skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: The effect of conjunctions on the transit timing variations of exoplanets

Abstract

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 common case among the Kepler planets, the effect of a single conjunction can be best described as: (1) a step-like change of the transit timing ephemeris with subsequent transits of the inner planet being delayed and those of the outer planet being sped up, and (2) a discrete change in sampling of the underlying oscillations from eccentricity-related interaction terms. In the limit of small orbital eccentricities, our analytic model gives explicit equations for these effects as a function of the mass and orbital separation of planets. We point out that a detection of the conjunction effect in real data is of crucial importance for the physical characterization of planetary systems from transit timing variations.

Authors:
 [1];  [2]
  1. Department of Space Studies, Southwest Research Institute, 1050 Walnut Street, Suite 300, Boulder, CO 80302 (United States)
  2. Institute of Astronomy, Charles University, V Holešovičkách 2, CZ-18000 Prague 8 (Czech Republic)
Publication Date:
OSTI Identifier:
22364898
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 790; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DETECTION; EQUATIONS; GRAVITATIONAL FIELDS; INTERACTIONS; MASS; ORBITS; OSCILLATIONS; PLANETS; SOLAR PROTONS; VARIATIONS

Citation Formats

Nesvorný, David, and Vokrouhlický, David, E-mail: davidn@boulder.swri.edu, E-mail: vokrouhl@cesnet.cz. The effect of conjunctions on the transit timing variations of exoplanets. United States: N. p., 2014. Web. doi:10.1088/0004-637X/790/1/58.
Nesvorný, David, & Vokrouhlický, David, E-mail: davidn@boulder.swri.edu, E-mail: vokrouhl@cesnet.cz. The effect of conjunctions on the transit timing variations of exoplanets. United States. doi:10.1088/0004-637X/790/1/58.
Nesvorný, David, and Vokrouhlický, David, E-mail: davidn@boulder.swri.edu, E-mail: vokrouhl@cesnet.cz. 2014. "The effect of conjunctions on the transit timing variations of exoplanets". United States. doi:10.1088/0004-637X/790/1/58.
@article{osti_22364898,
title = {The effect of conjunctions on the transit timing variations of exoplanets},
author = {Nesvorný, David and Vokrouhlický, David, E-mail: davidn@boulder.swri.edu, E-mail: vokrouhl@cesnet.cz},
abstractNote = {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 common case among the Kepler planets, the effect of a single conjunction can be best described as: (1) a step-like change of the transit timing ephemeris with subsequent transits of the inner planet being delayed and those of the outer planet being sped up, and (2) a discrete change in sampling of the underlying oscillations from eccentricity-related interaction terms. In the limit of small orbital eccentricities, our analytic model gives explicit equations for these effects as a function of the mass and orbital separation of planets. We point out that a detection of the conjunction effect in real data is of crucial importance for the physical characterization of planetary systems from transit timing variations.},
doi = {10.1088/0004-637X/790/1/58},
journal = {Astrophysical Journal},
number = 1,
volume = 790,
place = {United States},
year = 2014,
month = 7
}
  • The Transit Timing Variation (TTV) method relies on monitoring changes in timing of transits of known exoplanets. Nontransiting planets in the system can be inferred from TTVs by their gravitational interactions with the transiting planet. The TTV method is sensitive to low-mass planets that cannot be detected by other means. Inferring the orbital elements and mass of the nontransiting planets from TTVs, however, is more challenging than for other planet detection schemes. It is a difficult inverse problem. Here, we extended the new inversion method proposed by Nesvorny and Morbidelli to eccentric transiting planets and inclined orbits. We found thatmore » the TTV signal can be significantly amplified for hierarchical planetary systems with substantial orbital inclinations and/or for an eccentric transiting planet with anti-aligned orbit of the planetary companion. Thus, a fortuitous orbital setup of an exoplanetary system may significantly enhance our chances of TTV detection. We also showed that the detailed shape of the TTV signal is sensitive to the orbital inclination of the nontransiting planetary companion. The TTV detection method may thus provide important constraints on the orbital inclination of exoplanets and be used to test theories of planetary formation and evolution.« less
  • 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 anticorrelations 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.
  • We confirm 27 planets in 13 planetary systems by showing the existence of statistically significant anti-correlated transit timing variations (TTVs), which demonstrates that the planet candidates are in the same system, and long-term dynamical stability, which places limits on the masses of the candidates---showing that they are planetary. %This overall method of planet confirmation was first applied to \kepler systems 23 through 32. All of these newly confirmed planetary systems have orbital periods that place them near first-order mean motion resonances (MMRs), including 6 systems near the 2:1 MMR, 5 near 3:2, and one each near 4:3, 5:4, and 6:5.more » In addition, several unconfirmed planet candidates exist in some systems (that cannot be confirmed with this method at this time). A few of these candidates would also be near first order MMRs with either the confirmed planets or with other candidates. One system of particular interest, Kepler-56 (KOI-1241), is a pair of planets orbiting a 12th magnitude, giant star with radius over three times that of the Sun and effective temperature of 4900 K---among the largest stars known to host a transiting exoplanetary system.« less
  • We report nine new transit epochs of the extrasolar planet WASP-5b, observed in the Bessell I band with the Southern Astrophysical Research Telescope at the Cerro Pachon Observatory and with the SMARTS 1 m Telescope at the Cerro Tololo Inter-American Observatory, between 2008 August and 2009 October. The new transits have been combined with all previously published transit data for this planet to provide a new Transit Timing Variation (TTV) analysis of its orbit. We find no evidence of TTV rms variations larger than 1 minute over a 3 year time span. This result discards the presence of planets moremore » massive than about 5 M{sub Circled-Plus }, 1 M{sub Circled-Plus }, and 2 M{sub Circled-Plus} around the 1:2, 5:3, and 2:1 orbital resonances, respectively. These new detection limits exceed by {approx}5-30 times the limits imposed by current radial velocity observations in the mean motion resonances of this system. Our search for the variation of other parameters, such as orbital inclination and transit depth, also yields negative results over the total time span of the transit observations. This result supports formation theories that predict a paucity of planetary companions to hot Jupiters.« less
  • The transit timing variation (TTV) method relies on monitoring changes in timing of transits of known exoplanets. Non-transiting planets in the system can be inferred from TTVs by their gravitational interaction with the transiting planet. The TTV method is sensitive to low-mass planets that cannot be detected by other means. Here we describe a fast algorithm that can be used to determine the mass and orbit of the non-transiting planets from the TTV data. We apply our code, ttvim.f, to a wide variety of planetary systems to test the uniqueness of the TTV inversion problem and its dependence on themore » precision of TTV observations. We find that planetary parameters, including the mass and mutual orbital inclination of planets, can be determined from the TTV data sets that should become available in near future. Unlike the radial velocity technique, the TTV method can therefore be used to characterize the inclination distribution of multi-planet systems.« less