This guest post was written by Agastya Rana, a high school junior living in India. His interests lie in planetary astronomy and astrobiology, and he hopes to pursue a career in the field in the future. He is currently working on research regarding the Planet 9 hypothesis and panspermia (the transfer of life from one body to another). He enjoys listening to and writing about EDM in his free time.

Title: Shepherding in a Self-Gravitating Disk of Trans Neptunian Objects

Authors: Antranik A. Sefilian, Jihad R. Touma

First Author’s Institution: Department of Applied Math and Theoretical Physics, University of Cambridge, UK

Status: Published in the Astronomical Journal, open access

As a young child, I learnt about the nine planets of the Solar System, starting at Mercury and ending with Pluto. In 2006, Pluto was notoriously (and justifiably) downgraded from full planet to dwarf planet status – and so it was that our Solar System would now have only eight planets.

The search for another ninth planet, however, has never ceased. It is now becoming one of the most exciting areas within planetary astronomy! The reason for this interest is a perplexing observation made by Mike Brown, who ironically (and aptly) is the Caltech planetary astronomer responsible for demoting Pluto in the first place.

The origin of the Planet 9 hypothesis

Through some of the most powerful telescopes on Earth, such as the Subaru telescope on Mauna Kea, we have been able to painstakingly detect small bodies that orbit near the very edge of the solar system, well beyond Neptune’s orbit. These objects are appropriately dubbed trans-Neptunian objects, or TNOs in short. Over the past couple of decades, more than ten objects with perihelia (the point in the orbit of a planet that is closest to the Sun) more than five times that of Neptune’s, have been found and their orbits exhibit an unexplained phenomenon.

A curious observation, revealed in the seminal 2016 paper by Mike Brown and Konstantin Batygin, showed that the these objects were physically clustered, meaning that their orbits were similarly oriented in space. This posed an enormous puzzle to all planetary astronomers, because such a pattern is not expected due to the effect of differential precession. What this term essentially means is that over long periods of time (millions of years), the orbits of all bodies themselves rotate, like tops, due to their interaction with the other bodies in our Solar System. This effect varies significantly with the parameters of the orbit and the object, meaning that all objects should experience different rates of precession. This means that any ‘clustering’ in the orbits would likely disperse over longer timescales. The fact that we still see this clustering means that there must be something preventing the precession. In order to suggest potential mechanism for this effect, Batygin & Brown invoked a ninth planet in our Solar System, an idea which has been explored comprehensively through many dozens of papers in subsequent years.

Not a planet, but a disk

Today’s paper from a graduate student at the University of Cambridge and a physicist at the University of Tel Aviv puts a novel spin on the existing Planet 9 hypothesis by invoking a ‘ring’ of small bodies in the outer reaches of the Solar System as a possible explanation for the observations. This theory could potentially be developed in conjunction with, or as an alternative to, the large Planet 9 hypothesis.

A giant disk of small bodies nearly 20 times the distance from the Sun than Neptune might sound preposterous, yet it nonetheless is not the most surprising hypothesis in the paper. The authors propose that the TNOs that we have observed in this ‘clustering’ are part of this larger, eccentric disk of TNOs – the very same disk invoked to trigger the alignment of these TNOs in the first place. While this may seem like circular reasoning, the stability of such a ‘self-consistent’ disk is backed up by mathematical and physical predictions in the paper.

The balance of precession

In the paper, the authors begin by analytically deriving the effect of this giant ring and the four giant planets on the dynamics (long-term motion) of the constituent objects of the ring itself. The paper claims that this ring will allow the prograde precession (counterclockwise) caused by the giant planets to be exactly counteracted by the retrograde (clockwise) precession caused by the ring itself, meaning that the orbits stay stationary and remain clustered (see Figure 1).

Figure 1. This graph of the precession rates of small bodies (TNOs) against the semi-major axis of the TNOs. The different lines plotted correspond to different eccentricities of these TNOs. The significance of this graph emerges from the fact that for every semi-major axis between 200 and 500 AU, it is possible for a body to have a zero rate of precession (there will be a particular eccentricity corresponding to this 0 rate of precession). This means that all these bodies can remain in stable, aligned orbits for millions of years. (Figure 1 in paper).

They show that with this ring present, a family of stable orbits that remain permanently aligned with one another, which could potentially be the TNOs that we observe in the far reaches of the solar system. Curiously, this family of orbits is anti-aligned with (have perihelia in the opposite direction to) the disk itself (see Fig 2). The reason that this is disk is ‘self-consistent’ is that simulations also predict a family of objects which are aligned with the disk, and could make up the bulk of the disk. They further argue that these patterns of ‘clustering’ are obtained for a wide variety of disk parameters – making their model quite robust. The underlying motif is that the macroscopic effects of the disk’s gravitational influence arise from each of the small bodies it is made up of.

Figure 2. This figure plots the eccentricity of predicted (and observed) TNOs as a result of interactions with an initial disk (shown by the green line). One can separate these bodies into three ‘families’ as shown by the key in the graph. The ‘self-consistency’ of this model is seen in this graph specifically – the family of bodies denoted with blue circles have an eccentricity-semimajor axis similar to that of the green line (showing the disk used), meaning that these bodies could be responsible for making up the disk itself – a concept admittedly hard to wrap your head around. Meanwhile, the blue triangles represent the population of bodies which we observe today, and the predictions fit the observations (yellow diamonds) decently well, although some fine-tuning of the model might be needed. (Figure 3 in paper).

But can such a disk actually exist?

After considering the effect of different properties of the disk on their hypothesis, the authors discuss the possibility of such a disk existing based on currently accepted measurements and theories. Most standard models of the outer solar system predict that the region of the solar system within which this disk is theorized to reside contains only on the order of 0.1 Earth masses, predicted by continuing the observed trend in disk mass. However, this amount of matter is insufficient to explain the clustering that we observe (which requires around 10 Earth masses of material). The authors cite a few papers which suggest that the region in question may contain much more material, eventually concluding that both the Planet 9 hypothesis and their hypothesis require similar masses of material, with their idea being more plausible as the mass can remain scattered instead of having to have been conglomerated within a planet.

Even if a ninth planet does exist, and it causes TNOs to maintain their alignment as observed, the authors of the study note that if the mass of these TNOs is on the order of 1 Earth mass, their effect on each other will also become important. The authors note that one of the observed TNOs has an orbit that is hard to explain with the Planet 9 hypothesis, but the combined action of Planet 9 and their disk easily allows for such an orbit to be stable. With this example in mind, they show how a combined disk planet model can account for the stability of a much wider range of orbits than either model could on its own.

While this paper does take into account factors such as inclination of orbits, and has had its credibility tested against the bodies we have detected to date (even providing a better explanation for one body than Planet 9 does), it is still in its early stages, and requires a lot more work to see how exactly its predictions differ from the Planet 9 hypothesis. It is nonetheless a very exciting proposal!