Исследование динамической эволюции компактной планетной системы KEPLER-51

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Abstract

В работе исследуется динамическая эволюция компактной трехпланетной системы Kepler-51. Анализируются возможные резонансные состояния системы и проводится поиск потенциальных цепочек резонансов средних движений. С помощью программного комплекса Posidonius исследуется динамическая эволюция системы на интервале времени 100 млн лет с учетом приливного взаимодействия. Также для различных начальных значений эксцентриситетов, наклонов, аргументов перицентров и долгот восходящих узлов орбит проводится моделирование динамической эволюции планетной системы в рамках численно-аналитической теории движения. Показано, что компактная планетная система Kepler-51 не является резонансной. При начальных условиях, соответствующих массам и элементам орбит планет, определенным из наблюдений с учетом их погрешностей, эволюция системы является устойчивой и регулярной на исследуемом интервале 100 млн лет.

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About the authors

Э. Д. Кузнецов

Уральский федеральный университет

Author for correspondence.
Email: eduard.kuznetsov@urfu.ru
Russian Federation, Екатеринбург

А. С. Перминов

Уральский федеральный университет

Email: perminov12@yandex.ru
Russian Federation, Екатеринбург

References

  1. Antoniadou K.I., Voyatzis G. Periodic orbits in the 1:2:3 resonant chain and their impact on the orbital dynamics of the Kepler-51 planetary system // Astron. and Astrophys. 2022. V. 661. id. A62 (16 p.).
  2. Blanco-Cuaresma S., Bolmont E. Studying tidal effects in planetary systems with Posidonius. A N-body simulator written in rust // EWASS Spec. Session 4 (2017): Star-planet interactions (EWASS-SS4-2017). 2017. doi: 10.5281/zenodo.1095095.
  3. Charalambous C., Teyssandier J., Libert A.-S. Tidal interactions shape period ratios in planetary systems with three-body resonant chains // Astron. and Astrophys. 2023. V. 677. id. A160 (11 p.).
  4. Christiansen J.L., Crossfield I.J.M., Barentsen G., Lintott C.J., Barclay T., Simmons B.D., Petigura E., Schlieder J.E., Dressing C.D., Vanderburg A., Allen C., McMaster A., Miller G., Veldthuis M., Allen S., Wolfenbarger Z., Cox B., Zemiro J., Howard A.W., Livingston J., Sinukoff E., Catron T., Grey A., Kusch J.J.E., Terentev I., Vales M., Kristiansen M.H. The K2-138 system: A near-resonant chain of five sub-Neptune planets discovered by citizen scientists // Astron. J. 2018. V. 155. id. 57 (9 p.).
  5. Gillon M., Jehin E., Lederer S.M., Delrez L., de Wit J., Burdanov A., Van Grootel V., Burgasser A.J., Triaud A.H.M.J., Opitom C., Demory B.-O., Sahu D.K., Bardalez Gagliuffi D., Magain P., Queloz D. Temperate Earth-sized planets transiting a nearby ultracool dwarf star // Nature. 2016. V. 533. P. 221–224.
  6. 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. Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1 // Nature. 2017. V. 542. P. 456–460.
  7. Huang S., Ormel C.W. The dynamics of the TRAPPIST-1 system in the context of its formation // Mon. Notic. Roy. Astron. Soc. 2022. V. 511. P. 3814–3831.
  8. Jontof-Hutter D., Dalba P.A., Livingston J.H. TESS observations of Kepler systems with transit timing variations // Astron. J. 2022. V. 164. id. 42.
  9. Kholshevnikov K.V. The Hamiltonian in the planetary or satellite problem as a d’Alembertian function // Astron. Reports. 2001. V. 45. № 7. P. 577–579.
  10. Kuznetsov E.D., Perminov A.S. Search for chains of resonances in the compact planetary system K2-72 // The Thirteenth Moscow Solar System Symp. 13M-S3, October 10–14, 2022, Space Res. Inst. Russian Acad. Sci., Moscow, Russia. 2022. P. 382–384.
  11. Leleu A., Lillo-Box J., Sestovic M., Robutel P., Correia A.C.M., Hara N., Angerhausen D., Grimm S.L., Schneider J. Co-orbital exoplanets from close-period candidates: the TOI-178 case // Astron. and Astrophys. 2019. V. 624. id. A46 (9 p.).
  12. Lissauer J.J., Marcy G.W., Bryson S.T., Rowe J.F., Jontof-Hutter D., Agol E., Borucki W.J., Carter J.A., Ford E.B., Gilliland R.L., Kolbl R., Star K.M., Steffen J.H., Torres G. Validation of Kepler's multiple planet candidates. II. Refined statistical framework and descriptions of systems of special interest // Astrophys. J. 2014. V. 784. id. 44 (21 p.).
  13. MacDonald M.G., Feil L., Quinn T., Rice D. Confirming the 3:2 resonance chain of K2-138 // Astron. J. 2022. V. 163. id. 162 (12 p.).
  14. Mills S.M., Fabrycky D.C., Migaszewski C., Ford E.B., Petigura E., Isaacson H. A resonant chain of four transiting, sub-Neptune planets // Nature. 2016. V. 533. P. 509–512.
  15. Murphy M.M., Armitage P.J. Instability from high-order resonant chains in wide-separation massive planet systems // Mon. Notic. Roy. Astron. Soc. 2022. V. 512. P. 2750–2757.
  16. Perminov A.S., Kuznetsov E.D. The orbital evolution of the Sun–Jupiter–Saturn–Uranus–Neptune system on long time scales // Astrophys. and Space Sci. 2020. V. 365. id. 144.
  17. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical recipes. The art of scientific computing. New York: Cambridge Univ. Press, 2007. 1235 p.
  18. Rivera E.J., Laughlin G., Butler R.P., Vogt S.S., Haghighipour N., Meschiari S. The Lick-Carnegie Exoplanet Survey: a Uranus-Mass fourth planet for GJ 876 in an extrasolar Laplace configuration // Astrophys. J. 2010. V. 719. P. 890–899.
  19. Rowe J.F., Bryson S.T., Marcy G.W., Lissauer J.J., Jontof-Hutter D., Mullally F., Gilliland R.L., Issacson H., Ford E., Howell S.B., Borucki W.J., Haas M., Huber D., Steffen J.H., Thompson S.E., Quintana E., Barclay T., Still M., Fortney J., Gautier T.N. III, Hunter R., Caldwell D.A., Ciardi D.R., Devore E., Cochran W., Jenkins J., Agol E., Carter J.A., Geary J. Validation of Kepler's multiple planet candidates. III. Light curve analysis and announcement of hundreds of new multi-planet systems // Astrophys. J. 2014. V. 784. id. 45 (20 p.).
  20. Volk K., Malhotra R. Dynamical instabilities in systems of multiple short-period planets are likely driven by secular chaos: A case study of Kepler-102 // Astron. J. 2020. V. 160. id. 98.

Supplementary files

Supplementary Files
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1. JATS XML
2. Fig. 1. Distribution of low-order resonance regions (up to and including the fourth order) in the Kepler-51 system, taking into account errors in determining the masses of the planets and the eccentricities of their orbits.

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3. Fig. 2. Evolution of the orbital elements of the planets (1 – Kepler-51 b, 2 – Kepler-51 c, 3 – Kepler-51 d) over an interval of 100 million years for different values ​​of the stellar mass M: (a) – major semi-axes at , (b) – major semi-axes at , (c) – eccentricities at , (d) – eccentricities at .

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4. Fig. 3. Evolution of the relationships between the orbital periods of the planets (blue dots): (a) Kepler-51 c and Kepler-51 b; (b) Kepler-51 d and Kepler-51 c. The red dotted lines correspond to the resonances of the mean motions.

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5. Fig. 4. Evolution of the Kepler-51 system in the region of three-body resonances – chains of two-body resonances of mean motions. The red lines correspond to the position of three-body resonances. The system evolves from left to right.

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6. Fig. 5. Evolution of the mean orbital elements of the planets over an interval of 100 million years for zero initial values ​​of orbital inclinations and longitudes of the ascending nodes: 1 – Kepler-51 b, 2 – Kepler-51 c, 3 – Kepler-51 d.

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7. Fig. 6. Evolution of the mean elements of planetary orbits over an interval of 100 thousand years for zero initial values ​​of orbital inclinations and longitudes of ascending nodes: 1 – Kepler-51 b, 2 – Kepler-51 c, 3 – Kepler-51 d.

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8. Fig. 7. Evolution of the average eccentricities of the planetary orbits (1 – Kepler-51 b, 2 – Kepler-51 c, 3 – Kepler-51 d) over an interval of 100 million years for the corresponding initial values ​​of the osculating elements of the orbits: I1 = 0.9°, I2 =I3 = 0°, Ω2 = Ω3 = 0°, arguments of pericenters are nominal, orbital eccentricities are maximum, Ω1 varies in increments of 30°.

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9. Fig. 8. Evolution of the average orbital inclinations of the planets (1 – Kepler-51 b, 2 – Kepler-51 c, 3 – Kepler-51 d) over an interval of 100 million years for the corresponding initial values ​​of the osculating elements of the orbits: I1 = 0.9°, I2 =I3 = 0°, Ω2 = Ω3 = 0°, arguments of pericenters are nominal, orbital eccentricities are maximum, Ω1 varies in 30° increments.

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10. Fig. 9. Evolution of the average eccentricities of the planetary orbits (1 – Kepler-51 b, 2 – Kepler-51 c, 3 – Kepler-51 d) over an interval of 100 million years for the corresponding initial values ​​of the osculating elements of the orbits: I2 = 0.6°, I1 =I3 = 0°, Ω1 = Ω3 = 0°, arguments of pericenters are nominal, orbital eccentricities are maximum, Ω2 varies in 30° increments.

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11. Fig. 10. Evolution of the average orbital inclinations of the planets (1 – Kepler-51 b, 2 – Kepler-51 c, 3 – Kepler-51 d) over an interval of 100 million years for the corresponding initial values ​​of the osculating elements of the orbits: I2 = 0.6°, I1 =I3 = 0°, Ω1 = Ω3 = 0°, arguments of pericenters are nominal, orbital eccentricities are maximum, Ω2 varies in 30° increments.

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12. Fig. 11. Maps of minimum (left column) and maximum (right column) values ​​of planetary orbital eccentricities over a time interval of 100 million years (NU: orbital eccentricities are nominal, I1 = 0.9°, I2 = 0.6°, I3 = 0°, g1 = 252.1, g2 = 322.9°, g3 = 263.5°): (a) – minimum achievable values ​​of orbital eccentricity of planet Kepler-51 b; (b) – maximum achievable values ​​of orbital eccentricity of planet Kepler-51 b; (c) – minimum achievable values ​​of orbital eccentricity of planet Kepler-51 c; (d) – maximum achievable values ​​of orbital eccentricity of planet Kepler-51 c; (d) – minimum achievable values ​​of the orbital eccentricity of the planet Kepler-51 d; (e) – maximum achievable values ​​of the orbital eccentricity of the planet Kepler-51 d.

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13. Fig. 12. Maps of the minimum (left column) and maximum (right column) values ​​of the planetary orbital inclinations over a time interval of 100 million years (NU: orbital eccentricities are nominal, I1 = 0.9°, I2 = 0.6°, I3 = 0°, g1 = 252.1, g2 = 322.9°, g3 = 263.5°): (a) – minimum achievable values ​​of the orbital inclination of the planet Kepler-51 b; (b) – maximum achievable values ​​of the orbital inclination of the planet Kepler-51 b; (c) – minimum achievable values ​​of the orbital inclination of the planet Kepler-51 c; (d) – maximum achievable values ​​of the orbital inclination of the planet Kepler-51 c; (d) – minimum achievable values ​​of the orbital inclination of the planet Kepler-51 d; (e) – the maximum achievable values ​​of the orbital inclination of the planet Kepler-51 d.

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14. Fig. 13. Maps of minimum (left column) and maximum (right column) values ​​of planetary orbital eccentricities over a time interval of 100 million years (NU: orbital eccentricities are nominal, I1 = 0.9°, I2 = 0.6°, I3 = 0°, g1 = 252.1, g2 = 269.4°, g3 = 316.9°): (a) – minimum achievable values ​​of orbital eccentricity of planet Kepler-51 b; (b) – maximum achievable values ​​of orbital eccentricity of planet Kepler-51 b; (c) – minimum achievable values ​​of orbital eccentricity of planet Kepler-51 c; (d) – maximum achievable values ​​of orbital eccentricity of planet Kepler-51 c; (d) – minimum achievable values ​​of the orbital eccentricity of the planet Kepler-51 d; (e) – maximum achievable values ​​of the orbital eccentricity of the planet Kepler-51 d.

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15. Fig. 14. Maps of the minimum (left column) and maximum (right column) values ​​of the planetary orbital inclinations over a time interval of 100 million years (NU: orbital eccentricities are nominal, I1 = 0.9°, I2 = 0.6°, I3 = 0°, g1 = 252.1, g2 = 269.4°, g3 = 316.9°): (a) – minimum achievable values ​​of the orbital inclination of the planet Kepler-51 b; (b) – maximum achievable values ​​of the orbital inclination of the planet Kepler-51 b; (c) – minimum achievable values ​​of the orbital inclination of the planet Kepler-51 c; (d) – maximum achievable values ​​of the orbital inclination of the planet Kepler-51 c; (d) – minimum achievable values ​​of the orbital inclination of the planet Kepler-51 d; (e) – the maximum achievable values ​​of the orbital inclination of the planet Kepler-51 d.

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