The Inner Oort Cloud Connection

The census of Kuiper belt objects spanning the distant solar system has sure come a long way. Even if we strictly limit our object sample to those with semi-major axes above 250 AU, or equivalently, an orbital period greater than about 4,000 years, the number of TNOs clocks in at nineteen — a staggering improvement from the six we had back in 2016. 

Some of these TNOs cluster together, while others do not. More importantly, a simple glance at the orbital structure of the outer solar system reveals an intriguing pattern: the degree of clustering is intimately connected to their present-day dynamical stability. In other words, orbits strongly perturbed by Neptune and those on their way out of the solar system (rendered in green) are all over the place. Meanwhile, long-term stable Sedna-like orbits (rendered in purple) appear as though a cosmic florist has carefully arranged them into a bunched bundle of trajectories. Meta-stable orbits (shown in gray) experiencing slow orbital diffusion are caught somewhere in the middle.

The degree to which the overall orbital clustering is a physical effect, as opposed to being a figment of observational bias or a statistical chance, has been a subject of discussion ever since the Planet Nine Hypothesis saw the light of day (see here, here, here, here and here, as well as Mike’s post below). To this end, individual surveys having only searched limited areas of the sky cannot sufficiently overcome their own observational biases to determine the absence or presence of orbital alignment rigorously. However, even after taking observational biases into account, a combined observability analysis of all available data shows that distant KBOs jointly cluster in eccentricity and angular momentum vectors at the ~99.8% significance level.

Dynamical sorting of KBOs is another matter: although there are distinct biases pertinent to high-eccentricity orbits documented in the literature, no conceivable observational bias can differentiate KBOs based upon their dynamical stability, thereby causing long-term stable orbits to cluster more strongly than their unstable counterparts. Put simply, when astronomers discover TNOs, pretty much the only well-known information about them is RA/DEC, heliocentric radius, and Vmag for approximately one year preceding follow-up. For this reason, it is impossible for surveys to bias themselves based on the Lyapunov exponent, or the rapidity of exponential divergence of cloned initial conditions, of an orbit. On the contrary, within the framework of the Planet Nine hypothesis, there is a close link between the degree of orbital clustering and dynamical stability. Thus, if we interpret the picture insinuated by the data at face value, the observed “width” of the stable-orbit cluster tells us something about Planet Nine’s mass and orbit.

A couple of years ago, we published a review article detailing thousands of simulations suggesting that P9 is less eccentric and less massive than we initially thought (i.e., m~5 Earth masses and e~0.3 instead of m~10 Earth masses and e~0.6). Even more refined models having more particles and matching the data more precisely are possible and are worthwhile to pursue. However, the question we asked ourselves during the height of the pandemic is a different one: are essential physics missing from our simulations? Through our continued and incessant probing of the model, we have discovered that the answer to this question is “yes.”

All our P9 calculations thus far have treated the solar system as an isolated entity, with the sun at the center of the simulation and all objects that attain a heliocentric distance over 10,000 AU as being forever lost to the abyss. Although this is a viable approximation scheme for understanding the present-day solar system, it is an unrealistic full-scale model considering the sun’s birth environment. After all, enrichment of meteorites in short-lived radiogenic isotopes suggests that the sun formed in a massive cluster of stars, somewhat akin to the Orion Nebular Cluster. This fact immediately renders the formation of a perihelion-detached quasi-toroidal cloud of icy debris at a few thousand AU all but inevitable. As our newly published P9 simulations show, this cloud of debris does not remain dormant throughout the lifetime of the solar system. Instead, Planet Nine’s gravity acts to inject these “inner Oort Cloud” objects into the trans-Neptunian region of the solar system, mixing them in with the distant scattered disk. A necessary consequence of the process is that newly-injected debris tends to broaden the cluster, requiring a more eccentric P9 to match the data.

Let us discuss this process in greater detail. The formation of giant planets, particularly Jupiter and Saturn, happens while the sun is encircled by its primordial disk of gas and dust during the first three million years of its lifetime. As the giant planets gain mass, they necessarily scatter icy debris outwards. If the solar system were to evolve in isolation, the debris would eventually attain positive orbital energy and become unbound from the sun. In a star cluster, however, the situation is more delicate. As the planetesimal obits become sufficiently elongated, they become susceptible to perturbations from passing stars that can detach them from the gravitational bashing of newly-born Jupiter and Saturn, thereby “freezing” them in place. Distinct from the classical Oort Cloud that likely formed later, we refer to this hypothetical population of icy asteroids envisioned to orbit the sun at thousands of astronomical units as the inner Oort Cloud.

We have simulated the formation of the inner Oort Cloud, modeling the sun’s birth cluster as a Plummer sphere, with parameters chosen to mimic the Orion Nebular Cluster and solar residence time chosen such that it does not violate cold classical Kuiper belt constraints. Shown in terms of Keplerian orbital elements, a typical inner Oort Cloud that forms in our simulations looks as follows:

Now, the conventional story is that the inner Oort Cloud formation stops the moment the sun leaves its birth cluster, and this frigid cloud of icy debris sits there “forever.” Planet Nine, however, alters this picture on a qualitative level. Due to the long-term gravitational pull of P9’s orbit, inner Oort Cloud objects evolve on billion-year timescales, slowly getting re-injected into the outer solar system. So what happens to them? We have simulated this process, accounting for perturbations from the canonical giant planets, P9, passing stars, as well as the galactic tide, and have found that these re-injected inner Oort Cloud objects can readily mix in with the census of distant Kuiper belt objects, and even exhibit orbital clustering. However, the degree of clustering they show is prominently weaker, suggesting that a more eccentric P9 is required to explain the data. Another intriguing aspect of these calculations is that they produce a more radially extended distribution of long-period TNOs, providing an intriguing potential explanation for the abundance of highly long-period orbits, such as that of the Goblin.

All in all, as scientists, our primary role is to continue hammering away at the hypothesis, and our new simulations indicate that there exists an intriguing additional mode of P9-induced dynamics affecting our efforts to pin down the orbit of Planet Nine. With each theoretical breakthrough, the observational search comes into sharper focus.