Very Slow Rotators from Tidally Synchronized Binaries

Abstract

A recent examination of K2 lightcurves indicates that ∼15% of Jupiter Trojans have very slow rotation (spin periods P s > 100 h). Here we consider the possibility that these bodies formed as equal-size binaries in the massive outer disk at ∼20-30 au. Prior to their implantation as Jupiter Trojans, tight binaries tidally evolved toward a synchronous state with P s ∼ P b , where P b is the binary orbit period. They may have been subsequently dissociated by impacts and planetary encounters with at least one binary component retaining its slow rotation. Surviving binaries on Trojan orbits would continue to evolve by tides and spin-changing impacts over 4.5 Gyr. To explain the observed fraction of slow rotators, we find that at least ∼15-20% of outer disk bodies with diameters 15 < D < 50 km would have to form as equal-size binaries with 12 a b /R 30, where a b is the binary semimajor axis and R = D/2. The mechanism proposed here could also explain very slow rotators found in other small body populations.

Instabilities in the Early Solar System Due to a Self-gravitating Disk

“…The median instability epoch is increasing for these simulations with increasing particle number, but the rate of increase is not dramatic. In terms of mean object mass, our 12,000 particle disk is comparable to the mean mass expected for the 12,000 most massive bodies in the primordial belt (Shankman et al 2013;Nesvorný & Vokrouhlický 2016). From Figure 5, we find that an isolated 4500 particle disk has an e-heating rate within 15% of an isolated 12,000 particle disk and an a-spreading rate within 30 -40% with an isolated disk without any planetary stirring.…”

“…In the second scenario (Figs. 2b & 3b), we keep the surface area of the disk fixed and vary the number of Pluto-mass bodies (1000-4000) present to simulate more realistic conditions (i.e., Nesvorný & Vokrouhlický 2016). We find that the viscous self-stirring increases with the number of Pluto-mass bodies included, which is likely due to the relative strength and frequency of close encounters between particles.…”

“…We find that the viscous self-stirring increases with the number of Pluto-mass bodies included, which is likely due to the relative strength and frequency of close encounters between particles. Levison et al (2011) performed simulations that employed 1000 Pluto-mass bodies, but more recent studies of Kuiper belt formation indicate that the primordial belt may have contained as many as 4000 Pluto-mass bodies (Nesvorný & Vokrouhlický 2016). When we introduce the planets to our simulations in our 4 planet systems (Fig.…”

“…Mass resolution undoubtedly plays a role in the excitation of the disk particles and can contribute to an enhancement to the actual self-stirring within a disk, where more realistic conditions (Nesvorný & Vokrouhlický 2016) would offset this enhancement, but then a large number of particles would be required. To investigate the potential effects on our results, we simulate isolated 20 M ⊕ disks varying the number (750-24000) of equal-mass planetesimals with an inner edge of the disk beginning at 22.7 AU for 10 Myr.…”

“…Until now, each of our simulations employs only one mass for every primordial belt object, and that mass is at least 2 Pluto Masses in most of our simulations. Meanwhile, KBO observations and formation models suggest that the primordial belt possessed 1000-4000 Pluto-mass objects and a much larger population of smaller objects (Shankman et al 2013;Nesvorný & Vokrouhlický 2016). The number of particles necessary to accurately model the lower bounds of this constraint is ∼80,000 assuming a bimodal distribution consisting of 2000 Pluto-mass particles and the remainder in bodies that are 0.1 M P for a 20 M ⊕ disk.…”