Investigating Gravitational Collapse of Pebble Clouds to form Trans-Neptunian Binaries
Authors: Robinson James E. , Fraser Wesley C. , Fitzsimmons Alan , Lacerda Pedro 
Published: October 2020

INTRODUCTIONIn the trans-Neptunian region a relatively large fraction of minor bodies are found to exist as mutually bound binary pairs. The binary fraction varies for different dynamical classes and is highest for the Cold Classicals, which are dynamically unexcited planetesimals generally found at 39 < a < 48 AU, with estimates of up to 30% of the Cold Classicals being binaries (Noll et al. 2008).A distinct feature of the observed trans-Neptunian binaries is that they often have components that are of a similar size. These components also have similar optical colours which likely indicates similar surface compositions. Furthermore, the binary orbits span a range of separations but it is not uncommon for them to be found on wide (abin > 0.05 RHill) dynamically fragile orbits. The binary orbit inclinations range from prograde to retrograde, with ~80% of the known trans-Neptunian binaries having prograde orbits. The discovery of the bi-lobate nature of the Cold Classical contact binary 2014 MU69 Arrokoth, with its similar size and colour lobes, indicates that this object is likely the end state of a previously separated trans-Neptunian binary (Stern et al. 2019).Previous work (Nesvorn&#253; et al. 2010) has shown that the formation of planetesimals via gravitational collapse is a promising mechanism that can reproduce the unique properties of the trans-Neptunian binaries. We assume that a slowly rotating cloud of pebbles grows in the protoplanetary disk, for example via the streaming instability. Eventually this cloud collapses under its own self gravity and merging collisions lead to the rapid growth of ~100 km planetesimals. Conservation of angular momentum in the rotating cloud means that these planetesimals are frequently formed as a binary pair. For a given binary orbit the angular momentum is maximised by forming a system with similar mass components. Additional work (Nesvorn&#253; et al. 2019) has shown that the inclination distribution of binary planetesimals formed via streaming instability and gravitational collapse is a good match for the observed inclination distribution.METHODSWe performed N-body simulations of the gravitational collapse of a pebble cloud using the Symplectic Epicyclic Integrator within the REBOUND package (Rein &amp; Liu 2012). The pebble cloud was approximated by a rotating uniform spherical distribution of 105 computational particles. The radii of the computational particles was inflated in order to replicate the collisional behaviour of a high number density pebble cloud. Collisions were detected when particles were found to be overlapping and we considered the timestep required to ensure that collision detection was robust. We performed a deep search for systems of gravitationally bound particles and tested their stability. For all systems produced we investigated the population characteristics of their mass and orbital parameters.RESULTSOur results demonstrate that gravitational collapse is an efficient producer of bound planetesimal systems, and frequently forms multiple bound systems per cloud. On average there were ~1.5 bound systems produced per cloud in the mass range we have studied. As well as the large equal-sized binaries which were the focus of previous work, we found that gravitational collapse can produce a range of systems such as massive bodies with small satellites and low mass binaries with a high mass ratio. The binaries with equal-size components have bound orbits with low inclinations and low to moderate eccentricity, similar to the observed trans-Neptunian binaries. The additional binaries with dissimilar-sized components or low system mass span a large range of inclinations and eccentricities. Our results disfavour the collapse of the high mass clouds in our dataset (Mc = 1.8e21 kg), as they form large equal-sized binaries that are not observed (figure 1). This finding is in line with reported upper mass limits of clouds formed by the streaming instability. Gravitational collapse of low mass clouds (Mc &#8804; 4.2e18 kg) can create binary systems with similar total mass and mass ratio as the contact binary Arrokoth (figure 1). Furthermore, we find that collisions between planetesimals growing in such a collapsing cloud should be gentle enough to preserve a bi-lobed structure, which further supports the gravitational collapse origin of Arrokoth.&#160;Figure 1. Primary V&#160;band magnitude against magnitude difference between primary and secondary components for binaries produced by gravitational collapse simulations. Marker colour and shape indicates the initial cloud mass. The vertical line indicates the mass ratio cut off of m2/m1 &#8805; 10&#8722;3 in the orbit search algorithm. The observed trans-Neptunian binaries from Grundy (2019) are shown as black 'x's. We represent 'special cases' and dwarf planets as red '+'s. The red circle with error-bars represents how Arrokoth would appear if its components could be separately resolved. An approximate empirical detection limit (Noll et al. 2008) and a lower magnitude limit of 25 are shown as red dotted lines.REFERENCESGrundy, W. (2019). Mutual Orbits of Binary Transneptunian Objects. Retrieved December 2nd, 2019, from online webpage website:&#160;http://www2.lowell.edu/users/grundy/tnbs/Nesvorn&#253;, D., Youdin, A. N., &amp; Richardson, D. C. (2010). Formation of Kuiper Belt Binaries by Gravitational Collapse. The Astronomical Journal, 140, 785&#8211;793. https://doi.org/10.1088/0004-6256/140/3/785Nesvorn&#253;, D., Li, R., Youdin, A. N., Simon, J. B., &amp; Grundy, W. M. (2019). Trans-Neptunian binaries as evidence for planetesimal formation by the streaming instability. Nature Astronomy, 3, 808&#8211;812. https://doi.org/10.1038/s41550-019-0806-zNoll, K. S., Grundy, W. M., Chiang, E. I., Margot, J.-L., &amp; Kern, S. D. (2008). Binaries in the Kuiper Belt. In The Solar System Beyond Neptune (pp. 345&#8211;363). Tucson: The University of Arizona Press.Rein, H., &amp; Liu, S. F. (2012). REBOUND: An open-source multi-purpose N-body code for collisional dynamics. Astronomy and Astrophysics, 537, A128. https://doi.org/10.1051/0004-6361/201118085Stern, S. A., Weaver, H. A., Spencer, J. R., Olkin, C. B., Gladstone, G. R., Grundy, W. M., &#8230; Zurbuchen, T. H. (2019). Initial results from the New Horizons exploration of 2014 MU69, a small Kuiper Belt object. Science, 364(6441). https://doi.org/10.1126/science.aaw9771&#160;&#160;&#160;&#160;&#160;&#160;