Early Instability Model
The Small Mars Problem
Numerical models for the formation of the terrestrial planets that assume the planets grew from a uniform distribution of material between the Sun and Jupiter (often referred to as the classic model: Wetherill, 1980; Chambers, 2001) systematically struggle to replicate the low masses of Mars and the Asteroid Belt. In the actual solar system, Earth is 9 times more massive than Mars, and the total mass of all asteroids is less than 0.1% of the Earth's mass. Conversely, simulations of the classic model for terrestrial accretion typically form Earth massed planets near Mars' modern orbit, and often form large planets in the asteroid belt as well. An example of this evolutionary scheme can be seen in this video:
There is an obvious solution to this problem. Simply put, if Mars and the asteroid belt are growing too large, why not start with less stuff out there? This is exactly what was proposed by Hansen (2009). The next video shows the terrestrial planets growing out of a narrow annulus of material that spans the region between the modern orbits of Venus and Earth. These initial conditions are highly successful at generating good systems of terrestrial planets, and inspired some of the aforementioned evolutionary models (namely the Grand Tack and Low Mass Asteroid Belt models, which provide physical justifications for these initial conditions):
It is important to remember that the Early Instability model was not developed because there was anything wrong with any of the other models. The major motivation for studying an early instability is related to problems with the instability itself.
The Nice Model
Fernandez and Ip (1984; a foundational paper that went largely unnoticed for a decade) demonstrated that, as the giant planets interact with an external disk of small bodies (the primordial Kuiper Belt), the outer three planets (Saturn, Uranus and Neptune) are more likely to gravitationally pull the objects closer to Jupiter. Conversely, Jupiter preferentially ejects these icy bodies from the solar system entirely. To conserve angular momentum throughout these gravitational encounters, the orbits of Saturn, Uranus and Neptune move away from the Sun overtime, while Jupiter moves inward. Taken to its logical conclusion, this concept implies that the giant worlds must have formed in a more compact configuration than they are in today. Through the 1990s, this idea was expanded to explain the capture of Kuiper Belt objects, like Pluto, in orbital resonances with Neptune (Pluto, for example, orbits the Sun exactly two times for every three Neptune orbits). Malhotra (1995) used the concept of planet migration to predict the resonant structure of the Kuiper Belt (see accompanying figure):
This prediction is truly amazing given that, at the time, only a few Kuiper Belt Objects had been discovered. Here is a plot I made of all Kuiper Belt detections (over 4,000 objects!) as of 6 December 2019:
The Late Heavy Bombardment
The Late Heavy Bombardment (Tera et al., 1974) hypothesis was developed after all the basins (dark areas on the Moon) sampled by the Apollo missions returned ages close to 3.9 billion years (about 650 million years after the formation of the solar system). Thus, cratering declined on the terrestrial planets after they completed forming, and then suddenly spiked. Because the Nice Model instability destabilizes many comets and asteroids on to orbits that place them on collision courses with the terrestrial planets, it was originally proposed to coincide with the Late Heavy Bombardment (Gomes et al., 2005). This is commonly referred to as a "late instability."
Sequence of Events
The early instability scenario for terrestrial planet formation makes use of the giant planets' excited orbits (their orbital eccentricities and inclinations: the degree to which the orbits deviate from being circular and co-planar) to halt the formation of Mars and remove material from the asteroid belt. This prevents the Mars-sized objects from eventually combining in to a larger planet. In fact, most are ejected out of the solar system or displaced inward towards Earth and Venus. In many cases, the system finishes with just one Mars-sized object near Mars' modern orbit which did not grow after the instability ensued. Earth and Venus, however, are less perturbed by the giant planets, and continue to grow. The early instability model also requires a very specific timing for the Nice Model; about 1-5 million years after the dispersal of the primordial gas nebula. If the instability happens too soon, the remaining material can "spread" back out, resulting in a system of planets that are all under-massed. However, if the instability happens too late, Mars has already grown too large.
We are continually working to develop the model! Check back for more updates!