Transit-timing variation

{{Short description|Exoplanet detection method using transit timing variations}}

File:201008-2a PlanetOrbits 16x9- Transit timing of 1-planet vs 2-planet systems.ogv

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.{{ cite web|url=https://www.nasa.gov/home/hqnews/2012/jan/HQ_12-032_Kepler_23-33.html|title= The Transit Timing Variation (TTV) Planet-finding Technique Begins to Flower}}{{cite journal |arxiv=1208.3499 |doi=10.1093/mnras/sts090 |title=Transit timing observations from Kepler – VII. Confirmation of 27 planets in 13 multiplanet systems via transit timing variations and orbital stability |year=2013 |last1=Steffen |first1=Jason H. |last2=Fabrycky |first2=Daniel C. |last3=Agol |first3=Eric |last4=Ford |first4=Eric B. |last5=Morehead |first5=Robert C. |last6=Cochran |first6=William D. |last7=Lissauer |first7=Jack J. |last8=Adams |first8=Elisabeth R. |last9=Borucki |first9=William J. |last10=Bryson |first10=Steve |last11=Caldwell |first11=Douglas A. |last12=Dupree |first12=Andrea |last13=Jenkins |first13=Jon M. |last14=Robertson |first14=Paul |last15=Rowe |first15=Jason F. |last16=Seader |first16=Shawn |last17=Thompson |first17=Susan |last18=Twicken |first18=Joseph D. |s2cid=14676852 |journal=Monthly Notices of the Royal Astronomical Society |volume=428 |issue=2 |pages=1077–1087 |doi-access=free |bibcode=2013MNRAS.428.1077S }}{{cite journal |arxiv=1208.3312 |doi=10.1088/0067-0049/208/2/22 |title=Transit Timing Variation of Near-Resonance Planetary Pairs: Confirmation of 12 Multiple-Planet Systems |year=2013 |last1=Xie |first1=Ji-Wei |s2cid=17160267 |journal=The Astrophysical Journal Supplement Series |volume=208 |issue=2 |page=22 |bibcode=2013ApJS..208...22X }}{{Cite journal| last1 = Yang| first1 = Ming| last2 = Liu| first2 = Hui-Gen| last3 = Zhang| first3 = Hui| last4 = Yang| first4 = Jia-Yi| last5 = Zhou| first5 = Ji-Lin| title = Eight Planets in Four Multi-planet Systems via Transit Timing Variations in 1350 Days| journal = The Astrophysical Journal| volume = 778| issue = 2| pages = 110| year = 2013| doi = 10.1088/0004-637X/778/2/110| arxiv = 1308.0996| bibcode = 2013ApJ...778..110Y}}{{cite journal|author1=Miralda-Escude|s2cid=7536842|title=Orbital perturbations on transiting planets: A possible method to measure stellar quadrupoles and to detect Earth-mass planets|date=2001|doi=10.1086/324279|journal=The Astrophysical Journal|volume=564|issue=2|pages=1019–1023|arxiv=astro-ph/0104034|bibcode = 2002ApJ...564.1019M }}{{cite journal |author1=Holman |author2=Murray|s2cid=41861725| title=The Use of Transit Timing to Detect Extrasolar Planets with Masses as Small as Earth|year=2005 |doi=10.1126/science.1107822 |volume=307 |issue=1291 |journal=Science |arxiv=astro-ph/0412028 |pmid=15731449 |pages=1288–91|bibcode=2005Sci...307.1288H}}{{cite journal|author1=Agol|author2=Sari|author3=Steffen|author4=Clarkson|s2cid=16196696|title=On detecting terrestrial planets with timing of giant planet transits|year=2005|doi=10.1111/j.1365-2966.2005.08922.x|journal=Monthly Notices of the Royal Astronomical Society|volume=359|issue=2|pages=567–579 |doi-access=free |arxiv=astro-ph/0412032|bibcode = 2005MNRAS.359..567A }} "Timing variation" asks whether the transit occurs with strict periodicity or if there exists 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.{{cite web | url=http://kepler.nasa.gov/news/nasakeplernews/index.cfm?FuseAction=ShowNews&NewsID=148 | archive-url=https://web.archive.org/web/20111019083552/http://kepler.nasa.gov/news/nasakeplernews/index.cfm?FuseAction=ShowNews&NewsID=148 | url-status=dead | archive-date=19 October 2011 | title=Invisible World Discovered | publisher = NASA Kepler News | date = 8 September 2011}}{{Citation | last1 = Ballard | first1 = S. | last2 = Fabrycky | first2 = D. | last3 = Fressin | first3 = F. | last4 = Charbonneau | first4 = D. | last5 = Desert | first5 = J.-M. | last6 = Torres | first6 = G. | last7 = Marcy | first7 = G. | last8 = Burke | first8 = C. J. | last9 = Isaacson | first9 = H. | last10 = Henze | first10 = C. | last11 = Steffen | first11 = J. H. | last12 = Ciardi | first12 = D. R. | last13 = Howell | first13 = S. B. | last14 = Cochran | first14 = W. D. | last15 = Endl | first15 = M. | last16 = Bryson | first16 = S. T. | last17 = Rowe | first17 = J. F. | last18 = Holman | first18 = M. J. | last19 = Lissauer | first19 = J. J. | last20 = Jenkins | first20 = J. M. | last21 = Still | first21 = M. | last22 = Ford | first22 = E. B. | last23 = Christiansen | first23 = J. L. | last24 = Middour | first24 = C. K. | last25 = Haas | first25 = M. R. | last26 = Li | first26 = J. | last27 = Hall | first27 = J. R. | last28 = McCauliff | first28 = S. | last29 = Batalha | first29 = N. M. | last30 = Koch | first30 = D. G. | last31 = Borucki | first31 = W. J. | s2cid = 42698813 | title = The Kepler-19 System: A Transiting 2.2 R_🜨 Planet and a Second Planet Detected via Transit Timing Variations | year = 2011 | journal = Astrophysical Journal | volume = 743 | issue = 2 | pages = 200| arxiv = 1109.1561 | bibcode = 2011ApJ...743..200B| doi = 10.1088/0004-637X/743/2/200 }}

In 2010, researchers proposed a second planet orbiting WASP-3 based on transit-timing variation,[http://www.astronomynow.com/news/n1007/09exo/ Planet found tugging on transits] {{Webarchive|url=https://web.archive.org/web/20100713155937/http://www.astronomynow.com/news/n1007/09exo/ |date=2010-07-13 }}, Astronomy Now, 9 July 2010{{Citation | last1 = Maciejewski | first1 = G. | last2 = Dimitrov | first2 = D. | last3 = Neuhäuser | first3 = R. | last4 = Niedzielski | first4 = A. | last5 = Raetz | first5 = S. | last6 = Ginski | first6 = C. | last7 = Adam | first7 = C. | last8 = Marka | first8 = C. | last9 = Moualla | first9 = M. | last10 = Mugrauer | first10 = M. | title = Transit timing variation in exoplanet WASP-3b | year = 2010 | journal = MNRAS | volume = 407 | issue = 4 | pages = 2625| arxiv = 1006.1348 | bibcode = 2010MNRAS.407.2625M| doi = 10.1111/j.1365-2966.2010.17099.x | doi-access = free | s2cid = 120998224 }} but this proposal was debunked in 2012.{{cite journal |

title=A new analysis of the WASP-3 system: no evidence for an additional companion

|date=Nov 2, 2012

|author= M Montalto

|s2cid=59381004

|display-authors= etal|arxiv=1211.0218

|journal=MNRAS|bibcode = 2012MNRAS.427.2757M |doi = 10.1111/j.1365-2966.2012.21926.x|volume=427|issue=4

|pages=2757–2771|doi-access=free

}}

Transit-timing variation was first convincingly detected for planets Kepler-9b and Kepler-9c

{{cite web|url = https://www.nasa.gov/home/hqnews/2010/aug/HQ_10-197_Kepler_Results.html|title=NASA's Kepler Mission Discovers Two Planets Transiting Same Star|first=J.D.|last=Harrington|date=26 August 2010|website=nasa.gov|access-date=4 September 2018}} and gained popularity by 2012 for confirming exoplanet discoveries.{{cite web|url=https://www.nasa.gov/home/hqnews/2012/jan/HQ_12-032_Kepler_23-33.html|title=NASA's Kepler Announces 11 Planetary Systems Hosting 26 Planets|first=Michele|last=Johnson|date=26 January 2012|website=nasa.gov|access-date=4 September 2018}}

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{{Citation | last1 = Agol | first1 = E. | last2 = Deck | first2 = K. | s2cid = 38941103 | title = Transit Timing to First Order in Eccentricity | year = 2016 | journal = Astrophysical Journal | volume = 818 | issue = 2 | pages = 177| arxiv = 1509.01623 | bibcode = 2016ApJ...818..177A| doi = 10.3847/0004-637X/818/2/177 | doi-access = free }}) and numerical (TTVFast{{Citation | last1 = Deck | first1 = K. M. | last2 = Agol | first2 = E. | last3 = Holman | first3 = M. J. | last4 = Nesvorný | first4 = D. | s2cid = 53965722 | title = TTVFast: An Efficient and Accurate Code for Transit Timing Inversion Problems | year = 2014 | journal = Astrophysical Journal | volume = 787 | issue = 2 | pages = 132| arxiv = 1403.1895 | bibcode = 2014ApJ...787..132D| doi = 10.1088/0004-637X/787/2/132 }} and Mercury{{Citation | last1 = Chambers | first1 = J. E. | title = A hybrid symplectic integrator that permits close encounters between massive bodies | year = 1999 | journal = MNRAS | volume = 304 | issue = 4 | pages = 793–799| bibcode = 1999MNRAS.304..793C| doi = 10.1046/j.1365-8711.1999.02379.x | doi-access = free | citeseerx = 10.1.1.25.3257 }}) 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.{{Citation | last1 = Gillon | first1 = M. | last2 = Triaud | first2 = A. H. M. J. | last3 = Demory | first3 = B.-O. | last4 = Jehin | first4 = E. | last5 = Agol | first5 = E. | last6 = Deck | first6 = K. M. | last7 = Lederer | first7 = S. M. | last8 = de | first8 = Wit J. | last9 = Burdanov | first9 = A. | last10 = Ingalls | first10 = J. G. | last11 = Bolmont | first11 = E. | last12 = Leconte | first12 = J. | last13 = Raymond | first13 = S. N. | last14 = Selsis | first14 = F. | last15 = Turbet | first15 = M. | last16 = Barkaoui | first16 = K. | last17 = Burgasser | first17 = A. | last18 = Burleigh | first18 = M. R. | last19 = Carey | first19 = S. J. | last20 = Chaushev | first20 = A. | last21 = Copperwheat | first21 = C. M. | last22 = Delrez | first22 = L. | last23 = Fernandes | first23 = C. S. | last24 = Holdsworth | first24 = D. L. | last25 = Kotze | first25 = E. J. | last26 = Van | first26 = Grootel V. | last27 = Almleaky | first27 = Y. | last28 = Benkhaldoun | first28 = Z. | last29 = Magain | first29 = P. | last30 = Queloz | first30 = D. | title = Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1 | year = 2017 | journal = Nature | volume = 542 | issue = 7642 | pages = 456–460| bibcode = 2017Natur.542..456G| arxiv = 1703.01424 | doi = 10.1038/nature21360 | pmid = 28230125 | pmc = 5330437 }}