Haumea’s Shape, Composition, and Internal Structure

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 Cℓm, Sℓm 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 χ2 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, P1 = (1.822359 ± 0.004156) d, P2 = (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, m1 = (1.49 ± 0.16) × 10−12 M⊙ or 2.97 × 1018 kg, is significantly lower than previously thought. An implication explained in the accompanying paper is that (216) Kleopatra is a critically rotating body.

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“…For comparison, let us recall the basic parameters of the Haumea moon system (Ortiz et al 2017;Dunham et al 2019).…”

Section: Implications For the Moonsmentioning

confidence: 99%

An advanced multipole model for (216) Kleopatra triple system

Brož

Marchis

Jordá

et al. 2021

A&A

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show abstract

“…For comparison, let us recall basic parameters of the Haumea moon system (Ortiz et al 2017;Dunham et al 2019). Although everything is about 10 times larger, the central body is very elongated triaxial ellipsoid (2.0:1.6:1), which is rapidly rotating (3,9 h).…”

Section: Implications For the Moonsmentioning

confidence: 99%

An advanced multipole model for (216) Kleopatra triple system

Brož,

Marchis,

Jorda

et al. 2021

Preprint

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Aims. To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution of multiple moons, orbiting an extremely irregular body and including their mutual interactions. Such orbits are generally non-Keplerian and orbital elements are not constants. Methods. Consequently, we use 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 (2nd moon with respect to 1st), angular velocities, and also 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 meanmotion resonance, but their osculating eccentricities are too small compared to other perturbations (multipole, mutual), so 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 (Marchis et al.) is that (216) Kleopatra is a critically rotating body.

show abstract

“…Haumea was discovered in 2005, the same year as two other dwarf planets (Makemake and Eris). With dimensions of about 2,000 x 1,000 km [1], Haumea's size is on the same order as Pluto. As part of the family of dwarf planets in the Kuiper Belt, Haumea intrinsically carries information on formation and evolutionary processes of icy bodies, such as other KBOs, comets, Centaurs, as well as giant planet cores.…”

Section: Science Backgroundmentioning

confidence: 99%

“…The axis ratios derived from this occultation are in disagreement with those expected for the hydrostatic equilibrium models [5], which would require a much higher density (given its short period and elongated shape). However, the currently measured value for the density could be explained by granular physics [6] or a differentiation of the body [1,7]. The highly detailed shape and topographic information achievable by a spacecraft visit would allow for the study of the behavior of icy material under unusual stress fields and what that implies for a body's shape, as well as the shapes of differentiated layers in the case of extreme rotation.…”

Section: Science Backgroundmentioning

confidence: 99%