Presentation #504.04 in the session Seek and Find (Asteroids).
We have produced a fast C++ implementation of the heliolinc3D algorithm for asteroid discovery (described below), and tested it extensively on simulated LSST data at realistic scale. In tests spanning two weeks of data across the whole sky, we find pure linkages for 98.8% of potentially discoverable main-belt asteroids (197620 out of 200063) and 97% of NEOs (437 out of 449). Here, the requirements for ‘potentially discoverable’ are a pair of observations 5-90 minutes apart on each of at least three nights within the two-week test interval. This implementation meets requirements for Rubin’s asteroid discovery system (95% completeness).
Algorithmic description: An observation of an asteroid at specific sky coordinates (RA and Dec) defines a unit vector whose origin is the observer’s position at the time of observation. The asteroid’s distance from the sun, if known, would define a heliocentric sphere that the observational unit vector, extended outward, would intersect at the true 3-D position of the asteroid. Given a hypothesis for the heliocentric distance as a function of time, and a pair of observations made at different times, we calculate two 3-D positions and hence a 3-D velocity and a fully specified hypothetical orbit. Given input data in the form of millions of pairs of observations, we convert each pair to an orbit using a hypothesis for the heliocentric distance r(t), and use the orbit to predict the asteroid’s position and velocity at a fixed reference time. Multiple pairs that correspond to the same real object are identified (linked) by the fact that their reference-time positions and velocities are tightly clustered when the r(t) hypothesis is close to reality for that object. By searching a wide range of possible hypotheses for r(t), nearly all feasibly discoverable objects may eventually be found. Pairs corresponding to objects not well matched by a given r(t) hypothesis form an unclustered background, as do pairs that do not correspond to two observations of the same real object. The density of this background determines how small a clustering radius is needed to avoid contamination, and hence how fine the hypothesis sampling must be to ensure that real clusters are sufficiently tight.