Triple Vision: Hierarchical Triple Planetesimal Systems Created from Gravitational Collapse

Relict planetesimals in the Kuiper Belt record the earliest epochs of planet formation. In particular, multi-component Kuiper Belt systems are relied upon as primary evidence of planetesimal formation via gravitational collapse. However, two of these systems, (47171) Lempo and (148780) Altjira, are hierarchical triple systems. Unlike a satellite triple system (e.g., Mars, Phobos, and Deimos), hierarchical triple systems lack a dominant central object—instead, they contain an ordered set of relationships (e.g., the Sun, Earth, and the Moon). Ambiguously, Kuiper Belt hierarchical triple systems could either be long-lived systems established during gravitational collapse or more recent creations from collisions or other processes. Here, we show that gravitational collapse can directly create hierarchical triples with dynamical architectures consistent with the observed systems. Using numerical simulations, we demonstrate that angular momentum conservation combined with inefficient orbital energy loss during the gravitational collapse process results in multiple-component systems, some of which are hierarchical triple systems like Lempo and Altjira.

The streaming instability and the subsequent gravitational collapse of self-gravitating pebble clouds have been proposed as an origin for hierarchical triples. Gravitational collapse enables pebbles (~mm-cm-sized objects) to rapidly and efficiently accrete to form large (~10-100 km sized) planetesimals. Crucially, excess angular momentum is imparted onto the pebble clouds via vorticity leftover from the streaming instability such that they are rotating as they collapse. This excess angular momentum is preserved during the collapse, such that pebbles are prevented from accreting into a single central object and instead form binary systems with near-equal-mass components. Numerical models have so far shown that gravitational collapse is a viable mechanism to reproduce the orbits, high rate of binarity (~30%), and physical characteristics of relict planetesimal systems comparable to those within the cold-classical Kuiper Belt. Numerical models have also shown that gravitational collapse can create higher order planetesimal systems (triples, quaternaries, etc.), planetesimals on very tight orbits, and even contact binary planetesimals. However, the creation of hierarchical triples has so far remained elusive due to model limitations and computational constraints.

In order to model the gravitational collapse of a pebble cloud, we used an astrophysical N-body algorithm (PKDGRAV) to calculate the gravitational collapse of a cloud of pebbles in the protoplanetary disk tracking the collapse until accreted planetesimals formed. The original pebble cloud would have contained approximately 10²¹ cm-sized pebbles, which is computationally infeasible, so we were forced to rely on the use of 10⁵ km-sized super-particles. Prior models of gravitational collapse adopted a perfect-merger modeling approach, such that colliding super-particle combine into a new spherical particle and conserve both mass and momentum in the process. However, because the perfect-merging method creates planetesimals as perfect spheres, it cannot adequately record their spin and shape characteristics. Moreover, prior models used inflation factors to increase the super-particle surface areas to resemble the surface areas of a sub-cloud of pebbles and to enhance the super-particle collision rates. Although this is effective at the start of gravitational collapse when innumerable collisions would theoretically occur, it has critical disadvantages. Inflated particles form unrealistically low planetesimal densities (<< 1 g/cm³) and preclude the formation tight binary orbits because mutually orbiting planetesimals inevitably make contact and accrete to form a single spherical planetesimal. However, we avoided the use of inflated particles, which do allow simulation speed-up but prevent the modeling of tight orbits; instead super-particles possess realistic densities (1 g/cm³). We used a soft-sphere discrete element method (SSDEM) to model the contact physics between super-particles. This method models collisions between super-particles with mutual surface penetration that allows them to effectively stick and rest upon one another. Therefore, the SSDEM can create planetesimals as super-particle aggregates with a wide range of shapes and spin states. Furthermore, the SSDEM can track both accretion and decretion from the growing aggregate planetesimals as the collapsing cloud evolves.

With the SSDEM we can effectively create hierarchical triple planetesimal systems from gravitational collapse for the first time (e.g., Figs. 1 and 2). The example hierarchical triple in Figure 1 has mass ratios m₂/m₁ ~ 0.998 and m₃/m₂ ~ 0.963, rotation periods P₁ ~ 27 hours, P₂ ~ 124 hours, and P₃ ~ 9.1 hours, and separations d₁₂ ~ 419 km and d₂₃ ~ 1313 km. The example hierarchical triple in Figure 2 has mass ratios m₂/m₁ ~ 0.643 and m₃/m₂ ~ 0.065, rotation periods P₁ ~ 9.71 hours, P₂ ~ 16.4 hours, and P₃ ~ 19.1 hours, and separations d₁₂ ~ 871 km and d₂₃ ~ 170 km. With our results, we provide evidence that hierarchical triples form directly from gravitational collapse, and they may have been prevalent throughout the early solar system.

 

Fig. 1: An example of one type of hierarchical triple system created during a simulation of planetesimal formation via gravitational collapse (image dimensions 3,000 km x 3,000 km). This hierarchical triple is composed of an inner tight binary with a small mutual semimajor axis and a third companion planetesimal on a circumbinary orbit with a semimajor axis several times larger than the size of the inner binary orbit.

 

Fig. 2: An example of another type of hierarchical triple system created during a simulation of planetesimal formation via gravitational collapse (image dimensions 2,000 km x 2,000 km). This hierarchical triple is composed of a tight binary planetesimal system orbiting about a single central planetesimal several times more massive than its companions.