Abstract
Transiting exoplanets in multi-planet systems have non-Keplerian orbits which can cause the times and durations of transits to vary. The theory and observations of transit-timing variations (TTVs) and transit duration variations (TDVs) are reviewed. Since the last review, the Kepler spacecraft has detected several hundred perturbed planets. In a few cases, these data have been used to discover additional planets, similar to the historical discovery of Neptune in our own solar system. However, the more impactful aspect of TTV and TDV studies has been characterization of planetary systems in which multiple planets transit. After addressing the equations of motion and parameter scalings, the main dynamical mechanisms for TTV and TDV are described, with citations to the observational literature for real examples. We describe parameter constraints, particularly the origin of the mass/eccentricity degeneracy and how it is overcome by the high-frequency component of the signal. On the observational side, derivation of timing precision and introduction to the timing diagram are given. Science results are reviewed, with an emphasis on mass measurements of transiting sub-Neptunes and super-Earths, from which bulk compositions may be inferred.
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References
Adams JC (1847) An explanation of the observed irregularities in the motion of Uranus, on the hypothesis of disturbances caused by a more distant planet; with a determination of the mass, orbit, and position of the disturbing body. MmRAS 16:427
Agol E, Deck K (2016) Transit timing to first order in eccentricity. ApJ 818:177
Agol E, Steffen J, Sari R, Clarkson W (2005) On detecting terrestrial planets with timing of giant planet transits. MNRAS 359:567–579
Almenara JM, Díaz RF, Mardling R et al (2015) Absolute masses and radii determination in multiplanetary systems without stellar models. MNRAS 453:2644–2652
Almenara JM, Díaz RF, Bonfils X, Udry S (2016) Absolute densities, masses, and radii of the WASP-47 system determined dynamically. A&A 595:L5
Ballard S, Fabrycky D, Fressin F et al (2011) The Kepler-19 system: a transiting 2.2 R ⊕ planet and a second planet detected via transit timing variations. ApJ 743:200
Barnes JW, van Eyken JC, Jackson BK, Ciardi DR, Fortney JJ (2013) Measurement of spin-orbit misalignment and nodal precession for the planet around pre-main-sequence star PTFO 8-8695 from gravity darkening. ApJ 774:53
Barros SCC, Boué G, Gibson NP et al (2013) Transit timing variations in WASP-10b induced by stellar activity. MNRAS 430:3032–3047
Becker JC, Vanderburg A, Adams FC, Rappaport SA, Schwengeler HM (2015) WASP-47: a hot Jupiter system with two additional planets discovered by K2. ApJ 812:L18
Beichman C, Benneke B, Knutson H et al (2014) Observations of transiting exoplanets with the James webb space telescope (JWST). PASP 126:1134–1173
Borkovits T, Érdi B, Forgács-Dajka E, Kovács T (2003) On the detectability of long period perturbations in close hierarchical triple stellar systems. A&A 398:1091–1102
Carter JA, Winn JN (2009) Parameter estimation from time-series data with correlated errors: a wavelet-based method and its application to transit light curves. ApJ 704:51–67
Carter JA, Yee JC, Eastman J, Gaudi BS, Winn JN (2008) Analytic approximations for transit light-curve observables, uncertainties, and covariances. ApJ 689:499-512
Carter JA, Agol E, Chaplin WJ et al (2012) Kepler-36: a pair of planets with neighboring orbits and dissimilar densities. Science 337:556
Cochran WD, Fabrycky DC, Torres G et al (2011) Kepler-18b, c, and d: a system of three planets confirmed by transit timing variations, light curve validation, warm-spitzer photometry, and radial velocity measurements. ApJS 197:7
Dawson RI, Johnson JA, Fabrycky DC et al (2014) Large eccentricity, low mutual inclination: the three-dimensional architecture of a hierarchical system of giant planets. ApJ 791:89
Deck KM, Agol E (2015) Measurement of planet masses with transit timing variations due to synodic “chopping” effects. ApJ 802:116
Deck KM, Agol E (2016) Transit timing variations for planets near eccentricity-type mean motion resonances. ApJ 821:96
Dobrovolskis AR, Borucki WJ (1996a) Influence of Jovian extrasolar planets on transits of inner planets. In: AAS/Division for planetary sciences meeting abstracts #28. Bulletin of the American astronomical society, vol 28, p 1112
Dobrovolskis AR, Borucki WJ (1996b) Influence of Jovian extrasolar planets on transits of inner planets. In: Bulletin of the American astronomical society, BAAS, vol 28, p 1112
Doyle LR, Carter JA, Fabrycky DC et al (2011) Kepler-16: a transiting circumbinary planet. Science 333:1602
Eastman J, Siverd R, Gaudi BS (2010) Achieving better than 1 minute accuracy in the heliocentric and barycentric Julian dates. PASP 122:935–946
Fabrycky DC, Ford EB, Steffen JH et al (2012) Transit timing observations from Kepler. IV. Confirmation of four multiple-planet systems by simple physical models. ApJ 750:114
Ford EB, Fabrycky DC, Steffen JH et al (2012a) Transit timing observations from Kepler. II. Confirmation of two multiplanet systems via a non-parametric correlation analysis. ApJ 750:113
Ford EB, Ragozzine D, Rowe JF et al (2012b) Transit timing observations from Kepler. V. Transit timing variation candidates in the first sixteen months from polynomial models. ApJ 756:185
Foreman-Mackey D, Agol E, Angus R, Ambikasaran S (2017) Fast and scalable Gaussian process modeling with applications to astronomical time series. ArXiv e-prints https://arxiv.org/abs/1703.09710
Gibson NP, Aigrain S, Roberts S et al (2012) A Gaussian process framework for modelling instrumental systematics: application to transmission spectroscopy. MNRAS 419:2683–2694
Gillon M, Triaud AHMJ, Demory BO et al (2017) Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1. Nature 542:456–460
Ginzburg S, Schlichting HE, Sari R (2016) Super-Earth atmospheres: self-consistent gas accretion and retention. ApJ 825:29
Hadden S, Lithwick Y (2014) Densities and eccentricities of 139 Kepler planets from transit time variations. ApJ 787:80
Hadden S, Lithwick Y (2016) Numerical and analytical modeling of transit timing variations. ApJ 828:44
Hadden S, Lithwick Y (2017) Kepler planet masses and eccentricities from TTV analysis. Astron J 154(1):5. https://doi.org/10.3847/1538-3881/aa71ef
Heyl JS, Gladman BJ (2007) Using long-term transit timing to detect terrestrial planets. MNRAS 377:1511–1519
Holczer T, Mazeh T, Nachmani G et al (2016) Transit timing observations from Kepler. IX. Catalog of the full long-cadence data set. ApJS 225:9
Holman MJ, Murray NW (2005) The use of transit timing to detect terrestrial-mass extrasolar planets. Science 307:1288–1291
Holman MJ, Fabrycky DC, Ragozzine D et al (2010) Kepler-9: a system of multiple planets transiting a sun-like star, confirmed by timing variations. Science 330:51
Ioannidis P, Huber KF, Schmitt JHMM (2016) How do starspots influence the transit timing variations of exoplanets? Simulations of individual and consecutive transits. A&A 585:A72
Jontof-Hutter D, Ford EB, Rowe JF et al (2016) Secure mass measurements from transit timing: 10 Kepler exoplanets between 3 and 8 M⊕ with diverse densities and incident fluxes. ApJ 820:39
Kipping DM (2014) Characterizing distant worlds with asterodensity profiling. MNRAS 440:2164–2184
Kostov VB, McCullough PR, Hinse TC et al (2013) A gas giant circumbinary planet transiting the F star primary of the eclipsing binary star KIC 4862625 and the independent discovery and characterization of the two transiting planets in the Kepler-47 system. ApJ 770:52
Kostov VB, McCullough PR, Carter JA et al (2014) Kepler-413b: a slightly misaligned, Neptune-size transiting circumbinary planet. ApJ 784:14
Laughlin G, Chambers JE (2001) Short-term dynamical interactions among extrasolar planets. ApJ 551:L109–L113
Le Verrier UJ (1877) Tables du mouvement de Neptune fondees sur la comparaison de la theorie avec les observations. Annales de l’Observatoire de Paris 14:1
Lee EJ, Chiang E (2016) Breeding super-earths and birthing super-puffs in transitional disks. ApJ 817:90
Lissauer JJ, Fabrycky DC, Ford EB et al (2011) A closely packed system of low-mass, low-density planets transiting Kepler-11. Nature 470:53–58
Lithwick Y, Xie J, Wu Y (2012) Extracting planet mass and eccentricity from TTV data. ApJ 761:122
Martin DV (2017) Circumbinary planets – II. When transits come and go. MNRAS 465:3235–3253
Masuda K (2014) Very low density planets around Kepler-51 revealed with transit timing variations and an anomaly similar to a planet-planet eclipse event. ApJ 783:53
Mayer P (1971) Eclipsing variable IU Aurigae. Bull Astron Inst Czech 22:168
Mazeh T, Nachmani G, Holczer T et al (2013) Transit timing observations from Kepler. VIII. Catalog of transit timing measurements of the first twelve quarters. ApJS 208:16
Meschiari S, Laughlin GP (2010) Systemic: a testbed for characterizing the detection of extrasolar planets. II. Numerical approaches to the transit timing inverse problem. ApJ 718: 543–550
Mills SM, Fabrycky DC (2017) Kepler-108: a mutually inclined giant planet system. Astron J 153(1):45. http://stacks.iop.org/1538-3881/153/i=1/a=45
Mills SM, Mazeh T (2017) The planetary mass-radius relation and its dependence on orbital period as measured by transit timing variations and radial velocities. ApJ 839:L8
Mills SM, Fabrycky DC, Migaszewski C et al (2016) A resonant chain of four transiting, sub-Neptune planets. Nature 533:509–512
Miralda-Escudé J (2002) Orbital perturbations of transiting planets: a possible method to measure stellar quadrupoles and to detect earth-mass planets. ApJ 564:1019–1023
Montet BT, Johnson JA (2013) Model-independent stellar and planetary masses from multi-transiting exoplanetary systems. ApJ 762:112
Montet BT, Yee JC, Penny MT (2017) Measuring the galactic distribution of transiting planets with WFIRST. PASP 129(4):044,401
Nesvorný D (2009) Transit timing variations for eccentric and inclined exoplanets. ApJ 701:1116–1122
Nesvorný D, Beaugé C (2010) Fast inversion method for determination of planetary parameters from transit timing variations. ApJ 709:L44–L48
Nesvorný D, Morbidelli A (2008) Mass and orbit determination from transit timing variations of exoplanets. ApJ 688:636–646
Nesvorný D, Vokrouhlický D (2014) The effect of conjunctions on the transit timing variations of exoplanets. ApJ 790:58
Nesvorný D, Vokrouhlický D (2016) Dynamics and transit variations of resonant exoplanets. ApJ 823:72
Nesvorný D, Kipping DM, Buchhave LA et al (2012) The detection and characterization of a nontransiting planet by transit timing variations. Science 336:1133
Nesvorný D, Kipping D, Terrell D et al (2013) KOI-142, the king of transit variations, is a pair of planets near the 2:1 resonance. ApJ 777:3
Oshagh M, Santos NC, Boisse I et al (2013) Effect of stellar spots on high-precision transit light-curve. A&A 556:A19
Pál A, Kocsis B (2008) Periastron precession measurements in transiting extrasolar planetary systems at the level of general relativity. MNRAS 389:191–198
Price EM, Rogers LA (2014) Transit light curves with finite integration time: fisher information analysis. ApJ 794:92
Ragozzine D, Wolf AS (2009) Probing the interiors of very hot Jupiters using transit light curves. ApJ 698:1778–1794
Rauer H, Catala C, Aerts C et al (2014) The PLATO 2.0 mission. Exp Astron 38:249–330
Ricker GR, Winn JN, Vanderspek R et al (2015) Transiting exoplanet survey satellite (TESS). J Astron Telesc Instrum Syst 1(1):014003
Rowe JF, Coughlin JL, Antoci V et al (2015) Planetary candidates observed by Kepler. V. Planet sample from q1–q12 (36 months). Astrophys J Suppl Ser 217(1):16. https://doi.org/10.1088/0067-0049/217/1/16
Schmitt JR, Agol E, Deck KM et al (2014) Planet hunters. VII. Discovery of a new low-mass, low-density planet (PH3 C) orbiting Kepler-289 with mass measurements of two additional planets (PH3 B and D). ApJ 795:167
Schneider J (2003) Multi-planet system detection by transits. In: Combes F, Barret D, Contini T, Pagani L (eds) SF2A-2003: semaine de l’Astrophysique Francaise, p 149. http://adsabs.harvard.edu/abs/2003sf2a.conf..149S
Schneider J (2004) Multi-planet system detection with Eddington. In: Favata F, Aigrain S, Wilson A (eds) Stellar structure and habitable planet finding, vol 538. ESA Special Publication, Noordwijk, p 407–410
Seager S, Mallén-Ornelas G (2003) A unique solution of planet and star parameters from an extrasolar planet transit light curve. ApJ 585:1038–1055
Steffen J (2006) Detecting new planets in transiting systems. PhD thesis, University of Washington
Steffen JH (2016) Sensitivity bias in the mass–radius distribution from transit timing variations and radial velocity measurements. Mon Not R Astron Soc 457(4):4384–4392. https://doi.org/10.1093/mnras/stw241
Steffen JH, Agol E (2005) An analysis of the transit times of TrES-1b. MNRAS 364: L96–L100
Steffen JH, Fabrycky DC, Ford EB et al (2012) Transit timing observations from Kepler – III. Confirmation of four multiple planet systems by a Fourier-domain study of anticorrelated transit timing variations. MNRAS 421:2342–2354
Sterken C (2005) The O-C diagram: basic procedures. In: Sterken C (ed) The light-time effect in astrophysics: causes and cures of the O-C diagram. Astronomical society of the pacific conference series, vol 335. Astronomical Society of the Pacific, San Francisco, p 3
Szabó GM, Pál A, Derekas A et al (2012) Spin-orbit resonance, transit duration variation and possible secular perturbations in KOI-13. Mon Not R Astron Soc Lett 421(1):L122–L126. https://doi.org/10.1111/j.1745-3933.2012.01219.x
Ulrich RK (1986) Determination of stellar ages from asteroseismology. ApJ 306:L37–L40
Welsh WF, Orosz JA, Carter JA et al (2012) Transiting circumbinary planets Kepler-34 b and Kepler-35 b. Nature 481:475–479
Wilson C (1985) The great inequality of Jupiter and Saturn: from Kepler to laplace. Arch Hist Exact Sci 33:15–290
Wolszczan A (1994) Confirmation of earth-mass planets orbiting the millisecond pulsar PSR B1257+12. Science 264:538–542
Xie JW (2013) Transit timing variation of near-resonance planetary pairs: confirmation of 12 multiple-planet systems. ApJS 208:22
Xie JW (2014) Transit timing variation of near-resonance planetary pairs. II. Confirmation of 30 planets in 15 multiple-planet systems. ApJS 210:25
Acknowledgements
EA acknowledges support from NASA Grants NNX13AF20G, NNX13A124G, and NNX13AF62G, from National Science Foundation (NSF) grant AST-1615315, and from NASA Astrobiology Institute’s Virtual Planetary Laboratory, supported by NASA under cooperative agreement NNH05ZDA001C. DCF acknowledges support from NASA under Grant No. NNX14AB87G issued through the Kepler Participating Scientist Program and from the Alfred P. Sloan Foundation. We thank Sam Hadden, Jack Lissauer, Kento Masuda, Mahmoudreza Oshagh, and Jason Steffen for feedback, and we thank the Other Worlds Laboratory at UC Santa Cruz for hospitality while revising this paper.
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Agol, E., Fabrycky, D.C. (2018). Transit-Timing and Duration Variations for the Discovery and Characterization of Exoplanets. In: Deeg, H., Belmonte, J. (eds) Handbook of Exoplanets . Springer, Cham. https://doi.org/10.1007/978-3-319-55333-7_7
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