Numerical and Analytical Modeling of Transit timing variations

Hadden, Sam; Lithwick, Yoram

doi:10.3847/0004-637x/828/1/44

Cited by 99 publications

(111 citation statements)

References 46 publications

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“…Hadden & Lithwick (2015) performed an independent analysis of the TTVs of Kepler-307 using transit times measured from longcadence data, and their dynamical results are consistent with ), respectively. However, our precise constraints on the stellar parameters imply slightly lower masses for the planets, smaller radii, and higher densities, as shown in Section 5.…”

Section: Kepler-307 (Koi-1576)mentioning

confidence: 78%

“…In some cases, however, the degeneracy can be broken where high-frequencyTTVs are detected, like the socalled choppingat synodic frequencies (Nesvorný & Morbidelli 2008;Agol & Deck 2015;Deck & Agol 2015a;Hadden & Lithwick 2015).…”

Section: Validating Analytical Approximationsmentioning

confidence: 99%

“…All simulations were stable to 1 Myr, and we adopt these as reliable dynamical masses. Hadden & Lithwick (2015) performed an independent analysis of the TTVs of Kepler-26 using transit times measured from long-cadence data. Their measured dynamical masses are closely consistent with ours.…”

Section: Kepler-26 (Koi-250)mentioning

confidence: 99%

“…These include the three planets of Kepler-138 (Jontof-Hutter et al 2015). Other studies have measured precise masses using the data through Q16 (Kepler-79; Jontof-Hutteret al 2014), Q14 (Kepler-11;Lissauer et al 2013), or earlier data sets, as well as Q17 data in long cadence (e.g., Hadden & Lithwick 2015;Goździewski et al 2016).…”

Section: Introductionmentioning

confidence: 99%

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SECURE MASS MEASUREMENTS FROM TRANSIT TIMING: 10 KEPLER EXOPLANETS BETWEEN 3 AND 8 M _⊕ WITH DIVERSE DENSITIES AND INCIDENT FLUXES

Jontof-Hutter

Ford

Rowe

et al. 2016

ApJ

178

147

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We infer dynamical masses in eight multiplanet systems using transit times measured from Keplerʼs complete dataset, including short-cadence data where available. Of the 18dynamical masses that we infer, 10pass multiple tests for robustness. These are in systemsKepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), , and Kepler-307 (KOI-1576). Kepler-105 c has a radius of 1.3 R ⊕ and a density consistent with an Earth-like composition. Strong transit timing variation(TTV) signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently measured transit times, including planets orbitingKepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115), and Kepler-177 (KOI-523). Nonetheless, strong upper limits on the mass of Kepler-177 c imply an extremely low density of∼0.1 g cm −3 . In most cases, individual orbital eccentricities were poorly constrained owingto degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderatetohigh likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, nonlibrating solutions also match the transittiming data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have secure mass measurements. Placing these exoplanets on the mass-radius diagram, we find thata wide range of densities isobserved among sub-Neptune-mass planets and that the range in observed densities is anticorrelated with incident flux.

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Section: Kepler-307 (Koi-1576)mentioning

confidence: 78%

Section: Validating Analytical Approximationsmentioning

confidence: 99%

Section: Kepler-26 (Koi-250)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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SECURE MASS MEASUREMENTS FROM TRANSIT TIMING: 10 KEPLER EXOPLANETS BETWEEN 3 AND 8 M _⊕ WITH DIVERSE DENSITIES AND INCIDENT FLUXES

Jontof-Hutter

Ford

Rowe

et al. 2016

ApJ

178

147

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“…Transit timing variations (TTVs; Miralda-Escudé 2002; Agol et al 2005;Holman & Murray 2005) have proved useful for constraining the masses and orbital elements of exoplanets (e.g., Carter et al 2012;Huber et al 2013;Nesvorný et al 2013). To date, most TTV studies have focused on pairs of planets near mean motion resonances (MMRs) and in particular on those near first-order resonances.…”

Section: Introductionmentioning

confidence: 99%

Transit Timing Variations for Planets Near Eccentricity-Type Mean Motion Resonances

Deck

Agol

2016

ApJ

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We derive the transit timing variations (TTVs) of two planets near a second-order mean motion resonance (MMR) on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of --jn j n 2 2 1 ( ) , where  j 3 is an integer characterizing the resonance and n 2 and n 1 are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV depends on the mass of the perturbing planet, relative to the mass of the star, and on both the eccentricities and longitudes of pericenter of each planet. The TTVs of the two planets are approximated anti-correlated, with phases of f and f p » + , where the phase f also depends on the eccentricities and longitudes of pericenter. Therefore, the TTVs caused by proximity to a second-order MMR do not in general uniquely determine both planet masses, eccentricities, and pericenters. This is completely analogous to the case of TTVs induced by two planets near a first-order MMR. We explore how other TTV signals, such as the short-period synodic TTV or a first-order resonant TTV, in combination with the second-order resonant TTV, can break degeneracies. Finally, we derive approximate formulae for the TTVs of planets near any order eccentricity-type MMR; this shows that the same basic sinusoidal TTV structure holds for all eccentricity-type resonances. Our general formula reduces to previously derived results near first-order MMRs.

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Constraining the Densities of the Three Kepler-289 Planets with Transit Timing Variations

Greklek-McKeon

2020

Preprint

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Kepler-289 is a three-planet system containing two sub-Neptunes and one cool giant planet orbiting a young, Sun-like star. All three planets exhibit transit timing variations (TTVs), with both adjacent planet pairs having orbital periods close to the 2:1 orbital resonance. We observe two transits of Kepler-289c with the Wide-field InfraRed Camera (WIRC) on the 200" Hale Telescope at Palomar Observatory, using diffuser-assisted photometry to achieve space-like photometric precision from the ground. These new transit observations extend the original four-year Kepler TTV baseline by an additional 7.5 years. We re-reduce the archival Kepler data with an improved stellar activity correction and carry out a joint fit with the Palomar data to constrain the transit shapes and derive updated transit times. We then model the TTVs to determine the masses of the three planets and constrain their densities and bulk compositions. Our new analysis improves on previous mass and density constraints by a factor of two or more for all three planets, with the innermost planet showing the largest improvement. Our updated atmospheric mass fractions for the inner two planets indicate that they likely have hydrogenrich envelopes, consistent with their location on the upper side of the radius valley. We also constrain the heavy element composition of the outer saturn-mass planet, Kepler-289c, for the first time, finding that it contains 30.5 ± 6.9 M ⊕ of metals. We use dust evolution models to show that Kepler-289c must have formed beyond 1 au, and likely beyond 3 au, and then migrated inward.

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Numerical and Analytical Modeling of Transit timing variations

Cited by 99 publications

References 46 publications

SECURE MASS MEASUREMENTS FROM TRANSIT TIMING: 10 KEPLER EXOPLANETS BETWEEN 3 AND 8 M _⊕ WITH DIVERSE DENSITIES AND INCIDENT FLUXES

SECURE MASS MEASUREMENTS FROM TRANSIT TIMING: 10 KEPLER EXOPLANETS BETWEEN 3 AND 8 M _⊕ WITH DIVERSE DENSITIES AND INCIDENT FLUXES

Transit Timing Variations for Planets Near Eccentricity-Type Mean Motion Resonances

Constraining the Densities of the Three Kepler-289 Planets with Transit Timing Variations

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Numerical and Analytical Modeling of Transit timing variations

Cited by 99 publications

References 46 publications

SECURE MASS MEASUREMENTS FROM TRANSIT TIMING: 10 KEPLER EXOPLANETS BETWEEN 3 AND 8 M ⊕ WITH DIVERSE DENSITIES AND INCIDENT FLUXES

SECURE MASS MEASUREMENTS FROM TRANSIT TIMING: 10 KEPLER EXOPLANETS BETWEEN 3 AND 8 M ⊕ WITH DIVERSE DENSITIES AND INCIDENT FLUXES

Transit Timing Variations for Planets Near Eccentricity-Type Mean Motion Resonances

Constraining the Densities of the Three Kepler-289 Planets with Transit Timing Variations

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SECURE MASS MEASUREMENTS FROM TRANSIT TIMING: 10 KEPLER EXOPLANETS BETWEEN 3 AND 8 M _⊕ WITH DIVERSE DENSITIES AND INCIDENT FLUXES

SECURE MASS MEASUREMENTS FROM TRANSIT TIMING: 10 KEPLER EXOPLANETS BETWEEN 3 AND 8 M _⊕ WITH DIVERSE DENSITIES AND INCIDENT FLUXES