Detection of the Yarkovsky effect for main-belt asteroids

Abstract

The Yarkovsky effect, a non-gravitational acceleration produced by the anisotropic emission of thermal energy (Öpik, 1951, Proc. Roy. Irish Acad. 54, 165–199), plays an important role in the dynamical evolution of asteroids. Current theoretical models of the Yarkovsky effect, however, rely on a number of poorly known parameters that can only approximate how real asteroids respond to solar heating. To improve this situation, we investigated whether the orbital distribution of the Karin cluster, a 5.8±0.2 Myr old S-type asteroid family (Nesvorný et al., 2002a, Nature 417, 720–722), could be used to determine the rate at which multikilometer main-belt asteroids spread in semimajor axis due to the Yarkovsky effect. Our results indicate that the orbital histories of individual Karin cluster members bear clear signatures of having drifted in semimajor axis drift since their formation. Using numerical methods, we determined the drift speed of ≈70 Karin cluster members (asteroids 1–6 km in diameter). This is the first time the speed that main-belt asteroids evolve in the semimajor axis due to the non-gravitational effects have been measured. The magnitude of measured speeds is similar to those predicted by theoretical models of the Yarkovsky force. Taken together, our results represent the first direct detection of the Yarkovsky effect for main-belt asteroids, and they validate in significant ways the asteroid thermal models described in the recent literature (e.g., Vokrouhlický, 1999, Astron. Astrophys. 344, 362–366). By comparing the measured drift speeds to those calculated from theoretical models of the Yarkovsky effect, we determined that Karin cluster members do not have surface thermal conductivities K in excess of ∼0.1 W m −1 K −1 . Instead, their derived K values are consistent with the presence of regolith over most/all of their ∼5.8 Myr lifetimes. This low-conductive regolith layer may be thin because the penetration depth of the diurnal thermal wave is ≲5 cm. The regolith material may have been deposited in the immediate aftermath of the Karin cluster formation event or was produced over time by impacts. Our method also allows us to estimate spin obliquity values for Karin cluster members. We find that members with diameters ≳3.5-km are predominantly retrograde rotators, while those <3.5-km have obliquities more equally distributed between 0° and 180°. These data may be used to study the spin states of asteroids produced by catastrophic disruption events. Interestingly, we find that a few Karin members have drifted further than predicted by our standard Yarkovsky model. We hypothesize these objects may have: (i) faster drift speeds than predicted by theoretical models, (ii) high albedos (≳0.3), and/or (iii) densities ≲2 g cm −3 .