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Detection of Earth-mass and super-Earth Trojan planets using transit timing variation method

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Abstract

We have carried out an extensive study of the possibility of the detection of Earth-mass and super-Earth Trojan planets using transit timing variation method with the Kepler space telescope. We have considered a system consisting of a transiting Jovian-type planet in a short period orbit, and determined the induced variations in its transit timing due to an Earth-mass/super-Earth Trojan planet. We mapped a large section of the phase space around the 1:1 mean-motion resonance and identified regions corresponding to several other mean-motion resonances where the orbit of the planet would be stable. We calculated transit timing variations (TTVs) for different values of the mass and orbital elements of the transiting and perturbing bodies as well as the mass of central star, and identified orbital configurations of these objects (ranges of their orbital elements and masses) for which the resulted TTVs would be within the range of the variations of the transit timing of Kepler’s planetary candidates. Results of our study indicate that in general, the amplitudes of the TTVs fall within the detectable range of timing precision obtained from the Kepler’s long-cadence data, and depending on the parameters of the system, their magnitudes may become as large as a few hours. The probability of detection is higher for super-Earth Trojans with slightly eccentric orbits around short-period Jovian-type planets with masses slightly smaller than Jupiter. We present the details of our study and discuss the implications of its results.

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References

  • Agol, E., Steffen, J., Saari, R., Clarkson, W.: On detecting terrestrial planets with timing of giant planet transits. Mon. Not. R. Astron. Soc. 359, 567–579 (2005)

    Article  ADS  Google Scholar 

  • Agol, E., Steffen, J.H.: A limit on the presence of Earth-mass planets around a Sun-like star. Mon. Not. R. Astron. Soc. 374, 941–948 (2007)

    Article  ADS  Google Scholar 

  • Beaugé, C., Sándor, Z., Érdi, B., Süli, Á.: Co-orbital terrestrial planets in exoplanetary systems: a formation scenario. Astron. Astrophys. 463, 359–367 (2007)

    Article  ADS  Google Scholar 

  • Chambers, J.E.: A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304, 793–799 (1999)

    Article  ADS  Google Scholar 

  • Chiang, E.I., Lithwick, Y.: Neptune Trojans as a test bed for planet formation. Astrophys. J. 628, 520–532 (2005)

    Article  ADS  Google Scholar 

  • Cincotta, P.M., Simó, C.: Simple tools to study global dynamics in non-axisymmetric galactic potentials—I. Astron. Astrophys. Suppl. 147, 205–228 (2000)

    Article  ADS  Google Scholar 

  • Cresswell, P., Nelson, R.P.: On the evolution of multiple protoplanets embedded in a protostellar disc. Astron. Astrophys. 450, 833–853 (2006)

    Article  ADS  Google Scholar 

  • Deeg, H.J.: Detection of terrestrial planets and Moons with the photometric transit method, In: Foing, B., Battrick, B. (eds.) Earth-Like Planets and Moons. Proceedings of the 36th ESLAB Symposium, pp. 237–243. ESA Publications Division, Noordwijk (2002)

  • Ford, E.B., Gaudi, B.S.: Observational constraints on Trojans of transiting extrasolar planets. Astrophys. J. 652, L137–L140 (2006)

    Google Scholar 

  • Ford, E.B., Holman, M.J.: Using transit timing observations to search for Trojans of transiting extrasolar planets. Astrophys. J. Lett. 664, L51–L54 (2007)

    Google Scholar 

  • Ford, E. B., et al.: Transit timing observations from Kepler. I. Statistical analysis of the first four months. Astrophys. J. Suppl. , 197, article id. 2 (2011)

    Google Scholar 

  • Goździewski, K., Bois, E., Maciejewski, A.J., Kiseleva-Eggleton, L.: Global dynamics of planetary systems with the MEGNO criterion. Astron. Astrophys. 378, 569–586 (2001)

    Article  ADS  Google Scholar 

  • Giuppone, C.A., Beaugé, C., Michtchenko, T.A., Ferraz-Mello, S.: Dynamics of two planets in co-orbital motion. Mon. Not. R. Astron. Soc. 407, 390–398 (2010)

    Article  ADS  Google Scholar 

  • Giuppone, C.A., Benítez-Llambay, P., Beaugé, C.: Origin and detectability of co-orbital planets from radial velocity data. Mon. Not. R. Astron. Soc. 421, 356–368 (2012)

    ADS  Google Scholar 

  • Hadjidemetriou, J.D., Psychoyos, D., Voyatzis, G.: The 1/1 resonance in extrasolar planetary systems. Celest. Mech. Dyn. Astron. 104, 23–38 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Hadjidemetriou, J.D., Voyatzis, G.: The 1/1 resonance in extrasolar systems. Migration from planetary to satellite orbits. Celest. Mech. Dyn. Astron. 111, 179–199 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  • Haghighipour, N., Kirste, S.: On the detection of (habitable) super-Earths around low-mass stars using Kepler and transit timing variation method. Celest. Mech. Dyn. Astron. 111, 267–284 (2011)

    Article  ADS  Google Scholar 

  • Heyl, J.S., Gladman, B.J.: Using long-term transit timing to detect terrestrial planets. Mon. Not. R. Astron. Soc. 377, 1511–1519 (2007)

    Article  ADS  Google Scholar 

  • Holman, M.J., Murray, N.W.: The use of transit timing to detect terrestrial-mass extrasolar planets. Science 307, 1288–1291 (2005)

    Article  ADS  Google Scholar 

  • Holman, M.J., et al.: Kepler-9: a system of multiple planets transiting a Sun-like star confirmed by timing variations. Science 330, 51–54 (2010)

    Article  ADS  Google Scholar 

  • Johnson, J. A., et al. : Characterizing the cool KOIs. II. The M Dwarf KOI-254 and its hot Jupiter. Astron. J. 143, article id. 111 (2012)

    Google Scholar 

  • Kipping, D.M.: Transit timing effects due to an exomoon. Mon. Not. R. Astron. Soc. 396, 1797–1804 (2009a)

    Article  ADS  Google Scholar 

  • Kipping, D.M.: Transit timing effects due to an exomoon—II. Mon. Not. R. Astron. Soc. 392, 181–189 (2009b)

    Article  ADS  Google Scholar 

  • Kipping, D., Bakos, G.: An independent analysis of Kepler-4b through Kepler-8b. Astrophys. J. 730, id. 50 (2011)

    Google Scholar 

  • Laughlin, G., Chambers, J.E.: Extrasolar Trojans: the viability and detectability of planets in the 1:1 resonance. Astron. J. 124, 592–600 (2002)

    Article  ADS  Google Scholar 

  • Lyra, W., Johansen, A., Klahr, H., Piskunov, N.: Standing on the Shoulders of giants. Trojan Earths and Vortex trapping in low mass self–gravitating protoplanetary disks of gas and solids. Astron. Astrophys. 493, 1125 (2009)

    Google Scholar 

  • Morbidelli, A., Crida, A., Masset, F., Nelson, R.P.: Building giant-planet cores at a planet trap. Astron. Astrophys. 478, 929–937 (2008)

    Article  ADS  Google Scholar 

  • Nesvorný, D., Morbidelli, A.: Mass and orbit determination from transit timing variations of exoplanets. Astrophys. J. 688, 636–646 (2008)

    Article  ADS  Google Scholar 

  • Nesvorný, D.: Transit timing variations for eccentric and inclined exoplanets. Astrophys. J. 701, 1116–1122 (2009)

    Article  ADS  Google Scholar 

  • Nesvorný, D., Beaugé, C.: Fast inversion method for determination of planetary parameters from transit timing variations. Astrophys. J. Lett. 709, L44–L48 (2010)

    Google Scholar 

  • Nesvorný, D., Kipping, D.M., Buchhave, L.A., Bakos, G.A., Hartman, J., Schmitt, A.R.: The detection and characterization of a nontransiting planet by transit timing variations. Science 336, 1133–1136 (2012)

    Article  ADS  Google Scholar 

  • Sartoretti, P., Schneider, J.: On the detection of satellites of extrasolar planets with the method of transits. Astron. Astrophys. 134, 553–560 (1999)

    ADS  Google Scholar 

  • Simon, A., Szatmáry, K., Szabó, G.M.: Determination of the size, mass, and density of “exomoons” from photometric transit timing variations. Astron. Astrophys. 470, 727–731 (2007)

    Article  ADS  Google Scholar 

  • Steffen, J.H., Agol, E.: An analysis of the transit times of TrES-1b. Mon. Not. R. Astron. Soc. 364, L96–L100 (2005)

    ADS  Google Scholar 

  • Thommes, E.W.: A safety net for fast migrators: interactions between gap-opening and sub-gap-opening bodies in a protoplanetary disk. Astrophys. J. 626, 1033–1044 (2005)

    Article  ADS  Google Scholar 

  • Veras, D., Ford, E.B., Payne, M.J.: Quantifying the challenges of detecting unseen planetary companions with transit timing variations. Astrophys. J., 727, article id. 74 (2011)

    Google Scholar 

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Acknowledgments

N.H. acknowledges support from NASA EXOB Grant NNX09AN05G and from the NASA Astrobiology Institute under Cooperative Agreement NNA09DA77A at the Institute for Astronomy (IfA), University of Hawaii. S.C. acknowledges support from the IfA NSF-funded REU program. T.C.H. acknowledges support from the Korea Astronomy and Space Science Institute (KASI) Grant 2012-1-410-02 and the Korea Research Council for Fundamental Science and Technology (KRCF) through the Young Research Scientist Fellowship Program. The MEGNO computations were carried out at the SFI/HEA Irish Center for High-End Computing (ICHEC) Center and the PLUTO computing cluster at KASI. T.C.H. would also like to thank the Institute for Astronomy and the NASA Astrobiology Institute at the University of Hawaii-Manoa for their hospitality during the course of this project.

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Authors and Affiliations

  1. Institute for Astronomy and NASA Astrobiology Institute, University of Hawai’i-Manoa, 2680 Woodlawn Drive, Honolulu, HI, 96822, USA

    Nader Haghighipour

  2. Department of Education, University of Hawai’i-Manoa, Honolulu, HI, 96822, USA

    Stephanie Capen

  3. Korea Astronomy and Space Science Institute, Daejeon, 304-358, Republic of Korea

    Tobias C. Hinse

  4. Armagh Observatory, College Hill, Armagh, BT61 9DG, UK

    Tobias C. Hinse

Authors
  1. Nader Haghighipour
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  2. Stephanie Capen
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  3. Tobias C. Hinse
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Correspondence to Nader Haghighipour.

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Haghighipour, N., Capen, S. & Hinse, T.C. Detection of Earth-mass and super-Earth Trojan planets using transit timing variation method. Celest Mech Dyn Astr 117, 75–89 (2013). https://doi.org/10.1007/s10569-013-9510-y

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  • DOI: https://doi.org/10.1007/s10569-013-9510-y

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