Transit-timing variation

Transit-timing variation is a method for detecting exoplanets by observing variations in the timing of a transit. This provides an extremely sensitive method capable of detecting additional planets in the system with masses potentially as small as that of Earth. In tightly packed planetary systems, the gravitational pull of the planets among themselves causes one planet to accelerate and another planet to decelerate along its orbit. The acceleration causes the orbital period of each planet to change. Detecting this effect by measuring the change is known as Transit Timing Variations.[1][2][3][4][5][6] "Timing variation" asks whether the transit occurs with strict periodicity or if there's a variation.

The first significant detection of a non-transiting planet using transit-timing variations was carried out with NASA's Kepler telescope. The transiting planet Kepler-19b shows transit-timing variation with an amplitude of 5 minutes and a period of about 300 days, indicating the presence of a second planet, Kepler-19c, which has a period that is a near-rational multiple of the period of the transiting planet.[7][8]

In 2010, researchers proposed a second planet orbiting WASP-3 based on transit-timing variation,[9][10] but this proposal was debunked in 2012.[11]

Transit-timing variation was first convincingly detected for planets Kepler-9b and Kepler-9c [12] and gained popularity by 2012 for confirming exoplanet discoveries.[13]

TTV can also be used to indirectly measure the mass of the exoplanets in compact, multiple-planet systems and/or system whose planets are in resonant chains. By performing a series of analytical (TTVFaster[14]) and numerical (TTVFast[15] and Mercury[16]) n-body integrations of a system of six gravitationally interacting, co-planar planets, the initial mass estimates for the six inner planets of TRAPPIST-1, along with their orbital eccentricities, were determined.[17]

References
  1. "The Transit Timing Variation (TTV) Planet-finding Technique Begins to Flower".
  2. Steffen, Jason H.; Fabrycky, Daniel C.; Agol, Eric; Ford, Eric B.; Morehead, Robert C.; Cochran, William D.; Lissauer, Jack J.; Adams, Elisabeth R.; Borucki, William J.; Bryson, Steve; Caldwell, Douglas A.; Dupree, Andrea; Jenkins, Jon M.; Robertson, Paul; Rowe, Jason F.; Seader, Shawn; Thompson, Susan; Twicken, Joseph D. (2013). "Transit timing observations from Kepler – VII. Confirmation of 27 planets in 13 multiplanet systems via transit timing variations and orbital stability". Monthly Notices of the Royal Astronomical Society. 428 (2): 1077–1087. arXiv:1208.3499. Bibcode:2013MNRAS.428.1077S. doi:10.1093/mnras/sts090. S2CID 14676852.
  3. Xie, Ji-Wei (2013). "Transit Timing Variation of Near-Resonance Planetary Pairs: Confirmation of 12 Multiple-Planet Systems". The Astrophysical Journal Supplement Series. 208 (2): 22. arXiv:1208.3312. Bibcode:2013ApJS..208...22X. doi:10.1088/0067-0049/208/2/22. S2CID 17160267.
  4. Miralda-Escude (2001). "Orbital perturbations on transiting planets: A possible method to measure stellar quadrupoles and to detect Earth-mass planets". The Astrophysical Journal. 564 (2): 1019–1023. arXiv:astro-ph/0104034. Bibcode:2002ApJ...564.1019M. doi:10.1086/324279. S2CID 7536842.
  5. Holman; Murray (2005). "The Use of Transit Timing to Detect Extrasolar Planets with Masses as Small as Earth". Science. 307 (1291): 1288–91. arXiv:astro-ph/0412028. Bibcode:2005Sci...307.1288H. doi:10.1126/science.1107822. PMID 15731449. S2CID 41861725.
  6. Agol; Sari; Steffen; Clarkson (2005). "On detecting terrestrial planets with timing of giant planet transits". Monthly Notices of the Royal Astronomical Society. 359 (2): 567–579. arXiv:astro-ph/0412032. Bibcode:2005MNRAS.359..567A. doi:10.1111/j.1365-2966.2005.08922.x. S2CID 16196696.
  7. "Invisible World Discovered". NASA Kepler News. 8 September 2011.
  8. Ballard, S.; Fabrycky, D.; Fressin, F.; Charbonneau, D.; Desert, J.-M.; Torres, G.; Marcy, G.; Burke, C. J.; Isaacson, H.; Henze, C.; Steffen, J. H.; Ciardi, D. R.; Howell, S. B.; Cochran, W. D.; Endl, M.; Bryson, S. T.; Rowe, J. F.; Holman, M. J.; Lissauer, J. J.; Jenkins, J. M.; Still, M.; Ford, E. B.; Christiansen, J. L.; Middour, C. K.; Haas, M. R.; Li, J.; Hall, J. R.; McCauliff, S.; Batalha, N. M.; Koch, D. G.; Borucki, W. J. (2011), "The Kepler-19 System: A Transiting 2.2 R $_⊕$ Planet and a Second Planet Detected via Transit Timing Variations", Astrophysical Journal, 743 (2): 200, arXiv:1109.1561, Bibcode:2011ApJ...743..200B, doi:10.1088/0004-637X/743/2/200, S2CID 42698813
  9. Planet found tugging on transits Archived 2010-07-13 at the Wayback Machine, Astronomy Now, 9 July 2010
  10. Maciejewski, G.; Dimitrov, D.; Neuh\auser, R.; Niedzielski, A.; Raetz, S.; Ginski, C.; Adam, C.; Marka, C.; Moualla, M.; Mugrauer, M. (2010), "Transit timing variation in exoplanet WASP-3b", MNRAS, 407 (4): 2625, arXiv:1006.1348, Bibcode:2010MNRAS.407.2625M, doi:10.1111/j.1365-2966.2010.17099.x
  11. M Montalto; et al. (Nov 2, 2012). "A new analysis of the WASP-3 system: no evidence for an additional companion". MNRAS. 427 (4): 2757–2771. arXiv:1211.0218. Bibcode:2012MNRAS.427.2757M. doi:10.1111/j.1365-2966.2012.21926.x. S2CID 59381004.
  12. Harrington, J.D. (26 August 2010). "NASA's Kepler Mission Discovers Two Planets Transiting Same Star". nasa.gov. Retrieved 4 September 2018.
  13. Johnson, Michele (26 January 2012). "NASA's Kepler Announces 11 Planetary Systems Hosting 26 Planets". nasa.gov. Retrieved 4 September 2018.
  14. Agol, E.; Deck, K. (2016), "Transit Timing to First Order in Eccentricity", Astrophysical Journal, 818 (2): 177, arXiv:1509.01623, Bibcode:2016ApJ...818..177A, doi:10.3847/0004-637X/818/2/177, S2CID 38941103
  15. Deck, K. M.; Agol, E.; Holman, M. J.; Nesvorn\'y, D. (2014), "TTVFast: An Efficient and Accurate Code for Transit Timing Inversion Problems", Astrophysical Journal, 787 (2): 132, arXiv:1403.1895, Bibcode:2014ApJ...787..132D, doi:10.1088/0004-637X/787/2/132, S2CID 53965722
  16. Chambers, J. E. (1999), "A hybrid symplectic integrator that permits close encounters between massive bodies", MNRAS, 304 (4): 793–799, Bibcode:1999MNRAS.304..793C, CiteSeerX 10.1.1.25.3257, doi:10.1046/j.1365-8711.1999.02379.x
  17. Gillon, M.; Triaud, A. H. M. J.; Demory, B.-O.; Jehin, E.; Agol, E.; Deck, K. M.; Lederer, S. M.; de, Wit J.; Burdanov, A.; Ingalls, J. G.; Bolmont, E.; Leconte, J.; Raymond, S. N.; Selsis, F.; Turbet, M.; Barkaoui, K.; Burgasser, A.; Burleigh, M. R.; Carey, S. J.; Chaushev, A.; Copperwheat, C. M.; Delrez, L.; Fernandes, C. S.; Holdsworth, D. L.; Kotze, E. J.; Van, Grootel V.; Almleaky, Y.; Benkhaldoun, Z.; Magain, P.; Queloz, D. (2017), "Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1", Nature, 542 (7642): 456–460, arXiv:1703.01424, Bibcode:2017Natur.542..456G, doi:10.1038/nature21360, PMC 5330437, PMID 28230125
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