Constraints on Spin State and Hapke Parameters of Asteroid 4769 Castalia Using Lightcurves and a Radar-Derived Shape Model

Abstract

A 167-parameter, 3-D shape model of the Earth-crossing asteroid Castalia, obtained from inversion of delay-Doppler images (Hudson and Ostro, 1994,Science263,940–943) constrained the object's pole to lie on a cone of half angle 55 ± 10° centered on the radar line of sight (right ascension 0.3 hr, declination 25.4°) at the time of observations (Aug. 22, 1989) but could not constrain the pole's azimuthal orientation or the sense of rotation. Here we fit lightcurves obtained at Table Mountain Observatory on Aug. 23–25 with lightcurves calculated from Castalia's shape and Hapke's photometric model (Hapke 1981,J. Geophys. Res.86,3039–3054; 1984,Icarus59,41–59; 1986,Icarus67,264–280). The fits strongly constrain Castalia's spin state to one of two possibilities. One has a north pole within ∼13° of λ = 253°, β = 56° and a sidereal spin periodP= 4.089 ± 0.001 hr. The other has a south pole within ∼13° of λ = 242°, β = 7° and a sidereal spin periodP= 4.094 ± 0.001 hr. The north-pole solution has global-average Hapke photometric parametersw= 0.38 ± 0.07,g= −0.11 ± 0.09, θ = 46° ± 10° while the south-pole solution hasw= 0.24 ± 0.07,g= −0.30 ± 0.09, θ = 25° ± 10°. Due to the large solar phase angles (60°–90°) the fits are not sensitive to the opposition surge parametershandB0. At a more subtle level, the least-bifurcated shape (“lower-bound model”) allowed by the radar data (Hudson and Ostro, 1994,Science263,940–943) consistently gives statistically better fits than the more bifurcated possibilities. However, the differences are small enough that the possibility that they are due to unmodeled photometric effects cannot be discounted. The fits are improved by allowing the macroscopic roughness parameter θ to be a function of surface position. Statistically, this process improves the north-pole solution more than the south-pole solution suggesting that the radar observations viewed a northern latitude, thereby indicating a resolution of the “mirror ambiguity” inherent in the single-date radar data set.