Figure 1: Visualization of asteroids in the Solar System’s main Asteroid Belt. The circles represent the orbits of Mercury, Venus, Earth, Mars, and Jupiter (see this animation on YouTube by Alex Parker). (Click to enlarge images.)

Figure 1: Visualization of asteroids in the Solar System’s main Asteroid Belt. The circles represent the orbits of Mercury, Venus, Earth, Mars, and Jupiter (see this animation on YouTube by Alex Parker). (Click to enlarge images.)

The eight planetary inhabitants of the Solar System (sorry Pluto!) are well known. But in addition to them, there are millions of other, smaller, objects zipping through the space between the larger planets. These “minor planets” are bodies ranging in size from a few tens of meters to thousands of kilometers. Most of them inhabit two distinct regions in the Solar System.

Millions of smaller, rocky bodies – asteroids – are primarily found in the region between Mars and Jupiter, the main “asteroid belt.” Farther out beyond the orbit of Neptune is the domain of the dwarf planets – larger, icy, bodies, some of them approaching the size of our Moon.

The minor planets can tell us a lot about the history and evolution of the Solar System. For asteroid observations we can infer that planets must have been packed much more tightly early in the history of the Solar System. As the Solar System spread out, it became temporarily unstable, potentially ejecting a planet in the process and making Uranus and Neptune trade places (Gomes, Levison, Tsiganis and Morbidelli, 2005). Today, the clustering of the orbits of dwarf planets points to the tantalizing possibility of there still being another major planet hiding somewhere in the outskirts of the Solar System (the so-called ͞Planet X). Closer to home, we know that some of these asteroids occasionally collide with the planets – the last major impact with Earth is thought to have wiped out the dinosaurs some 65 million years ago.

These are some of the reasons that made the census of the asteroids and dwarf planets in the Solar System one of the top priorities for both NASA and the NSF! How do we discover these objects? They’re too small to be resolved by our telescopes and appear star-like; what differentiates them from stars is the fact they move. Taking one image tonight, and another a few nights later, will reveal a “star” has moved: that it’s not a star at all, but really a minor planet. This is what we call “linking” – establishing that an object we observed today has moved and is the same object we’ve seen a few nights ago. For something like our major planets, this linking process would be easy – after all, there are only eight of them (again, with apologies to Pluto), with little chance of confusing (say) Mars with Jupiter.

Figure 2: How are asteroids found today? A telescope must re-observe the same area of the sky at least twice each night, to produce a pair of detections. These pairs, called “tracklets,” are linked over multiple nights into curved “tracks” until there’s sufficient evidence they all belong to the same object.

Figure 2: How are asteroids found today? A telescope must re-observe the same area of the sky at least twice each night, to produce a pair of detections. These pairs, called “tracklets,” are linked over multiple nights into curved “tracks” until there’s sufficient evidence they all belong to the same object.

But modern telescopes (such as the Large Synoptic Survey Telescope (LSST) will be capable of observing some six million minor planets, and at that scale confusion begins to reign. Linking becomes difficult: any object observed today could be one of the tens of thousands of objects seen yesterday, or hundreds of thousands seen weeks ago. The number of possible combinations grows exponentially (of order of 1021, for the LSST!)

To get around this problem, asteroid-discovery surveys adopt a special observing cadence. Typically, the same field is revisited multiple times a night to create “tracklets”: sky-plane vectors composed of at least two detections that constrain the position and velocity of an object.

These are then relatively straightforward to link to objects observed on a past night, as the information about the direction and rate of motion drastically reduces the number of combinations we’d need to test (Kubica 2007, Jones et al. 2018, Holman et al. 2018). This is what nearly all state-of-the-art asteroid search programs have been doing in the past, and plan to do in the future (Figure 1).

This approach has major downsides, though. Because the telescope needs to return to the same field twice each night, the area of the sky that can be searched for asteroids is effectively cut in half. This leads to an unpleasant situation where after building telescopes worth hundreds of millions of dollars, we could be driving them at just 50% of their potential efficiency!

Secondly, data from telescopes that don’t observe at this cadence, including many decades of archival datasets, are unsuitable for asteroid searches with the current algorithms. That leaves lots of (otherwise useful) data off the table for asteroid searches.

Figure 3: How THOR finds asteroids: following a transformation to a heliocentric frame that follows a test asteroids, the motions of adjacent objects appear as lines (detectable using a generalized Hough transform coupled to a clustering algorithm).

Figure 3: How THOR finds asteroids: following a transformation to a heliocentric frame that follows a test asteroids, the motions of adjacent objects appear as lines (detectable using a generalized Hough transform coupled to a clustering algorithm).

This is where better algorithms can come to the rescue! Joachim Moeyens, a graduate student in the Astronomy Department and an IGERT Data Science FellowJes Ford, former WRF Innovation in Data Science Postdoctoral Fellow at the eScience Institute, Mario Juric, senior data science fellow, and colleagues at the UW’s Data Intensive Research in Astrophysics and Cosmology Institute (DIRAC) have recently presented a new algorithm named THOR (for “Tracklet-less Heliocentric Orbit Recovery”: Moeyens, Juric & Ford 2018), which employs coordinate transformations and clustering techniques to reduce the number of combinations needed to be tested to computationally tractable levels. The work on this algorithm was started by Ford and recently completed by Moeyens.

THOR begins by defining a set of (cleverly positioned) “test asteroids”: imaginary bodies that move through the solar system on orbits similar to what one would expect for a typical asteroid or dwarf planet. As a next step, the algorithm transforms the positions of all other nearby observations to how they would be seen not from Earth, but from a frame of reference centered in the Sun and following this test body.

When viewed from Earth the motions seen on the sky are complex curves (due to the motion of both the asteroid but also the Earth itself), making linking difficult. But viewed in this transformed space, they turn into (approximately) straight lines! This turns our asteroid linking problem into one equivalent to finding line segments – a problem with a rich history (and numerous solutions) in fields from computer vision to experimental particle physics.

So far, THOR has been tested on simulations and shown to recover 95% of observed objects. Our present implementation allows us to search out the majority of the asteroid belt with a relatively small number of test orbits. Next up, we’ll be applying this new algorithm to real data – especially the data from the Zwicky Transient Facility (ZTF) (see also the UW ZTF page), presently the largest optical time-domain survey in operation.

With planned generalizations to other populations (especially the Near-Earth Objects – the kind that could potentially impact the Earth), this algorithm could enable any telescope and any survey to effectively serve as an “asteroid search machine.” This will speed up the census of the Solar System, leading to a better understanding of its history and present structure, as well as hazards these bodies pose to Earth. And, as we said in a recent abstract at the meeting of the Division of Planetary Sciences of the American Astronomical Society, to finally take the hammer to the need for tracklets.

Research by Mario Juric, Joachim Moeyens, Jes Ford, et al. For more information, contact Juric at mjuric(at)astro.washington.edu.