Observed tidal evolution of Kleopatra’s outer satellite

The orbit of the outer satellite Alexhelios (216) Kleopatra is already constrained by adaptive-optics astrometry, obtained with VLT/SPHERE instrument. However, there also a preceding occultation event in 1980 attributed to this satellite. Hereinafter, we try link all observations, spanning 1980--2018. We find nominal exhibits an unexplained shift $+60^\circ$ true longitude. Using both periodogram analysis and $\ell = 10$ multipole model suitable for motion mutually interacting moons about irregular body, confirmed that it not possible adjust respective osculating period $P_2$. Instead, were forced use tidal dissipation (and increasing orbital periods) explain shift. analyzed light curves, 1977--2021, searched expected spin deceleration Kleopatra. According our best-fit model, observed rate $\dot P_2 (1.8\pm 0.1)\cdot 10^{-8}\,{\rm d}\,{\rm d}^{-1}$ corresponding time lag $\Delta t_2 42\,{\rm s}$ tides, assumed value Love number $k_2 0.3$. It first detection evolution orbiting 100-km asteroids. factor $Q$ comparable other terrestrial bodies, albeit at higher loading frequency $2|\omega-n|$. predict secular inner moon, P_1 5.0\cdot 10^{-8}$, as well Kleopatra, P_0 1.9\cdot 10^{-12}$. In alternative models, captured 3:2 mean-motion resonance or more massive moons, values t_2$ are 2--3 lower. Future astrometric observations direct imaging occultations should allow distinguish between these which important internal structure mechanical properties