Transit timing to first order in eccentricity
- Creators
- Agol, Eric
- Deck, Katherine
Abstract
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 challenging in multi-planet transiting systems, but fortunately these systems tend to be nearly plane-parallel and low eccentricity. Here we present a novel derivation of analytic formulae for TTVs that are accurate to first order in the planet–star mass ratios and in the orbital eccentricities. These formulae are accurate in proximity to first-order resonances, as well as away from resonance, and compare well with more computationally expensive N-body integrations in the low-eccentricity, low mass-ratio regime when applied to simulated and to actual multi-transiting Kepler planet systems. We make code available for implementing these formulae.
Additional Information
© 2016 The American Astronomical Society. Received 2015 September 4; accepted 2015 November 24; published 2016 February 18. E.A. acknowledges support from NASA grants NNX13AF20G, NNX13AF62G, and NASA Astrobiology Institutes Virtual Planetary Laboratory, supported by NASA under cooperative agreement NNH05ZDA001C. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. E.A. thanks the Kavli Institute for Theoretical Physics and the organizers of the "Dynamics and Evolution of Earth-like Planets" workshop, where a portion of this work was completed; this manuscript is preprint number NSF-KITP-15-132. K.D. acknowledges support from the Joint Center for Planetary Astronomy fellowship. We thank Jack Wisdom for sharing laplace.c, which computes Laplace coefficients and their derivatives with series summation; we thank Eric Ford for advice on implementation of the formula in Julia; and we thank Brett Morris and Ethan Kruse for advice on implementation of the formula in Python (requested by the referee).Attached Files
Published - apj_818_2_177.pdf
Submitted - 1509.01623v1.pdf
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Additional details
- Eprint ID
- 66212
- Resolver ID
- CaltechAUTHORS:20160415-090611776
- NNX13AF20G
- NASA
- NNX13AF62G
- NASA
- NNH05ZDA001C
- NASA
- PHY11-25915
- NSF
- Caltech Joint Center for Planetary Astronomy
- Kavli Institute for Theoretical Physics
- Created
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2016-04-15Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field