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Title: Transit Timing Observations from Kepler: III. Confirmation of 4 Multiple Planet Systems by a Fourier-Domain Study of Anti-correlated Transit Timing Variations
Authors: Jason H. Steffen (1), Daniel C. Fabrycky (2,3), Eric B. Ford (4), Joshua A. Carter (5,3), Jean-Michel Desert (5), Francois Fressin (5), Matthew J. Holman (5), Jack J. Lissauer (6), Althea V. Moorhead (1), Jason F. Rowe (7,6), Darin Ragozzine (5), William F. Welsh (8), Natalie M. Batalha (9), William J. Borucki (6), Lars A. Buchhave (18), Steve Bryson (6), Douglas A. Caldwell (7,6), David Charbonneau (5), David R. Ciardi (8), William D. Cochran (20), Michael Endl (20), Mark E. Everett (15), Thomas N. Gautier III (11), Ron L. Gilliland (21), Forrest R. Girouard (6,22), Jon M. Jenkins (7,6), Elliott Horch (16), Steve B. Howell (6), Howard Isaacson (13), Todd C. Klaus (6,22), David G. Koch (6), David W. Latham (5), Jie Li (7,6), Philip Lucas (12), Phillip J. MacQueen (20), Geoffrey W. Marcy (13), et al. (12 additional authors not shown)

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 anti-correlations 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.

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Title: Transit Timing Observations from Kepler: II. Confirmation of Two Multiplanet Systems via a Non-parametric Correlation Analysis
Authors: Eric B. Ford (1), Daniel C. Fabrycky (2,3), Jason H. Steffen (4), Joshua A. Carter (5,3), Francois Fressin (5), Matthew J. Holman (5), Jack J. Lissauer (6), Althea V. Moorhead (1), Robert C. Morehead (1), Darin Ragozzine (5), Jason F. Rowe (6,7), William F. Welsh (8), Christopher Allen (9), Natalie M. Batalha (10), William J. Borucki (6), Stephen T. Bryson (6), Lars A. Buchhave (11,12), Christopher J. Burke (6,7), Douglas A. Caldwell (6,7), David Charbonneau (5), Bruce D. Clarke (6,7), William D. Cochran (13), Jean-Michel Désert (5), Michael Endl (13), Mark E. Everett (14), Debra A. Fischer (15), Thomas N. Gautier III (16), Ron L. Gilliland (17), Jon M. Jenkins (6,7), Michael R. Haas (6), Elliott Horch (18), Steve B. Howell (6), Khadeejah A. Ibrahim (9), Howard Isaacson (19), David G. Koch (6), et al. (16 additional authors not shown)

We present a new method for confirming transiting planets based on the combination of transit timing variations (TTVs) and dynamical stability. Correlated TTVs provide evidence that the pair of bodies are in the same physical system. Orbital stability provides upper limits for the masses of the transiting companions that are in the planetary regime. This paper describes a non-parametric technique for quantifying the statistical significance of TTVs based on the correlation of two TTV data sets. We apply this method to an analysis of the transit timing variations of two stars with multiple transiting planet candidates identified by Kepler. We confirm four transiting planets in two multiple planet systems based on their TTVs and the constraints imposed by dynamical stability. An additional three candidates in these same systems are not confirmed as planets, but are likely to be validated as real planets once further observations and analyses are possible. If all were confirmed, these systems would be near 4:6:9 and 2:4:6:9 period commensurabilities. Our results demonstrate that TTVs provide a powerful tool for confirming transiting planets, including low-mass planets and planets around faint stars for which Doppler follow-up is not practical with existing facilities. Continued Kepler observations will dramatically improve the constraints on the planet masses and orbits and provide sensitivity for detecting additional non-transiting planets. If Kepler observations were extended to eight years, then a similar analysis could likely confirm systems with multiple closely spaced, small transiting planets in or near the habitable zone of solar-type stars.

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Title: Transit Timing Observations from Kepler: IV. Confirmation of 4 Multiple Planet Systems by Simple Physical Models
Authors: Daniel C. Fabrycky, Eric B. Ford, Jason H. Steffen, Jason F. Rowe, Joshua A. Carter, Althea V. Moorhead, Natalie M. Batalha, William J. Borucki, Steve Bryson, Lars A. Buchhave, Jessie L. Christiansen, David R. Ciardi, William D. Cochran, Michael Endl, Michael N. Fanelli, Debra Fischer, Francois Fressin, John Geary, Michael R. Haas, Jennifer R. Hall, Matthew J. Holman, Jon M. Jenkins, David G. Koch, David W. Latham, Jie Li, Jack J. Lissauer, Philip Lucas, Geoffrey W. Marcy, Tsevi Mazeh, Sean McCauliff, Samuel Quinn, Darin Ragozzine, Dimitar Sasselov, Avi Shporer

Eighty planetary systems of two or more planets are known to orbit stars other than the Sun. For most, the data can be sufficiently explained by non-interacting Keplerian orbits, so the dynamical interactions of these systems have not been observed. Here we present 4 sets of lightcurves from the Kepler spacecraft, which each show multiple planets transiting the same star. Departure of the timing of these transits from strict periodicity indicates the planets are perturbing each other: the observed timing variations match the forcing frequency of the other planet. This confirms that these objects are in the same system. Next we limit their masses to the planetary regime by requiring the system remain stable for astronomical timescales. Finally, we report dynamical fits to the transit times, yielding possible values for the planets' masses and eccentricities. As the timespan of timing data increases, dynamical fits may allow detailed constraints on the systems' architectures, even in cases for which high-precision Doppler follow-up is impractical.

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Title: Almost All of Kepler's Multiple Planet Candidates are Planets
Authors: Jack J. Lissauer, Geoffrey W. Marcy, Jason F. Rowe, Stephen T. Bryson, Elisabeth Adams, Lars A. Buchhave, David R. Ciardi, William D. Cochran, Daniel C. Fabrycky, Eric B. Ford, Francois Fressin, John Geary, Ronald L. Gilliland, Matthew J. Holman, Steve B. Howell, Jon M. Jenkins, Karen Kinemuchi, David G. Koch, Robert C. Morehead, Darin Ragozzine, Shawn E. Seader, Peter G. Tanenbaum, Guillermo Torres, Joseph D. Twicken

We present a statistical analysis that demonstrates that the overwhelming majority of Kepler candidate multiple transiting systems (multis) indeed represent true, physically-associated transiting planets. Binary stars provide the primary source of false positives among Kepler planet candidates, implying that false positives should be nearly randomly-distributed among Kepler targets. In contrast, true transiting planets would appear clustered around a smaller number of Kepler targets if detectable planets tend to come in systems and/or if the orbital planes of planets encircling the same star are correlated. There are more than one hundred times as many Kepler planet candidates in multi-candidate systems as would be predicted from a random distribution of candidates, implying that the vast majority are true planets. Most of these multis are multiple planet systems orbiting the Kepler target star, but there are likely cases where (a) the planetary system orbits a fainter star, and the planets are thus significantly larger than has been estimated, or (b) the planets orbit different stars within a binary/multiple star system. We use the low overall false positive rate among Kepler multis, together with analysis of Kepler spacecraft and ground-based data, to validate the closely-packed Kepler-33 planetary system, which orbits a star that has evolved somewhat off of the main sequence. Kepler-33 hosts five transiting planets with periods ranging from 5.67 to 41 days.

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