THOR: An Algorithm for Cadence-Independent Asteroid Discovery

Abstract: We present "Tracklet-less Heliocentric Orbit Recovery" (THOR), an algorithm for linking of observations of Solar System objects across multiple epochs that does not require intra-night tracklets or a predefined cadence of observations within a search window. By sparsely covering regions of interest in the phase space with "test orbits", transforming nearby observations over a few nights into the co-rotating frame of the test orbit at each epoch, and then performing a generalized Hough transform on the transformed detections followed by orbit determination (OD) filtering, candidate clusters of observations belonging to the same objects can be recovered at moderate computational cost and little to no constraints on cadence. We validate the effectiveness of this approach by running on simulations as well as on real data from the Zwicky Transient Facility (ZTF). Applied to a short, 2-week, slice of ZTF observations, we demonstrate THOR can recover 97.4% of all previously known and discoverable objects in the targeted ($a > 1.7$ au) population with 5 or more observations and with purity between 97.7% and 100%. This includes 10 likely new discoveries, and a recovery of an $e \sim 1$ comet C/2018 U1 (the comet would have been a ZTF discovery had THOR been running in 2018 when the data were taken). The THOR package and demo Jupyter notebooks are open source and available at https://github.com/moeyensj/thor.

• The paper presents THOR, a novel algorithm that discovers minor planets by applying test orbits to scatter observations without relying on traditional intra-night tracklets or survey cadence.
• Numerical results show THOR achieved a 91.3% recovery rate for orbits with five or more observations in simulations and recovered 97.2% of known objects from ZTF data despite non-ideal cadence.
• THOR's cadence-independent approach significantly increases discovery efficiency for current and future surveys, with ongoing work focusing on enhancing completeness for diverse populations like NEOs and improving computational efficiency.

An Analysis of "THOR: An Algorithm for Cadence-Independent Asteroid Discovery"

The computational astronomy community has witnessed significant growth in the discovery of minor planets due to advanced surveys like Pan-STARRS and upcoming projects such as the LSST. However, identifying and linking the orbital parameters of discovered objects remains computationally challenging. Moeyens et al. present "Tracklet-less Heliocentric Orbit Recovery" (THOR), an innovative algorithm designed to address these challenges by moving away from traditional tracklet-based discovery methods.

Overview and Methodology

THOR sets itself apart by not depending on intra-night tracklets or a predefined cadence. Instead, it applies "test orbits" to a scatter of observations over several nights, using a generalized Hough transform to identify clusters of detections that resemble real objects. Notably, this approach makes THOR cadence-independent, significantly enhancing flexibility and discovery potential especially in dynamically diverse regions of phase space.

The algorithm operates through several key steps:

1. Test Orbit Selection: Test orbits are selected based on known populations of solar system objects. The solar system's dynamical regions influence the spatial density of these orbits.
2. Data Transformation: Observations are rotated and transformed into the co-rotating frame of the chosen test orbit.
3. Hough Transform Utilization: This 3D transform efficiently identifies lines and patterns indicative of a minor planet’s orbital path over time.
4. Orbit Determination: The filtered candidate clusters undergo orbit determination to refine the orbital parameters and exclude spurious linkages. This stage involves both initial orbit determination (IOD) and a more robust differential correction (OD).

Numerical Results

The algorithm exhibits strong performance metrics in both simulated and real-world contexts. On simulated datasets, with a significant false positive component, THOR achieved a recovery rate of 91.3% for orbits having five or more observations, notably with high purity. Trials on data from the Zwicky Transient Facility (ZTF) validated THOR’s practical value, recovering 97.2% of known objects from a two-week observational window despite the non-ideal cadence for traditional linking methods.

Implications and Future Work

The results suggest that THOR could significantly increase the efficiency of current and upcoming surveys by allowing for the discovery of minor planets without stringent cadence requirements. Ongoing and future work involves enhancing test orbit selection to increase completeness, particularly for Near-Earth Objects (NEOs) and other dynamically complex populations. Additionally, improving the algorithm’s computational efficiency will be crucial for scaling to large-scale surveys like LSST.

Conclusion

THOR represents a substantial evolution in the methodology of asteroid detection. While the emphasis in this paper is on increasing Main Belt asteroid discoverability, the potential expansions into NEO orbits and ISOs signify a promising shift in how discovery algorithms might evolve. By enabling a broader and more comprehensive sampling of orbital phase space without cadence constraints, THOR promises to enrich our understanding of solar system dynamics and the evolution of celestial populations.