Matt Holman (Harvard CfA, director of Minor Planet Center)

100,000 Asteroids Down the Back of the Couch:
A Novel Approach to the Minor Planet Linking Problem

A number of ongoing surveys, such as Pan-STARRS, the Catalina Sky
Survey, OSSOS, and NEOWISE, as well as planned surveys such as ZTF,
LSST, and NEOCam, are designed to pursue goals ranging from
constraining models of planet formation, through finding evidence of
additional planets in our solar system, to fulfilling the US
Congressional mandate to discover 90% of the potential hazardous
asteroids with diameters exceeding 140m.

The typical asteroid search strategy is based on identifying
`tracklets’, a sequence of two or more observations that are taken
over a time span that is short enough that it is likely that the
detections correspond to the same moving object, and a long enough to
distinguish solar system objects from stationary background sources.
A primary goal is to obtain enough tracklets for each object that the
corresponding orbit is accurately determined. By design, most objects
are naturally re-observed in the course of these surveys. However,
which observations correspond to which object must still be identified
before the orbits of those objects can be determined. This is known
as the `linking problem.’

The best current solution to the linking problem, the Pan-STARRS Moving
Object Processing System (MOPS), employs a sophisticated variation of
the brute force approach, bringing groups of three tracklets together
to be tested with orbit fitting. The computational load of MOPS
scales as $\mathcal{O}(N_t^3)$, where $N_t$ is the number of tracklets.

We present a novel approach, heliocentric linking and clustering, that
scales as $\mathcal{O}(N_t \log N_t)$. We use this approach to
identify thousands of new objects within the Minor Planet Center’s
“Isolated Tracklet File”. Finally, we discuss the implications of
our results for ongoing and future surveys.