Tuesday, August 2, 2016


If I was to pick a single characteristic of daily (academic) life that never ceases to amaze, it would be the rate at which time flies. It has been a little over six months since the publication of the original P9 paper, and the number of follow-up studies that have been unveiled since then edge on thirty. A subset of these studies have, rather than attempting to further characterize Planet Nine’s present-day state, considered the intriguing question of Planet Nine’s origins. Having finished teaching a class on the formation and evolution of planetary systems last quarter, this question has been on my mind as well. 

In essence, there are three potential scenarios for the formation of Planet Nine that have been discussed in the literature. They are (I) outward scattering (II) external capture and (III) in-situ formation. Within the framework of the first picture, P9 forms alongside other solar system planets, but is perturbed onto a highly elliptical, long-period orbit after the dissipation of the solar nebula. In other words, the extreme orbit of Planet Nine is generated through the honest labor of gravitational planet-planet interactions (with a bit of work done at the end by passing stars; see below). 

Orbit of an outward-scattered planet. Made with Super Planet Crash (http://www.stefanom.org/spc/).

External capture, on the other hand, paints the solar system in a more conniving light. In this story, Planet Nine is kidnapped by the Sun’s gravitational pull from an unsuspecting passing star, rendering P9 a bonafide exoplanet. Finally, the in-situ formation scenario simply envisions that the solar system’s protoplanetary disk extended to ~1000AU, and over time a distant annulus of material coalesced into a ~10 Earth mass body.

Although I’m a fan of the theory of in-situ formation of giant planets in the inner nebula, in-situ formation of P9 seems to be the least likely of the three aforementioned alternatives. If we extend the classical minimum mass solar nebula to ~1000AU with a Mestel-like surface density profile, we obtain a disk mass of Mdisk ~ (2 pi) (1700 g/cm^2) (1AU) (1000AU) ~ 1.2 solar masses. In addition to being straight-up gnarly, such a disk severely violates the gravitational stability criterion, and with its sub-Jovian mass, P9 is probably not a product of direct gravitational collapse. 

So if P9 didn’t form in place, it was either scattered outwards or it was stolen. Interestingly, both of these processes require the solar system to be embedded within its birth cluster to operate successfully. This is because in the capture scenario, a dense stellar environment is necessary for stars to get close enough to exchange planets, and in the outward scattering scenario, perturbations from passing stars are needed to lift Planet Nine’s perihelion from q ~ 5AU (i.e. Jupiter’s orbit) to its present-day value of q ~ 250 AU. 

The solar system embedded within a very dense birth cluster (a snapshot from a movie created by A. M. Geller http://faculty.wcas.northwestern.edu/aaron-geller/visuals.php)

The dynamics of interactions between Planet Nine and passing stars were addressed in a paper by Li & Adams. In short, Li & Adams find that external capture (despite being dramatic and esthetically satisfying) is a fundamentally low-probability event: capture cross-sections are much smaller than ejection cross-sections in the birth cluster. Thus, the capture scenario can likely be ruled out on probabilistic grounds. 

Intriguingly, the outward scattering story (the only remaining option) is not immune to external kicks either. If left alone in the birth cluster for ~100 million years, the same gravitational perturbations from passing stars that act to lift P9’s perihelion can also strip the planet away all together. Although the exact limits depend on detailed parameter choices, these calculations imply a particular timing for the successful generation and retention of Planet Nine. Specifically, Planet Nine probably formed within the first 1-10 million years of the solar system’s lifetime and acquired its orbit a few 10s of millions of years later, towards the end of the birth cluster’s lifetime. 

From here, we can speculate a bit. On one hand, this timing seems inconsistent with early scattering as envisioned for example by Izidoro et al (2015), because any objects acquiring long-period orbits while the gas is still present would be stripped away by passing stars. But the nebular epoch is not the only time when the solar system could have conceivably ejected planets. The other reasonable instance is the era of transient dynamical instability associated with the Nice model. After all, N-body modeling shows that the solar system could have harbored an additional ice giant that would have been expelled at this time (see here, here and here). To this end, here is a simulation that starts out with an extra Neptune that ejects after about ten million years.

Dynamical evolution of an initially 5-planet outer solar system (from Batygin et al 2012)

If we subscribe to this point of view, then Planet Nine is the solar system’s original fifth giant planet. Pretty neat. But wait - by fixing the onset of giant planet instability to sometime before ~100 million years after the Sun’s birth, we have broken an attractive feature of the Nice model: the late heavy bombardment. The large-scale instability represents a natural trigger for the avalanche of debris that scarred our Moon’s surface, and this very notion served as the main motivation for rethinking how the instability gets activated in the first place. Bummer.

Now, terrestrial planets themselves require ~100 million years to form (seriously, why couldn’t all these timescales be a little more distinct from one another?!!), so in order to bombard the Moon, the instability would have had to happen after that. Moreover, a recent analysis linked Mercury’s weirdly excited orbit to a sweeping secular resonance that is associated with changes in system’s architecture during the dynamical reformation. But at the same time, another study that came out earlier this year pointed out that the terrestrial planets are unlikely to survive the Nice-model instability in the first place. So perhaps the fact that we exist to even ask these questions is evidence in itself that the instability proceeded before the formation of the terrestrial planets was complete?

At this point, my head is spinning and I want to stop speculating. With Planet Nine in the mix, the solar system’s origin story has once again began to resemble a jig-saw puzzle with pieces that don’t quite snap into place perfectly. But this is probably due to the fact that the piece that represents P9 has not yet been directly imaged, and one can only speculate as to what kind of additional constraints on the solar system’s early evolution will come to light once Planet Nine’s physical and orbital properties are revealed. But like I said, for now I want to stop speculating.