency of Earth-like planets in the habitable zones of other stars. The results include the detection of five new exoplanets, which confirm the existence of planets with densities substantially lower than those predicted for gas giant planets. Initial observations confirm the existence of planets with densities lower than those predicted for gas giant planets. The Kepler mission was designed to determine the frequency of Earth-sized planets in and near the habitable zone of Sun-like stars. The habitable zone is the region where planetary temperatures are suitable for water to exist on a planet’s surface. During the first 6 weeks of observations, Kepler monitored 156,000 stars, and five new exoplanets with sizes between 0.37 and 1.6 Jupiter radii and orbital periods from 3.2 to 4.9 days were discovered. The density of the Neptune-sized Kepler-4b is similar to that of Neptune and GJ 436b, even though the irradiation level is 800,000 times higher. Kepler-7b is one of the lowest-density planets (~0.17 gram per cubic centimeter) yet detected. Kepler-5b, -6b, and -8b confirm the existence of planets with densities lower than those predicted for gas giant planets.

Kepler Mission Design, Realized Photometric Performance, and Early Science

The Kepler Mission, launched on 2009 March 6, was designed with the explicit capability to detect Earth-size planets in the habitable zone of solar-like stars using the transit photometry method. Results from just 43 days of data along with ground-based follow-up observations have identified five new transiting planets with measurements of their masses, radii, and orbital periods. Many aspects of stellar astrophysics also benefit from the unique, precise, extended, and nearly continuous data set for a large number and variety of stars. Early results for classical variables and eclipsing stars show great promise. To fully understand the methodology, processes, and eventually the results from the mission, we present the underlying rationale that ultimately led to the flight and ground system designs used to achieve the exquisite photometric performance. As an example of the initial photometric results, we present variability measurements that can be used to distinguish dwarf stars from red giants.

OVERVIEW OF THE KEPLER SCIENCE PROCESSING PIPELINE

The Kepler Mission Science Operations Center (SOC) performs several critical functions including managing the ~156,000 target stars, associated target tables, science data compression tables and parameters, as well as processing the raw photometric data downlinked from the spacecraft each month. The raw data are first calibrated at the pixel level to correct for bias, smear induced by a shutterless readout, and other detector and electronic effects. A background sky flux is estimated from ~4500 pixels on each of the 84 CCD readout channels, and simple aperture photometry is performed on an optimal aperture for each star. Ancillary engineering data and diagnostic information extracted from the science data are used to remove systematic errors in the flux time series that are correlated with these data prior to searching for signatures of transiting planets with a wavelet-based, adaptive matched filter. Stars with signatures exceeding 7.1? are subjected to a suite of statistical tests including an examination of each stars centroid motion to reject false positives caused by background eclipsing binaries. Physical parameters for each planetary candidate are fitted to the transit signature, and signatures of additional transiting planets are sought in the residual light curve. The pipeline is operational, finding planetary signatures and providing robust eliminations of false positives.

Characteristics Of Kepler Planetary Candidates Based On The First Data Set

In the spring of 2009, the Kepler Mission commenced high-precision photometry on nearly 156,000 stars to determine the frequency and characteristics of small exoplanets, conduct a guest observer program, and obtain asteroseismic data on a wide variety of stars. On 15 June 2010 the Kepler Mission released data from the first quarter of observations. At the time of this publication, 706 stars from this first data set have exoplanet candidates with sizes from as small as that of the Earth to larger than that of Jupiter. Here we give the identity and characteristics of 306 released stars with planetary candidates. Data for the remaining 400 stars with planetary candidates will be released in February 2011. Over half the candidates on the released list have radii less than half that of Jupiter. The released stars include five possible multi-planet systems. One of these has two Neptune-size (2.3 and 2.5 Earth-radius) candidates with near-resonant periods.

Initial Characteristics of Kepler Long Cadence Data for Detecting Transiting Planets

The Kepler Mission seeks to detect Earth-size planets transiting solar-like stars in its ~115?deg2 field of view over the course of its 3.5 year primary mission by monitoring the brightness of each of ~156,000 Long Cadence stellar targets with a time resolution of 29.4 minutes. We discuss the photometric precision achieved on timescales relevant to transit detection for data obtained in the 33.5 day long Quarter 1 (Q1) observations that ended 2009 June 15. The lower envelope of the photometric precision obtained at various timescales is consistent with expected random noise sources, indicating that Kepler has the capability to fulfill its mission. The Kepler light curves exhibit high precision over a large dynamic range, which will surely permit their use for a large variety of investigations in addition to finding and characterizing planets. We discuss the temporal characteristics of both the raw flux time series and the systematic error-corrected flux time series produced by the Kepler Science Pipeline, and give examples illustrating Keplers large dynamic range and the variety of light curves obtained from the Q1 observations.

Instrument Performance in Kepler's First Months

The Kepler Mission relies on precise differential photometry to detect the 80 parts per million (ppm) signal from an Earth-Sun equivalent transit. Such precision requires superb instrument stability on timescales up to ~2 days and systematic error removal to better than 20 ppm. To this end, the spacecraft and photometer underwent 67 days of commissioning, which included several data sets taken to characterize the photometer performance. Because Kepler has no shutter, we took a series of dark images prior to the dust cover ejection, from which we measured the bias levels, dark current, and read noise. These basic detector properties are essentially unchanged from ground-based tests, indicating that the photometer is working as expected. Several image artifacts have proven more complex than when observed during ground testing, as a result of their interactions with starlight and the greater thermal stability in flight, which causes the temperature-dependent artifact variations to be on the timescales of transits. Because of Keplers unprecedented sensitivity and stability, we have also seen several unexpected systematics that affect photometric precision. We are using the first 43 days of science data to characterize these effects and to develop detection and mitigation methods that will be implemented in the calibration pipeline. Based on early testing, we expect to attain Keplers planned photometric precision over 80%-90% of the field of view.

Discovery and Rossiter-McLaughlin Effect of Exoplanet Kepler-8b

We report on the discovery and the Rossiter-McLaughlin (R-M) effect of Kepler-8b, a transiting planet identified by the NASA Kepler Mission. Kepler photometry and Keck-HIRES radial velocities yield the radius and mass of the planet around this F8IV subgiant host star. The planet has a radius R_P = 1.419 R_J and a mass M_P = 0.60 M_J, yielding a density of 0.26 g cm^(–3), one of the lowest planetary densities known. The orbital period is P = 3.523 days and the orbital semimajor axis is 0.0483^(+0.0006) _(–0.0012) AU. The star has a large rotational vsin i of 10.5 ± 0.7 km s^(–1) and is relatively faint (V ≈ 13.89 mag); both properties are deleterious to precise Doppler measurements. The velocities are indeed noisy, with scatter of 30 m s^(–1), but exhibit a period and phase that are consistent with those implied by transit photometry. We securely detect the R-M effect, confirming the planets existence and establishing its orbit as prograde. We measure an inclination between the projected planetary orbital axis and the projected stellar rotation axis of λ = –26o.4 ± 10o.1, indicating a significant inclination of the planetary orbit. R-M measurements of a large sample of transiting planets from Kepler will provide a statistically robust measure of the true distribution of spin-orbit orientations for hot Jupiters around F and early G stars.

THE KEPLER PIXEL RESPONSE FUNCTION

Kepler seeks to detect sequences of transits of Earth-size exoplanets orbiting Solar-like stars. Such transit signals are on the order of 100 ppm. The high photometric precision demanded by Kepler requires detailed knowledge of how the Kepler pixels respond to starlight during a nominal observation. This information is provided by the Kepler pixel response function (PRF), defined as the composite of Keplers optical point spread function, integrated spacecraft pointing jitter during a nominal cadence and other systematic effects. To provide sub-pixel resolution, the PRF is represented as a piecewise-continuous polynomial on a sub-pixel mesh. This continuous representation allows the prediction of a stars flux value on any pixel given the stars pixel position. The advantages and difficulties of this polynomial representation are discussed, including characterization of spatial variation in the PRF and the smoothing of discontinuities between sub-pixel polynomial patches. On-orbit super-resolution measurements of the PRF across the Kepler field of view are described. Two uses of the PRF are presented: the selection of pixels for each star that maximizes the photometric signal to noise ratio for that star, and PRF-fitted centroids which provide robust and accurate stellar positions on the CCD, primarily used for attitude and plate scale tracking. Good knowledge of the PRF has been a critical component for the successful collection of high-precision photometry by Kepler.

Transiting Planet Search in the Kepler Pipeline

The Kepler Mission simultaneously measures the brightness of more than 160,000 stars every 29.4 minutes over a 3.5-year mission to search for transiting planets. Detecting transits is a signal-detection problem where the signal of interest is a periodic pulse train and the predominant noise source is non-white, non-stationary (1/f) type process of stellar variability. Many stars also exhibit coherent or quasi-coherent oscillations. The detection algorithm first identifies and removes strong oscillations followed by an adaptive, wavelet-based matched filter. We discuss how we obtain super-resolution detection statistics and the effectiveness of the algorithm for Kepler flight data.

A neural network training algorithm utilizing multiple sets of linear equations

A fast algorithm is presented for the training of multilayer perceptron neural networks. In each iteration, there are two passes through the training data. In the first pass, linear equations are solved for the output weights. In the second data pass, linear equations are solved for hidden unit weight changes. Full batching is used in both data passes. An algorithm is described for calculating the learning factor for use with the hidden weights. It is shown that the technique is significantly faster than standard output weight optimization-backpropagation.