The representation of asteroid shapes: a test for the inversion of Gaia photometry

TL;DR

This study evaluates the effectiveness of using simple ellipsoidal models to represent asteroid shapes from Gaia photometry, assessing accuracy and volume estimation errors compared to complex shapes.

Contribution

It introduces a numerical comparison method and simulation framework to test the accuracy of ellipsoidal shape models derived from sparse Gaia photometry.

Findings

Ellipsoidal models closely match complex shapes in photometry inversion.

Volume estimation errors are typically around 10%.

Ellipsoidal approximation is effective for Gaia asteroid shape analysis.

Abstract

It is common practice nowadays to derive spins and 3D shapes of asteroids from the inversion of photometric light curves. However, this method requires a good number of photometric points and dedicated observing sessions. On the other hand, the photometric observations carried out by the Gaia mission will be sparse and their number relatively small. For this reason, a multi-parametric shape described by a large number of elementary facets cannot probably be derived from Gaia data alone. Therefore, the Data Processing and Analysis Consortium (DPAC), implemented a simpler solution as an unattended data reduction pipeline which relies on three axial ellipsoids for the shape representation. However, overall accuracy of such triaxial shape solutions has to be assessed. How adequate is an ellipsoidal approximation to represent the overall properties of an irregular body? Which error is made on the volume in comparison a more accurate model with irregular shape? To answer these questions, we have implemented numerical procedures for comparing ellipsoids to more complex and irregular shapes, and we performed a full simulation of the photometric signal from these objects, using both shape representations. Implementing the same software algorithm that will be used for the analysis of Gaia asteroid photometry, rotation period, spin axis orientation and ellipsoidal shape were derived from simulated observations of selected Main Belt asteroids assuming a geometric scattering model (work is in progress for more complex scattering models). We found that the ellipsoids by photometry inversion are closely similar to the best-fitting ellipsoids of the simulated complex shapes and that the error on the asteroid volume (relative to a complex shape) is generally low, usually around $10\%$.