Asteroid shapes from their light

Asteroids are too small and too distant to be seen as more than a point of light by almost any telescope. As an asteroid rotates, the amount of sunlight it reflects towards us changes. A record of its brightness over time is called a lightcurve.

Lightcurves observed over many years, from different directions and at different illumination, contain information about the shape of the asteroid, the direction of its spin axis and its rotation period. Recovering that information is a difficult inverse problem, and it needs a lot of computing.

The SAGE method

SAGE (Shaping Asteroids with Genetic Evolution) builds a three-dimensional shape model without assuming that the asteroid is convex, so it can reproduce concavities, large craters and two-lobed bodies. A model is a closed surface of 7680 triangles.

For every observation the model is rendered exactly as it was seen from the Earth at that moment, including the shadows the body casts on itself, and the computed brightness is compared with the measured one.

What your computer does

A task is an island of evolution. Starting from a parent model it makes small random changes: bumps and dents on the surface, stretching, a shift of the spin axis. It keeps the changes that fit the observations better and after about an hour of computing it reports the best models it found.

The server collects the results of thousands of islands. The best models become parents of new tasks, so the population slowly converges to the shapes that explain the data.

More than one answer

Brightness alone often allows several solutions, for example two spin axes that are mirror images in ecliptic longitude. The server keeps a separate niche for each distinct solution, so that one of them does not crowd out the others too early.

It also keeps every model that fits the data within the measurement uncertainty. The final result is therefore not only the best shape, but also a map of which parts of the surface are well determined and which are not.

Binary asteroids

Many small asteroids are pairs of bodies. SAGE models synchronous pairs, which rotate together as one rigid system, and asynchronous systems in which a small moon orbits a fast-spinning primary. Mutual eclipses and occultations of the two bodies are rendered directly.

Observations

The lightcurves come from published archives such as DAMIT and ALCDEF and from observing campaigns of the research team. The positions of the Sun, the Earth and the asteroid are taken from the JPL Horizons ephemeris service.

See the model gallery

Publication

Bartczak P., Dudziński G. (2018), Shaping asteroid models using genetic evolution (SAGE), Monthly Notices of the Royal Astronomical Society 473, 5050.