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

Title: TRANSIT TIMING VARIATIONS FOR INCLINED AND RETROGRADE EXOPLANETARY SYSTEMS

Abstract

We perform numerical calculations of the expected transit timing variations (TTVs) induced on a hot-Jupiter by an Earth-mass perturber. Motivated by the recent discoveries of retrograde transiting planets, we concentrate on an investigation of the effect of varying relative planetary inclinations, up to and including completely retrograde systems. We find that planets in low-order (e.g., 2:1) mean-motion resonances (MMRs) retain approximately constant TTV amplitudes for 0 deg. < i < 170 deg., only reducing in amplitude for i>170 deg. Systems in higher order MMRs (e.g., 5:1) increase in TTV amplitude as inclinations increase toward 45 deg., becoming approximately constant for 45 deg. < i < 135 deg., and then declining for i>135 deg. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0 deg. to 180 deg., whereas planets adjacent to resonances can exhibit a huge range of variability in TTV amplitude as a function of both eccentricity and inclination. For highly retrograde systems (135 deg. < i {<=} 180 deg.), TTV signals will be undetectable across almost the entirety of parameter space, with the exceptions occurring when the perturber has high eccentricity or is very close to an MMR. This high inclination decrease in TTVmore » amplitude (on and away from resonance) is important for the analysis of the known retrograde and multi-planet transiting systems, as inclination effects need to be considered if TTVs are to be used to exclude the presence of any putative planetary companions: absence of evidence is not evidence of absence.« less

Authors:
; ;  [1]
  1. Department of Astronomy, University of Florida, 211 Bryant Space Science Center, PO Box 112055, Gainesville, FL 32611-2055 (United States), E-mail: matthewjohnpayne@gmail.com
Publication Date:
OSTI Identifier:
21305079
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal Letters; Journal Volume: 712; Journal Issue: 1; Other Information: DOI: 10.1088/2041-8205/712/1/L86; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; AMPLITUDES; INCLINATION; JUPITER PLANET; RESONANCE; SIGNALS

Citation Formats

Payne, Matthew J., Ford, Eric B., and Veras, Dimitri. TRANSIT TIMING VARIATIONS FOR INCLINED AND RETROGRADE EXOPLANETARY SYSTEMS. United States: N. p., 2010. Web. doi:10.1088/2041-8205/712/1/L86; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Payne, Matthew J., Ford, Eric B., & Veras, Dimitri. TRANSIT TIMING VARIATIONS FOR INCLINED AND RETROGRADE EXOPLANETARY SYSTEMS. United States. doi:10.1088/2041-8205/712/1/L86; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Payne, Matthew J., Ford, Eric B., and Veras, Dimitri. 2010. "TRANSIT TIMING VARIATIONS FOR INCLINED AND RETROGRADE EXOPLANETARY SYSTEMS". United States. doi:10.1088/2041-8205/712/1/L86; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21305079,
title = {TRANSIT TIMING VARIATIONS FOR INCLINED AND RETROGRADE EXOPLANETARY SYSTEMS},
author = {Payne, Matthew J. and Ford, Eric B. and Veras, Dimitri},
abstractNote = {We perform numerical calculations of the expected transit timing variations (TTVs) induced on a hot-Jupiter by an Earth-mass perturber. Motivated by the recent discoveries of retrograde transiting planets, we concentrate on an investigation of the effect of varying relative planetary inclinations, up to and including completely retrograde systems. We find that planets in low-order (e.g., 2:1) mean-motion resonances (MMRs) retain approximately constant TTV amplitudes for 0 deg. < i < 170 deg., only reducing in amplitude for i>170 deg. Systems in higher order MMRs (e.g., 5:1) increase in TTV amplitude as inclinations increase toward 45 deg., becoming approximately constant for 45 deg. < i < 135 deg., and then declining for i>135 deg. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0 deg. to 180 deg., whereas planets adjacent to resonances can exhibit a huge range of variability in TTV amplitude as a function of both eccentricity and inclination. For highly retrograde systems (135 deg. < i {<=} 180 deg.), TTV signals will be undetectable across almost the entirety of parameter space, with the exceptions occurring when the perturber has high eccentricity or is very close to an MMR. This high inclination decrease in TTV amplitude (on and away from resonance) is important for the analysis of the known retrograde and multi-planet transiting systems, as inclination effects need to be considered if TTVs are to be used to exclude the presence of any putative planetary companions: absence of evidence is not evidence of absence.},
doi = {10.1088/2041-8205/712/1/L86; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Astrophysical Journal Letters},
number = 1,
volume = 712,
place = {United States},
year = 2010,
month = 3
}
  • 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
  • Analysis of the transit timing variations (TTVs) of candidate pairs near mean-motion resonances (MMRs) is an effective method to confirm planets. Hitherto, 68 planets in 34 multi-planet systems have been confirmed via TTVs. We analyze the TTVs of all candidates from the most recent Kepler data with a time span of upto about 1350 days (Q0-Q15). The anti-correlations of TTV signals and the mass upper limits of candidate pairs in the same system are calculated using an improved method suitable for long-period TTVs. If the false alarm probability of a candidate pair is less than 10{sup –3} and the massmore » upper limit for each candidate is less than 13 M {sub J}, we confirm them as planets in the same system. Finally, eight planets in four multi-planet systems are confirmed via analysis of their TTVs. All of the four planet pairs are near first-order MMRs, including KOI-2672 near 2:1 MMR and KOI-1236, KOI-1563, and KOI-2038 near 3:2 MMR. Four planets have relatively long orbital periods (>35 days). KOI-2672.01 has an orbital period of 88.51658 days and a fit mass of 17 M {sub ⊕}. To date, it is the longest-period planet confirmed near a first-order MMR via TTVs.« less
  • Knowledge of an exoplanet's oblateness and obliquity would give clues about its formation and internal structure. In principle, a light curve of a transiting planet bears information about the planet's shape, but previous work has shown that the oblateness-induced signal will be extremely difficult to detect. Here, we investigate the potentially larger signals due to planetary spin precession. The most readily detectable effects are transit depth variations (T{delta}V's) in a sequence of light curves. For a planet as oblate as Jupiter or Saturn, the transit depth will undergo fractional variations of order 1%. The most promising systems are those withmore » orbital periods of approximately 15-30 days, which are short enough for the precession period to be less than about 40 yr and long enough to avoid spin-down due to tidal friction. The detectability of the T{delta}V signal would be enhanced by moons (which would decrease the precession period) or planetary rings (which would increase the amplitude). The Kepler mission should find several planets for which precession-induced T{delta}V signals will be detectable. Due to modeling degeneracies, Kepler photometry would yield only a lower bound on oblateness. The degeneracy could be lifted by observing the oblateness-induced asymmetry in at least one transit light curve or by making assumptions about the planetary interior.« less