Abstract
The stability of the secular orbital dynamics of a number of potentially existing satellites of exoplanets has been analyzed. The secular dynamics of possible satellites (“exomoons”) of the planets KOI-268.01, Kepler-1000b, and Kepler-1442b have been found to be stable. The possible values of the exomoon orbital parameters for these systems have been estimated. The dynamics of the satellites discovered around the planets Kepler-1625b and Kepler-1708b from the analysis of observations are considered. It has been found that the semimajor axis of the orbit of the moon of the planet Kepler-1625b can range from 5 to 25 planetary radii. It has been shown that the solution available for the satellites of the planet Kepler-1708b (Kipping et al., 2022) corresponds to a stable orbit of the satellites.
Similar content being viewed by others
REFERENCES
Awiphan, S. and Kerins, E., The detectability of habitable exomoons with Kepler, Mon. Not. R. Astron. Soc., 2013, vol. 432, pp. 2549–2561.
Benettin, G., Galgani, L., and Strelcyn, J.-M., Kolmogorov entropy and numerical experiments, Phys. Rev. A, 1976, vol. 14, no. 6, pp. 2338–2345.
Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J.-M., Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems—A method for computing all of them. I—theory. II—numerical application, Meccanica, 1980, vol. 15, pp. 9–30.
von Bremen, H.F., Udwadia, F.E., and Proskurowski, W., An efficient QR based method for the computation of Lyapunov exponents, Phys. D (Amsterdam), 1997, vol. 101, pp. 1–16.
Cassese, B. and Kipping, D., Kepler-1708 b-i is likely undetectable with HST, Mon. Not. R. Astron. Soc., 2022, vol. 516, pp. 3701–3708.
Domingos, R.C., Winter, O.C., and Yokoyama, T., Stable satellites around extrasolar giant planets, Mon. Not. R. Astron. Soc., 2006, vol. 373, pp. 1227–1234.
Emel’yanov, N.V., Dinamika estestvennykh sputnikov planet na osnove nablyudenii (Dynamics of Natural Satellites of Planets Based on Observations), Fryazino: Vek 2, 2019.
Fox, C. and Wiegert, P., Exomoon candidates from transit timing variations: eight Kepler systems with TTVs explainable by photometrically unseen exomoons, Mon. Not. R. Astron. Soc., 2021, vol. 501, pp. 2378–2393.
Hairer, E., Norsett, S.P., and Wanner, G., Solving Ordinary Differential Equations. I. Nonstiff Problems, Berlin: Springer-Verlag, 1993.
Heller, R., Exomoon habitability constrained by energy flux and orbital stability, Astron. Astrophys., 2012, vol. 545.
Heller, R., Detecting extrasolar moons akin to Solar System satellites with an orbital sampling effect, Astrophys. J., 2014, vol. 787, p. 14.
Heller, R., The nature of the giant exomoon candidate Kepler-1625 b-i2018, Astron. Astrophys., 2018, vol. 610, p. A39.
Heller, R., Williams, D., Kipping, D., Limbach, M.A., Turner, E., Greenberg, R., Sasaki, T., Bolmont, É., Grasset, O., Lewis, K., Barnes, R., and Zuluaga, J.I., Formation, habitability, and detection of extrasolar moons, Astrobiology, 2014, vol. 14, no. 9, pp. 798–835.
Heller, R., Rodenbeck, K., and Bruno, G., An alternative interpretation of the exomoon candidate signal in the combined Kepler and Hubble data of Kepler-1625, Astron. Astrophys., 2019, vol. 624, p. A95.
Holman, M. and Wiegert, P., Long-term stability of planets in binary systems, Astron. J., 1999, vol. 117, no. 1, pp. 621–628.
Kaltenegger, L., Characterizing habitable exomoons, Astrophys. J., 2010, vol. 712, no. 2, pp. L125–L130.
Kaltenegger, L., How to charañterize habitable worlds and signs of life, Annu. Rev. Astron. Astrophys., 2017, vol. 55, no. 1, pp. 433–485.
Kipping, D.M., Transit timing effects due to an exomoon, Mon. Not. R. Astron. Soc., 2009, vol. 392, no. 1, pp. 181–189.
Kipping, D.M., LUNA: An algorithm for generating dynamic planet-moon transits, Mon. Not. R. Astron. Soc., 2011, vol. 416, pp. 689–709.
Kipping, D.M., An independent analysis of the six recently claimed exomoon candidates, Astrophys. J. Lett., 2020, vol. 900, no. 2, p. L44.
Kipping, D.M., Bakos, G.Á., Buchhave, L.A., Nesvorný, D., and Schmitt, A., The hunt for exomoons with Kepler (HEK). I. Description of a new observational project, Astrophys. J., 2012, vol. 750, p. 115.
Kipping, D.M., Forgan, D., Hartman, J., Nesvorný, D., Bakos, G.A., Schmitt, A., and Buchhave, L., The hunt for exomoons with Kepler (HEK). III. The first search for an exomoon around a habitable-zone planet, Astrophys. J., 2013a, vol. 777, no. 2, p. 134.
Kipping, D.M., Hartman, J., Buchhave, L.A., Schmitt, A.R., Bakos, G.A., and Nesvorný, D., The hunt for exomoons with Kepler (HEK). II. Analysis of seven viable satellite-hosting planet candidates, Astrophys. J., 2013b, vol. 770, no. 2, p. 101.
Kipping, D.M., Nesvorný, D., Buchhave, L.A., Hartman, J., Bakos, G.A., and Schmitt, A.R., The hunt for exomoons with Kepler (HEK). IV. A search for moons around eight M dwarfs, Astrophys. J., 2014, vol. 784, no. 1. p. 28.
Kipping, D.M., Schmitt, A.R., Huang, X., Torres, G., Nesvorný, D., Buchhave, L.A., Hartman, J., and Bakos, G.A., The hunt for exomoons with Kepler (HEK). V. A survey of 41 planetary candidates for exomoons, Astrophys. J., 2015, vol. 813, no. 1, p. 14.
Kipping, D., Bryson, S., Burke, C., Christiansen, J., Hardegree-Ullman, K., Quarles, B., Hansen, B., Szulágyi, J., and Teachey, A., An exomoon survey of 70 cool giant exoplanets and the new candidate Kepler-1708 b-i, Nat. Astron., 2022, vol. 6, pp. 367–380.
Lichtenberg and Lieberman, Regular and Stochastic Motion, New York: Springer, 1983.
Martin, D.V., Fabrycky, D.C., and Montet, B.T., Transits of in lined exomoons—hide and seek and an application to Kepler-1625, Astrophys. J., 2019, vol. 875, no. 2, p. L25.
Martinez-Rodríguez, H., Caballero, J.A., Cifuentes, C., Piro, A.L., and Barnes, R., Exomoons in the habitable zones of M dwarfs, Astrophys. J., 2019, vol. 887, no. 2, p. 261.
Melnikov, A.V., Numerical instruments for the analysis of secular dynamics of exoplanetary systems, Sol. Syst. Res., 2018, vol. 52, no. 5, pp. 417–425. https://doi.org/10.1134/S0038094618050064
Melnikov, A.V. and Shevchenko, I.I., The stability of the rotational motion of nonspherical natural satellites with respect to tilting the axis of rotation, Sol. Syst. Res., 1998, vol. 32, no. 6, pp. 480–490.
Melnikov, A.V. and Shevchenko, I.I., Rotational dynamics and evolution of planetary satellites in the solar and exoplanetary systems, Sol. Syst. Res., 2022, vol. 56, no. 1, pp. 1–22. https://doi.org/10.1134/S003809462201004X
Moraes, R.A. and Vieira Neto, E., Exploring formation scenarios for the exomoon candidate Kepler-1625b I, Mon. Not. R. Astron. Soc., 2020, vol. 495, no. 4, pp. 3763–3776.
Moraes, R.A., Borderes-Motta, G., Winter, O.C., and Monteiro, J., On the stability of additional moons orbiting Kepler-1625 b, Mon. Not. R. Astron. Soc., 2022, vol. 510, no. 2, pp. 2583–2596.
Nicholson, P.D., Ćuk, M., Sheppard, S.S., Nesvorný, D., and Johnson, T.V., Irregular satellites of the giant planets, The Solar System beyond Neptune, Barucci, M.A., Boehnhardt, H., Cruikshank, D.P., and Morbidelli, A., Eds., Tucson: Univ. Arizona Press, 2008, pp. 411–424.
Rosario-Franco, M., Quarles, B., Musielak, Z.E., and Cuntz, M., Orbital stability of exomoons and submoons with applications to Kepler 1625b-I, Astron. J., 2020, vol. 159, no. 6, p. 260.
Saha, S. and Sengupta, S., Transit light curves for exomoons: Analytical formalism, Astrophys. J., 2022, vol. 936, no. 1, p. 2.
Shevchenko, I.I. and Kouprianov, V.V., On the chaotic rotation of planetary satellites: The Lyapunov spectra and the maximum Lyapunov exponents, Astron. Astrophys., 2002, vol. 394, pp. 663–674.
Sucerquia, M., Alvarado-Montes, J.A., Zuluaga, J.I., Cuello, N., and Giuppone, C., Ploonets: Formation, evolution, and detectability of tidally detached exomoons, Mon. Not. R. Astron. Soc., 2019, vol. 489, pp. 2313–2322.
Sucerquia, M., Ramírez, V., Alvarado-Montes, J.A., and Zuluaga, J.I., Can lose-in giant exoplanets preserve detectable moons?, Mon. Not. R. Astron. Soc., 2020, vol. 492, no. 3, pp. 3499–3508.
Sucerquia, M., Alvarado-Montes, J.A., Bayo, A., Cuadra, J., Cuello, N., Giuppone, C.A., Montesinos, M., Olofsson, J., Schwab, C., Spitler, L., and Zuluaga, J.I., Cronomoons: Origin, dynamics, and light-curve features of ringed exomoons, Mon. Not. R. Astron. Soc., 2022, vol. 512, no. 1, pp. 1032–1044.
Teachey, A., The exomoon corridor for multiple moon systems, Mon. Not. R. Astron. Soc., 2021, vol. 506, no. 2, pp. 2104–2121.
Teachey, A. and Kipping, D.M., Evidence for a large exomoon orbiting Kepler-1625b, Sci. Adv., 2018, vol. 4, no. 10, p. Eaav1784.
Teachey, A., Kipping, D.M., and Schmitt, A.R., HEK. VI. On the dearth of Galilean analogs in Kepler, and the exomoon candidate Kepler-1625b I, Astron. J., 2018, vol. 155, no. 1, p. 36.
Teachey, A., Kipping, D., Burke, C.J., Angus, R., and Howard, A.W., Loose ends for the exomoon candidate host Kepler-1625b, Astron. J., 2020, vol. 159, no. 4, p. 142.
Tjoa, J.N.K.Y., Mueller, M., and van der Tak, F.F.S., The subsurface habitability of small, icy exomoons, Astron. Astrophys., 2020, vol. 636. p. A50.
Tokadjian, A. and Piro, A.L., Probing planets with exomoons: The cases of Kepler-1708 b and Kepler-1625 b, Astrophys. J. Lett., 2022, vol. 929, no. 1, p. L2.
Williams, D.M., Kasting, J.F., and Wade, R.A., Habitable moons around extrasolar giant planets, Nature, 1997, vol. 385, no. 6613, pp. 234–236.
ACKNOWLEDGMENTS
The author is grateful to the reviewer for the useful remarks.
Funding
The study was supported by grant no. 075-15-2020-780 “Theoretical and experimental studies of the formation and evolution of extrasolar planetary systems and characteristics of exoplanets” of the Ministry of Science and Higher Education of the Russian Federation.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declares that he has no conflicts of interest.
Additional information
Translated by M. Chubarova
Rights and permissions
About this article
Cite this article
Melnikov, A.V. Secular Orbital Dynamics of Exoplanet Satellite Candidates. Sol Syst Res 57, 380–387 (2023). https://doi.org/10.1134/S0038094623030061
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0038094623030061