Dependence of Lightcurves on Phase Angle and Asteroid Shape

TL;DR

This study models how asteroid lightcurves vary with phase angle and shape, using scattering laws to compare simple shapes and binary systems, and matches models with observations including 'Oumuamua.

Contribution

It introduces a numerical scattering model for asteroid lightcurves that accounts for phase angle effects and compares simple shape models with observed data.

Findings

Lightcurve amplitude varies with phase angle and shape.

Single ellipsoid models fit 'Oumuamua better than contact binary models.

Differences in spectral types have modest effects on lightcurve relations.

Abstract

We investigate the phase angle dependence of asteroid lightcurves using numerical scattering models applied to simple body shapes. For simplicity, the Kaasalainen scattering parameters are obtained from the corresponding Hapke scattering laws for C-type, S-type, and V-type asteroids. The spectral types differ substantially in the role of multiple scattering (which is largely a function of their geometric albedos) but we find that the differences on the light curve vs.~phase relations are modest. By using a Kaasalainen scattering law, the amplitudes and axis ratios with respect to different phase angles from $0^\circ$ to $140^\circ$ are plotted for these types asteroids based on a biaxial ellipsoid shape model. Additionally, we examine the relationship between amplitude and axis ratio for a contact binary represented by identical biaxial ellipsoids, including the effects of shadowing of one component by the other. We compare the models with published high phase angle observations, and with interstellar object 1I/`Oumuamua ($\Delta m = 2.5$ magnitude at phase angle $\alpha = 23^\circ$), finding axis ratio $5.2:1$ if represented as a single ellipsoid and $3.5:1$ for each component if represented as a nose-to-nose contact binary. While a detailed fit is not attempted, the comparison shows that the single ellipsoid model is better.