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NASA NTRS2010

Data Validation in the Kepler Science Operations Center Pipeline

We present an overview of the Data Validation (DV) software component and its context within the Kepler ScienceOperations Center (SOC) pipeline and overall Kepler Science mission. The SOC pipeline performs a transiting planetsearch on the corrected light curves for over 150,000 targets across the focal plane array. We discuss the DV strategy forautomated validation of Threshold Crossing Events (TCEs) generated in the transiting planet search. For each TCE, atransiting planet model is fitted to the target light curve. A multiple planet search is conducted by repeating the transitingplanet search on the residual light curve after the model flux has been removed; if an additional detection occurs, aplanet model is fitted to the new TCE. A suite of automated tests are performed after all planet candidates have beenidentified. We describe a centroid motion test to determine the significance of the motion of the target photocenterduring transit and to estimate the coordinates of the transit source within the photometric aperture; a series of eclipsingbinary discrimination tests on the parameters of the planet model fits to all transits and the sequences of odd and eventransits; and a statistical bootstrap to assess the likelihood that the TCE would have been generated purely by chancegiven the target light curve with all transits removed.

photometry↗
NASA NTRS2010

Photometric Analysis in the Kepler Science Operations Center Pipeline

We describe the Photometric Analysis (PA) software component and its context in the Kepler Science Operations Center (SOC) Science Processing Pipeline. The primary tasks of this module are to compute the photometric flux and photocenters (centroids) for over 160,000 long cadence (~thirty minute) and 512 short cadence (~one minute) stellar targets from the calibrated pixels in their respective apertures. We discuss science algorithms for long and short cadence PA: cosmic ray cleaning; background estimation and removal; aperture photometry; and flux-weighted centroiding. We discuss the end-to-end propagation of uncertainties for the science algorithms. Finally, we present examples of photometric apertures, raw flux light curves, and centroid time series from Kepler flight data. PA light curves, centroid time series, and barycentric timestamp corrections are exported to the Multi-mission Archive at Space Telescope [Science Institute] (MAST) and are made available to the general public in accordance with the NASA/Kepler data release policy.

photocenter↗
NASA NTRS2015

Mercury-T: A New Code to Study Tidally Evolving Multi-Planet Systems. Applications to Kepler-62

A large proportion of observed planetary systems contain several planets in a compact orbital configuration, and often harbor at least one close-in object. These systems are then most likely tidally evolving. We investigate how the effects of planet-planet interactions influence the tidal evolution of planets. We introduce for that purpose a new open-source addition to the Mercury N-body code, Mercury-T, which takes into account tides, general relativity and the effect of rotation-induced flattening in order to simulate the dynamical and tidal evolution of multi-planet systems. It uses a standard equilibrium tidal model, the constant time lag model. Besides, the evolution of the radius of several host bodies has been implemented (brown dwarfs, M-dwarfs of mass 0:1 M(sub ⨀), Sun-like stars, Jupiter). We validate the new code by comparing its output for one-planet systems to the secular equations results. We find that this code does respect the conservation of total angular momentum. We applied this new tool to the planetary system Kepler-62. We find that tides influence the stability of the system in some cases. We also show that while the four inner planets of the systems are likely to have slow rotation rates and small obliquities, the fifth planet could have a fast rotation rate and a high obliquity. This means that the two habitable zone planets of this system, Kepler-62e ad f are likely to have very different climate features, and this of course would influence their potential at hosting surface liquid water..

Dynamical evolution and stability↗
NASA NTRS1973

Discourse following award of Kepler Gold Medal

Kuiper briefly reviews Kepler's contributions to the field of planetary astronomy and physics, along with references to his own background in the study of stars, planets, and the solar system. He mentions his participation in NASA programs related to planetary astronomy. He concludes his remarks with thanks for being honored by the award of the Kepler Gold Medal.

Kuiper, G. P.↗
NASA NTRS1977

Stabilization of Kepler's problem

A regularization of Kepler's problem due to Moser (1970) is used to stabilize the equations of motion. In other words, a particular solution of Kepler's problem is imbedded in a Liapunov stable system. Perturbations can be introduced into the stabilized equations.

Stokes, A.↗
NASA NTRS1979

Evidence for X-ray emission from Kepler's supernova remnant

Evidence for weak soft X-ray emission from the remnant of Kepler's supernova has been acquired by the low energy detectors of the A 2 experiment on HEAO 1. A soft X-ray source has been detected using a narrow field of view sensitive to X rays between 0.2 and 3 keV and is found to be the only constant X-ray source within the error box containing Kepler's supernova remnant. The intensity of the X-ray source is calculated to be about 6.3 x 10 to the -2 counts/sq cm sec, with an intrinsic X-ray luminosity in the energy range 0.3 to 3 keV of about 28 x 10 to the 35 erg/sec if, as is widely believed, the remnant is at a distance of 4 kpc. Observations from HEAO 2 will allow the detection to be confirmed, the source to be imaged and its spectrum to be determined.

Tuohy, I. R.↗
NASA NTRS1980

X-ray spectrum of Kepler's SNR

Observations made with the solid state spectrometer aboard the Einstein Observatory confirm Kepler's SNR as an X-ray source with an intensity between 1-3 KeV of 7.2 x 10 to the-11th power ergs/sq cm-s. The X-ray spectrum is similar to those of Cas A and Tycho, with strong line emission from the helium-like species of Si, S, and Ar. Direct comparisons to Tycho's SNR suggest a distance of Kepler's SNR of greater than or equal to 5 kpc.

Becker, R. H.↗
NASA NTRS1980

X-ray spectrum of Kepler's supernova remnant

Observations made with the Solid State Spectrometer (SSS) aboard the Einstein Observatory confirm Kepler's SNR as an X-ray source with an intensity between 1 and 3 keV of 7.2 x 10 to the -11th ergs/sq cm s. The X-ray spectrum is similar to those of Cas A and Tycho, with strong line emission from the helium-like species of Si, S, and Ar. Direct comparisons to Tycho's SNR suggest a distance to Kepler's SNR of not less than 5 kpc.

Becker, R. H.↗
NASA NTRS1982

Comparison of starting values for iterative solutions to a universal Kepler's equation

General starting values for the iterative numerical solution of a universal Kepler's equation for position in a conic orbit at a specified time are investigated. Three starting values based on recent refinements of previously obtained bounds on the solution are derived and tested numerically. Of these, a simple starting value based on a cubic approximation to Kepler's equation provides the most rapid convergence using both first and second order Newton algorithms. The performance of the starting values are compared with similar studies which used the restricted case of elliptical orbits with the initial epoch at periapse.

Bergam, M. J.↗
NASA NTRS1983

The X-ray surface brightness of Kepler's supernova remnant

The first X-ray images of Kepler's supernova remnant (SN Ophiuchi 1604) are presented, and consequences for SNR models are discussed. Observations made with the Einstein Observatory Imaging Proportional Counter and High Resolution Imager show the remnant to be circular, with a strong shell brighter in the north than in the south. A flux of 1.2 x 10 to the -10th ergs/sq cm per sec was measured in the 0.15-4.5 keV region, which corresponds to an X-ray luminosity of 1.0 x 10 to the 36th ergs/sec at a distance of 5 kpc and an interstellar medium density of 2.8 x 10 to the 21st/sq cm. The X-ray observations do not allow the determination of whether the SNR is in the adiabatic or free expansion phase, but in either case it is shown that the mean ISM density must be greater than about 0.1/cu cm. In addition, the density of the X-ray emitting gas must be high, and its electron temperature must be fairly low. The high ISM densities derived for Kepler's SNR and other SNRs thus suggest an atypical ISM, possibly influenced by mass lost from the pre-supernova star.

White, R. L.↗
NASA NTRS1984

A detailed X-ray and radio comparison of Kepler's supernova remnant

High-resolution radio images of Kepler's SNR (SNR (SN 1604) at 6 and 21 cm have been obtained using the VLA. The orientation of linear polarization in the SNR implies a substantial nonrandom radial component for the magnetic field of the remnant. Based on a new X-ray picture of the SNR, obtained using the Einstein Observatory, a detailed comparison of the X-ray and radio morphology is carried out. There is a good correlation between rotation measure, obtained from the radio maps, and emission measure, an X-ray-derived quantity in the SNR shell. From the mean electron density value infered from an analysis of X-ray fluxes, a mean radial magnetic field of 14 micro G and a total magnetic field of 70 microG are estimated. The energy density of relativistic electrons in Kepler's SNR in the shell comparable to the energy density in the magnetic field; the relativistic electron-pressure is 2 percent of the thermal gas pressure. The strong correlation between radio emissivity and X-ray emissivity found over the SNR in somewhat large scale can be ascribed to acceleration of thermal electrons at the shock wave and insignificant diffusion of resultant relativistic electrons.

Matsui, Y.↗
NASA NTRS1987

Inverse solution of Kepler's equation for hyperbolic orbits

An algorithm is presented for efficient inverse solution of Kepler's equation for hyperbolic orbits. It is shown that an expansion of Barker's equation into a bicubic polynomial provides a good approximation to obtain accurate starting values for rapid numerical solution of Kepler's equation. In the approximate equation a cubic in normalized elapsed flight time from pericenter is set equal to a cubic in a function S of eccentricity and true anomaly. The initial estimate of S to use in an iteration formula is obtained by evaluating the cubic in normalized flight time and finding in most cases the single real root of the other cubic. This initial estimate has an accuracy corresponding to values of true anomaly in error by less than 0.5 degrees generally.

Boltz, Frederick W.↗
NASA NTRS1996

Homotopy Solutions of Kepler's Equations

Kepler's Equation is solved using an integrative algorithm developed using homotropy theory. The solution approach is applicable to both elliptic and hyperbolic forms of Kepler's Equation. The results from the proposed algorithm compare quite favorably with those from existing iterative schemes.

Fitz-Coy, Norman↗
NASA NTRS1998

Scientific Issues Addressed by the Kepler Mission

The Kepler Mission uses a wide field-of-view telescope to photometrically monitor 100,000 main-sequence stars for evidence of planetary transits. Because of the large number of stars monitored and because the mission is designed with a precision (0.002%) sufficient to readily recognize Earth-size planets transiting solar-like stars, several hundred Earth-size planets should be found. Based on the the Dopper velocity observations that find 2% of the main-sequence stars have Jupiter-size planets in short-period orbits, the Kepler mission is also expected to detect about 2000 giant planets. Several questions about the association of planet types and stellar characteristics can be investigated. For example; Are small planets found when Jupiter-mass planets are also present in inner orbits? What is the frequency of small planets compared to Jupiter-mass planets? What is the frequency and distribution of planets intermediate in size and mass to that of Earth and Jupiter? What correlations exist between planet size, distribution, and frequency with the characteristics of the stars they orbit? A comparison between model predictions and observation should be a useful step in evolving better models of planetary system formation and help put the formation of our Solar System in perspective.

Bourcki, W. J.↗
NASA NTRS2001

Kepler Mission: A Search for Terrestrial Planets

The Kepler Mission is a search for terrestrial planets by monitoring a large ensemble of stars for the periodic transits of planets. The mission consists of a 95-cm aperture photometer with 105 square deg field of view that monitors 100,000 dwarf stars for four years. The mission is unique in its ability to detect Earth-size planets in the habitable zone of other stars in the extended solar neighborhood. An Earth-size transit of a solar-like star causes a change in brightness of about 100 ppm. Laboratory testing has demonstrated that a total system noise level of 20 ppm is readily achievable on the timescale of transits. Earth-like transits have been created and reliably measured in an end-to-end system test that has all known sources of noise including, spacecraft jitter. To detect Earth-size planets, the photometer must be spaceborne; this also eliminates the day-night and seasonal cycle interruptions of ground-based observing. The photometer will stare at a single field of stars for four years, with an option to continue for two more years. This allows for detection of four transits of planets in Mars-like orbits and detection of planets even smaller than Earth especially for short period orbits, since the signal to noise improves as the square root of the number of transits observed. In addition to detection of planets, Kepler data are also useful for understanding the activity cycles and rotation rates of the stars observed. For the 3,000 stars brighter than mv= 11.4 p-mode oscillations are measured. The mission has been selected as one of three candidates for NASA's next Discovery mission.

Koch, D.↗
NASA NTRS2009

Kepler Data Validation and Follow-up Programs

The approach that the Kepler Mission uses to remove false positive events and to validate the discoveries consists of two parts; data validation (DPI) and follow up observations program (FOP). DV consists of several methods of examining the data from the spacecraft observations. First, to rule out statistical fluctuations in the data, accept only signals that show 3 or more transits and that have a total signal-to-noise ratio that exceeds 7 sigma. Second. to identify small stellar companions to the target star, we check for secondary eclipses and determine if the transit characteristics are appropriate for a planetary companion. Third, check for background binaries that are in the target aperture. Here we measure the movement of the image centroid before, during, and after the transit. If the target is producing the signal, a dimming wi11 move the image centroid in a known direction and magnitude. If the signal comes from a nearby star, the amplitude and direction of the motion wi11 be different, This test is expected to rule out the hundreds of binary signals expected from background stars. The precision of the measurement depends on the stellar fluxes and positions but can be better than 0.01 pixel; i.e., 0.04". Those candidates that pass these tests are examined using ground-based telescopes and radial velocity spectrometers. First medium precision RV is used to rule out any remaining stellar companions. Then high spatial resolution imaging is used to check for nearby stars that are in the aperture- (The Kepler apertures depend on magnitude but are of order 36 sq are sec in area.) If no stars are present that quid generate the observed signal, then the candidate goes to a large telescope such as Keck, HET, or Wi1lilam Herschel for high precision observations to get the planet mass or an upper limit to it, if there are some stars in the aperture, then the photometric observations are employed to look for the transit by cane of the confounding stars. If none are seen, then the candidate is sent to a large telescope such as Keck

William, Borucki J.↗
NASA NTRS2009

Kepler: NASA's First Mission Capable of Finding Earth-Size Planets

Kepler, a NASA Discovery mission, is a spaceborne telescope designed to search a nearby region of our galaxy for Earth-size planets orbiting in the habitable zone of stars like our sun. The habitable zone is that region around a start where the temperature permits water to be liquid on the surface of a planet. Liquid water is considered essential forth existence of life. Mission Phases: Six mission phases have been defined to describe the different periods of activity during Kepler's mission. These are: launch; commissioning; early science operations, science operations: and decommissioning

Borucki, William J.↗