Journal of The Korean Astronomical Society (천문학회지)

The Korean Astronomical Society (한국천문학회)
권호 표지
DOI QR코드

DOI QR Code

SUN FLUX VARIATIONS DUE TO ORBITING PLANETS: THE SOLAR SYSTEM AS A NON-COMPACT PLANETARY SYSTEM

  • Barbier, Hugo (Departamento de Fisica, Escuela Politecnica Nacional) ;
  • Lopez, Ericson D. (Departamento de Fisica, Escuela Politecnica Nacional) ;
  • Tipan, Bryan (Departamento de Fisica, Escuela Politecnica Nacional) ;
  • Vasconez, Christian L. (Departamento de Fisica, Escuela Politecnica Nacional)
  • Received : 2019.09.21
  • Accepted : 2020.05.04
  • Published : 2020.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

We study the photometric phase curves for the planets of our solar system which can be considered as a prototypical non-compact planetary system. We focus on modeling the small variations caused by three effects: reflection, ellipsoidal, and Doppler beaming. Theoretical predictions for these photometric variations are proposed, considering a hypothetical external observer. Unlike similar studies of multi-planetary systems, the physical and geometrical parameters for each planet of the solar system are well-known. Therefore, we can accurately evaluate the relationships that shape the planetary light curves for a fictitious external observer. Our results suggest that, for all planets, the ellipsoidal effect is very weak while the Doppler beaming effect (DBE) is, in general, dominant. In fact, the DBE seems to be the principal cause of variations of the light curves for the planets of the solar system. However, for Mercury and Venus the Doppler beaming and reflection effects have similar amplitudes. The phase curves obtained for the planets of the solar system show new interesting features of interest for the study of other non-compact planetary systems.

Keywords

References

  1. Alberti, T., Carbone, V., Lepreti, F., & Vecchio, A. 2017, Comparative Climates of the Trappist-1 Planetary System: Results from a Simple Climate-vegetation Model, ApJ, 844, 19 https://doi.org/10.3847/1538-4357/aa78a2
  2. Barnes, J. W. & Fortney, J. J. 2003, Measuring the Oblateness and Rotation of Transiting Extrasolar Giant Planets, ApJ, 588, 545 https://doi.org/10.1086/373893
  3. Batygin, K., Bodenheimer, P. H., & Laughlin, G. P. 2016, In Situ Formation and Dynamical Evolution of Hot Jupiter Systems, ApJ, 829, 114 https://doi.org/10.3847/0004-637X/829/2/114
  4. Borucki, W. J., Koch, D., Basri, G., et al. 2010, Kepler Planet-detection Mission: Introduction and First Results, Science, 327, 977 https://doi.org/10.1126/science.1185402
  5. Borucki, W. J. & Summers, A. L. 1984, The Photometric Method of Detecting other Planetary Systems, Icarus, 58, 121 https://doi.org/10.1016/0019-1035(84)90102-7
  6. Broeg, C., Fortier, A., Ehrenreich, D., et al. 2013, CHEOPS: A Transit Photometry Mission for ESA's Small Mission Programme, EPJ Web Conf., 47, 03005
  7. Cabrera, J., Csizmadia, Sz., Lehmann, H., et al. 2013, The Planetary System to KIC 11442793: a Compact Analogue to the Solar System, ApJ, 781, 18 https://doi.org/10.1088/0004-637X/781/1/18
  8. Carter, J. A. & Winn, J. N. 2010, The Detectability of Transit Depth Variations due to Exoplanetary Oblateness and Spin Precession, ApJ, 716, 850 https://doi.org/10.1088/0004-637X/716/1/850
  9. Cox, A. N. (ed.) 2000, Allens Astrophysical Quantities (Berlin: Springer)
  10. Esteves, L. J., De Mooij, E. J. W., & Jayawardhana, R. 2013, Optical Phase Curves of Kepler Exoplanets, ApJ, 772, 51 https://doi.org/10.1088/0004-637X/772/1/51
  11. Esteves, L. J., Mooij, E. J. W. D., & Jayawardhana, R. 2015, Changing Phases of Alien Worlds: Probing Atmospheres of Kepler Planets with High-precision Photometry, ApJ, 804, 1 https://doi.org/10.1088/0004-637X/804/1/1
  12. Faigler, S., Mazeh, T., Quinn, S. N., et al. 2012, Seven New Binaries Discovered in the Kepler Light Curves through the BEER Method Confirmed by Radial-velocity Observations, ApJ, 746, 185 https://doi.org/10.1088/0004-637X/746/2/185
  13. Gelino, D. M. & Kane, S. R. 2014, Phase Curves of the Kepler-11 Multi-planet System, ApJ, 787, 105 https://doi.org/10.1088/0004-637X/787/2/105
  14. Gillon, M., Triaud, A. H., Demory, B. O., et al. 2017, Seven Temperate Terrestrial Planets around the Nearby Ultracool Dwarf Star TRAPPIST-1, Nature, 542, 456 https://doi.org/10.1038/nature21360
  15. Hamers, A. S., Antonini, F., Lithwick, Y., et al. 2017, Secular Dynamics of Multiplanet Systems: Implications for the Formation of Hot and Warm Jupiters via High-eccentricity Migration, MNRAS, 464, 688 https://doi.org/10.1093/mnras/stw2370
  16. Hills, J. G. & Dale, T. M. 1974, The Orbit Evolution of the Eclipsing Binary System BD +16 516 and the Rotation Period of its White Dwarf, A&A, 30, 135
  17. Hippke, M. & Angerhausen, D. 2015, Photometrys Bright Future: Detecting Solar System Analogs with Future Space Telescopes, ApJ, 810, 29 https://doi.org/10.1088/0004-637X/810/1/29
  18. de Pater, I., Lissauer, J.J., & Hubbard, W.B. 2002, Planetary Sciences, Phys. Today, 55, 64 https://doi.org/10.1063/1.2408507
  19. Juric, M. & Tremaine, S. 2008, Dynamical Origin of Extrasolar Planet Eccentricity Distribution, ApJ, 686, 603 https://doi.org/10.1086/590047
  20. Laskar, J., Bou, G., & Correia, A. C. 2012, Tidal Dissipation in Multi-planet Systems and Constraints on Orbit Fitting, A&A, 538, A105 https://doi.org/10.1051/0004-6361/201116643
  21. Limbach, M. A. & Turner, E. L. 2015, Exoplanet Orbital Eccentricity: Multiplicity Relation and the Solar System, PNAS, 112, 20 https://doi.org/10.1073/pnas.1406545111
  22. Lissauer, J. J., Marcy, G. W., Rowe, J. F., et al. 2012, Almost All of Kepler's Multiple-planet Candidates are Planets, ApJ, 750, 112 https://doi.org/10.1088/0004-637X/750/2/112
  23. Loeb, A. & Gaudi, B. S. 2003, Periodic Flux Variability of Stars Due to the Reflex Doppler Effect Induced by Planetary Companions, ApJL, 588, L117 https://doi.org/10.1086/375551
  24. Lovis, C., Segransan, D., Mayor, M., et al. 2011, The HARPS Search for Southern Extra-solar Planets - XXVIII. Up to Seven Planets Orbiting HD 10180: Probing the Architecture of Low-mass Planetary Systems, A&A, 528, A112 https://doi.org/10.1051/0004-6361/201015577
  25. Mayor, M. & Queloz, D. 1995, A Jupiter-mass Companion to a Solar-type Star, Nature, 378, 355 https://doi.org/10.1038/378355a0
  26. Mazeh, T., Nachmani, G., Sokol, G., et al. 2012, Kepler KOI-13.01 - Detection of Beaming and Ellipsoidal Modulations Pointing to a Massive Hot Jupiter, A&A, 541, A56 https://doi.org/10.1051/0004-6361/201117908
  27. Rauer, H., Catala, C., Aerts, C., et al. 2014, The PLATO 2.0 Mission, Exp. Astron., 38, 249 https://doi.org/10.1007/s10686-014-9383-4
  28. Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2014, Transiting Exoplanet Survey Satellite, J. Astron. Telesc. Instrum. Syst., 1, 014003 https://doi.org/10.1117/1.JATIS.1.1.014003
  29. Rybicki, G. B. & Lightman, A. P. 2008, Radiative Processes in Astrophysics (Hoboken, NJ: Wiley & Sons)
  30. Schmitt, J. R., Wang, J., Fischer, D. A., et al. 2014, Planet Hunters. VI. An independent Characterization of KOI-351 and Several Long Period Planet Candidates from the Kepler Archival Data, AJ, 148, 28 https://doi.org/10.1088/0004-6256/148/2/28
  31. Seager, S. & Hui, L. 2002, Constraining the Rotation Rate of Transiting Extrasolar Planets by Oblateness Measurements, ApJ, 574, 1004 https://doi.org/10.1086/340994
  32. Serrano, L. M., Barros, S. C. C., Oshagh, M., et al. 2018, Distinguishing the Albedo of Exoplanets from Stellar Activity, A&A, 611, A8 https://doi.org/10.1051/0004-6361/201731206
  33. Shallue, C. J. & Vanderburg, A. 2018, Identifying Exoplanets with Deep Learning: A Five-planet Resonant Chain around Kepler-80 and an Eighth Planet around Kepler-90, AJ, 155, 94 https://doi.org/10.3847/1538-3881/aa9e09
  34. Tremaine, S. & Zakamska, N. L. 2004, Extrasolar Planet Orbits and Eccentricities, AIP Conf. Proc., 713, 243
  35. Tuomi, M. 2012, Evidence for Nine Planets in the HD 10180 System, A&A, 543, A52 https://doi.org/10.1051/0004-6361/201118518
  36. Welsh, W. F., Orosz, J. A., Seager, S., et al. 2010, The Discovery of Ellipsoidal Variations in the Kepler Light Curve of HAT-P-7, ApJL, 713, L145 https://doi.org/10.1088/2041-8205/713/2/L145
  37. Yu, Q. & Tremaine, S. 2001, Resonant Capture by Inwardmigrating Planets, AJ, 121, 1736 https://doi.org/10.1086/319401
  38. Zinzi, A. & Turrini, D. 2017, Anti-correlation Between Multiplicity and Orbital Properties in Exoplanetary Systems as a Possible Record of their Dynamical Histories, A&A, 605, L4 https://doi.org/10.1051/0004-6361/201731595
  39. Zucker, S., Mazeh, T. & Alexander, T. 2007, Beaming Binaries: A New Observational Category of Photometric Binary Stars, ApJ, 670, 1326 https://doi.org/10.1086/521389