We don’t need Planet 9!

Title: A Lopsided Outer Solar System

Authors: Alexander Zderic, Maria Tiongco, Angela Collier, Heather Wernke, Aleksey Generozov, Ann-Marie Madigan

First Author’s Institution: Department of Astrophysical and Planetary Sciences, CU Boulder

Paper Status: Accepted in ApJ [open access on ApJ]

We still don’t understand what is going on with the solar-system objects beyond Neptune! No, really, we don’t know much about this region of the solar system. To be fair, these trans-Neptunian objects (TNOs) are weird. Together, they form a disk of icy bodies, called the Kuiper Belt, where some of them, surprisingly, have clustered stable orbits, and others have very unstable orbits due to encounters with Neptune. The famous hypothesis that tries to explain the scattering of the TNOs is the hypothesis about Planet 9. The orbits of these TNOs are really hard to explain, because 1) they are too far away and not well-studied 2) we haven’t really had analogies to these kinds of motions. The latter might not be true anymore, because the researchers at CU Boulder have linked the behavior of these TNOs to the dynamics on a larger scale!

Physics is the same whether you’re in Africa or in America, you look at the Kuiper Belt or at galaxies. This is the main idea behind today’s paper. The authors decided to use the mechanism that explains stellar bar formation in  centers of disk galaxies (the so-called Lynden-Bell mechanism) as an analogy for the dynamics of TNOs. The idea behind this is that galactic bars can be approximated as ellipses that are reminiscent of the lopsided disk that we see in the outer solar system. So, to understand how the outer solar system came to be the way it is right now we need to understand the formation of this lopsided disk. In their previous work, the authors explained that the main mechanism driving the apsidal clustering (the clustering in perihelia and poles) is the inclination instability, – which exponentially grows the inclinations of orbits while decreasing their eccentricities, raising their perihelia and clustering their arguments of perihelion.

The authors run a series of N-body simulations of a primordial scattered disk with a different number of objects, and their objects have different semi-major axes from 100 to 1000 AU. They also looked at the simulations with and without the impact from giant planets (such as Jupiter) on the TNOs. Apsidal clustering in their simulations occurs after a Lynden-Bell clustering region appears. What they found is that apsidal clustering occurs because of the inclination instability, and that this inclination instability is key to the formation of the lopsided disk. In Figure 1, they show the results of the simulation with 400 objects without the impact from giant planets. In the top panels, the apsidal precession starts when the curve goes above the gray line. Only the orange curve goes above the gray area, and this tells us that apsidal clustering only forms near the inner edge of the disk in the 100–320 AU. This matches the growth in the middle panel where the inclination instability is the strongest. In the simulations with the giant planets, the results show a weaker clustering. In these simulations, the inclination instability is also slowed down due to the giant planets, and therefore, the apsidal clustering appears at later times.

Figure 1. Model with 400 objects and not impact from giant planets. Apsidal clustering occurring at the inner edge of the disk. The inclination instability is shown by exponential growth in the middle panel. At t ~ 125 t_sec, the instability is saturated. About 25 t_sec later, the in-plane apsidal clustering appears. About 50 tsec later, slight in-plane apsidal clustering appears in the next bin of semi-major axes. Figure 1 in the paper.
The visualization of the bowl-shape structure of the scattered disk. Figure 9 in the paper.

In Figure 2, the x-axis shows the eccentricity and the y-axis shows the semi-major axis. The colors show the region where the apsidal clustering appears for the model without the giant planets (more precisely, the colors show the time derivative of the longitude of the pericenter). The clustering region is the region where the colors switch from warmer to cooler colors. You can see how initially, all bodies in the scattered disk are on one line (left panel). Later (right panel), the inclination instability reduces the disk orbits’ eccentricity at roughly fixed semi-major axis and causes the disk to buckle into a bowl-shape. However, at later times, the authors notice that the clustering will disappear and then appear again. Once apsidal clustering has been established and the lopsided mode has grown, it is no longer reliant on the clustering region produced by the bowl-shape to exist. The bowl-shaped distribution oscillates back and forth across the original plane of the disk, causing the clustering region to repeatedly disappear and reappear, and eventually, the bowl-shape disappears. However, the lopsided mode created by the clustering region persists. The authors hypothesize that the mode eventually becomes massive enough to trap orbits without the help of the background disk.The general features found in this model are repeated in the model where the impact from giant planets is added. 

Figure 2. Model with 400 objects and not impact from giant planets. The eccentricity and semi-major axis of the disk particles are shown with black points. There is a clustering region at t = 104 t_sec and t = 151 t_sec for eccentricities between 0.25 and 0.60, and it is associated with the bowl-shaped orbital configuration (see above) created by the inclination instability. Figure 5 in the paper.

Trying to see if we actually see this lopsided disk in the observations of debris disks, the authors conclude that the structure in their simulations is reminiscent of some observed debris disks (e.g. of the star HD 61005). They also notice that later, the lopsided mode creates spiral arms. Observational signatures like this in exoplanet disks could be caused by the inclination instability provided there is something to pump-up the orbital eccentricity of the bodies in the disk (e.g. a giant planet). 

The authors of today’s paper modeled the structure of bodies beyond the orbit of Neptune. Even though we would love to have more planets in the solar system, the existence of Planet 9 is still questionable! The authors of today’s paper question whether the clustering of TNOs can be explained using a different model. So, they made models to explain the clustering with inclination instability. Though the models work well and actually show the clustering, there are still some caveats: the clustering appears only for bodies with lower semi-major axes and the number of bodies they used in the simulations might not be large enough! This is how science gets done – we start with simpler models that work and then extend them for more generalized cases. Stay tuned for the authors’ newer models that they’re working on right now!

Astrobite edited by Viraj Karambelkar

Featured image credit: Alexander Zderic 

About Sabina Sagynbayeva

I'm a graduate student at Stony Brook University and my main research area is planet formation. I'm currently working on planetary migration using hydrodynamical simulations. I'm also interested in protoplanetary disks but nearly any topic related to planets is fascinating to me! In addition to doing research, I'm also a singer-songwriter. I LOVE writing songs, and you can find them on any streaming platform.


  1. The evidence of clustering with inclination instability for TNOs with lower semi-major axis is itself proof of existence of an undetected planet hidden in outer solar system.

  2. The evidence of clustering noticed and the resulting inclination instability for TNOs with lower semi-major axis is itself proof of existence of an undetected planet hidden in outer solar system. So fairly this planet’s gravity influences the orbit eccentricity of some TNOs in the disk. It’s detection is only a matter of time.


Leave a Reply