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An advanced multipole model for (216) Kleopatra triple system

M. Brož 1 F. Marchis 2 L. Jorda 3 J. Hanuš 1 P. Vernazza 3 M. Ferrais 3 F. Vachier 4 N. Rambaux 4 M. Marsset 5 M. Viikinkoski 6 E. Jehin S. Benseguane E. Podlewska-Gaca B. Carry A. Drouard S. Fauvaud M. Birlan 4 J. Berthier P. Bartczak C. Dumas G. Dudziński J. Ďurech J. Castillo-Rogez F. Cipriani F. Colas 4 R. Fetick T. Fusco J. Grice A. Kryszczynska P. Lamy A. Marciniak T. Michalowski P. Michel M. Pajuelo 4 T. Santana-Ros P. Tanga Arthur Vigan 3 D. Vokrouhlický O. Witasse B. Yang
1 Institute of Astronomy [Prague]
2 SETI - Search for Extraterrestrial Intelligence Institute
3 LAM - Laboratoire d'Astrophysique de Marseille
4 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides
5 EAPS - Department of Earth, Atmospheric and Planetary Sciences [MIT, Cambridge]
6 TUT - Tampere University of Technology [Tampere]
Abstract : Aims. To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution of multiple moons orbiting an extremely irregular body and include their mutual interactions. Such orbits are generally non-Keplerian and orbital elements are not constants. Methods. Consequently, we used a modified N -body integrator, which was significantly extended to include the multipole expansion of the gravitational field up to the order ℓ = 10. Its convergence was verified against the ‘brute-force’ algorithm. We computed the coefficients C ℓm , S ℓm for Kleopatra’s shape, assuming a constant bulk density. For Solar System applications, it was also necessary to implement a variable distance and geometry of observations. Our χ 2 metric then accounts for the absolute astrometry, the relative astrometry (second moon with respect to the first), angular velocities, and silhouettes, constraining the pole orientation. This allowed us to derive the orbital elements of Kleopatra’s two moons. Results. Using both archival astrometric data and new VLT/SPHERE observations (ESO LP 199.C-0074), we were able to identify the true periods of the moons, P 1 = (1.822359 ± 0.004156) d, P 2 = (2.745820 ± 0.004820) d. They orbit very close to the 3:2 mean-motion resonance, but their osculating eccentricities are too small compared to other perturbations (multipole, mutual), meaning that regular librations of the critical argument are not present. The resulting mass of Kleopatra, m 1 = (1.49 ± 0.16) × 10 −12 M ⊙ or 2.97 × 10 18 kg, is significantly lower than previously thought. An implication explained in the accompanying paper is that (216) Kleopatra is a critically rotating body.
Keywords : minor planets asteroids: individual: (216) Kleopatra planets and satellites: fundamental parameters astrometry celestial mechanics methods: numerical Astrophysics - Earth and Planetary Astrophysics
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Submitted on : Wednesday, October 20, 2021 - 11:55:23 AM
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M. Brož, F. Marchis, L. Jorda, J. Hanuš, P. Vernazza, et al.. An advanced multipole model for (216) Kleopatra triple system. Astronomy and Astrophysics - A&A, EDP Sciences, 2021, 653, pp.A56. ⟨10.1051/0004-6361/202140901⟩. ⟨insu-03372817⟩

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