NUMERICAL AND ANALYTICAL MODELING OF TRANSIT TIMING VARIATIONS

@article{Hadden2016NUMERICALAA,
  title={NUMERICAL AND ANALYTICAL MODELING OF TRANSIT TIMING VARIATIONS},
  author={Sam Hadden and Yoram Lithwick},
  journal={The Astrophysical Journal},
  year={2016},
  volume={828},
  pages={44}
}
We develop and apply methods to extract planet masses and eccentricities from observed transit time variations (TTVs). First, we derive simple analytic expressions for the TTV that include the effects of both first- and second-order resonances. Second, we use N-body Markov chain Monte Carlo (MCMC) simulations, as well as the analytic formulae, to measure the masses and eccentricities of ten planets discovered by Kepler that have not previously been analyzed. Most of the ten planets have low… 
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References

SHOWING 1-10 OF 45 REFERENCES
Transit timing to first order in eccentricity
Characterization of transiting planets with transit timing variations (TTVs) requires understanding how to translate the observed TTVs into masses and orbital elements of the planets. This can be
Measurement of planet masses with transit timing variations due to synodic "chopping" effects
Gravitational interactions between planets in transiting exoplanetary systems lead to variations in the times of transit that are diagnostic of the planetary masses and the dynamical state of the
THE EFFECT OF CONJUNCTIONS ON THE TRANSIT TIMING VARIATIONS OF EXOPLANETS
We develop an analytic model for transit timing variations produced by orbital conjunctions between gravitationally interacting planets. If the planetary orbits have tight orbital spacing, which is a
EXTRACTING PLANET MASS AND ECCENTRICITY FROM TTV DATA
Most planet pairs in the Kepler data that have measured transit time variations (TTVs) are near first-order mean-motion resonances. We derive analytical formulae for their TTV signals. We separate
Mass and Orbit Determination from Transit Timing Variations of Exoplanets
The timing variations of transits of an exoplanet provide means of detecting additional planets in the system. The short-period and resonant variations of the transit signal are probably the most
Densities and Eccentricities of 139 Kepler Planets from Transit Time Variations
We extract densities and eccentricities of 139 sub-Jovian planets by analyzing transit time variations (TTVs) obtained by the Kepler mission through Quarter 12. We partially circumvent the
DENSITY AND ECCENTRICITY OF KEPLER PLANETS
We analyze the transit timing variations (TTV) obtained by the Kepler mission for 22 sub-Jovian planet pairs (19 published, 3 new) that lie close to mean motion resonances. We find that the TTV
The Use of Transit Timing to Detect Terrestrial-Mass Extrasolar Planets
TLDR
This work shows that timing measurements between successive transits will allow for the detection of additional planets in the system (not necessarily transiting) by their gravitational interaction with the transiting planet.
Transit timing observations from Kepler - III. : Confirmation of four multiple planet systems by a Fourier-domain study of anticorrelated transit timing variations
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
TTVFast: AN EFFICIENT AND ACCURATE CODE FOR TRANSIT TIMING INVERSION PROBLEMS
Transit timing variations (TTVs) have proven to be a powerful technique for confirming Kepler planet candidates, for detecting non-transiting planets, and for constraining the masses and orbital
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