Early Instability Model

The Early Instability Scenario is an evolutionary model for the solar system that aims to explain several peculiar aspects of the inner solar system. In particular, the Early Instability Scenario proposes a potential solution to the so-called Small Mars Problem (discussed further down on this page). It is important to point out that the Early Instability is not the only viable evolutionary model for the inner solar system. For example, the "Grand Tack" model argues that Jupiter migrated into the inner solar system (stopping around the location of Earth's current orbit) and subsequently back out when the solar system was in its infancy. This migration truncates the disk of planet forming embryos and planetesimals into a narrow annulus, and is highly successful at reproducing the modern terrestrial architecture. Another successful model is the "Low-Mass Asteroid Belt" model. I recommend reading Sean Raymond's article on the various terrestrial planet formation models, and watching the accompanying MOJO video to get a good sense of the different hypotheses. It is also important to understand that these different mechanisms could very well have sculpted the solar system in tandem with one another

The model is developed in the following papers:


We welcome you to use the following videos in any talks, presentations or articles (and appreciate it!):


1. Early Instability without collisional fragmentation (please include a citation to Clement et al. 2018)

2. Early Instability with collisional fragmentation (please include a citation to Clement et al. 2019b, in Icarus)

Simulation Inputs/Outputs:

  1. Initial conditions for instability models (i.e.: outer solar systems on the verge of instability) used in Clement et al. (2018) and Clement et al. (2019b)

  2. Simulation outputs from instability simulations in Clement et al. (2021d):

a. C20/2:1/0Myr (Terrestrial disk output from Clement et al. (2020b), 2:1 instability model from Clement et al. 2020a, 0 Myr instability delay)

b. C20/2:1/5Myr

c. C20/3:2/0Myr (3:2 instability model derived from Nesvorny & Morbidelli 2012)

d. C20/3:2/5Myr

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):

As scientists continued to learn more about the outer solar system and Kuiper Belt, the formal Nice Model (as in Nice, France) finally took shape in 2005. Simply put, the Nice Model argues that, in the solar system's infancy, the primordially compact system of giant planet orbits destabilized. This instability caused the giant planets to orbits to evolve rapidly; diverging from one another and becoming less circular in the process.

The Nice Model explains:

Figure Credit Malhotra 1995

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."

There are multiple reasons scientists have begun invoking an early instability (typically, "early instability" refers to a Nice Model timed within 100 million years of the solar system's birth). These motivations include:

  • New methods for dating the Lunar Basins and updated imagery from modern satellites studying the Moon conflict with a delayed cratering spike (Zellner, 2017)

  • High resolution dynamical simulations indicate that the giant planets likely destabilized quickly (Quarles & Kaib, 2019)

  • The difference in highly siderophile elements (elements that partition into Iron during planet core formation) between the mantles of the Earth and the Moon are consistent with an early instability (Morbidelli et al., 2018)

  • The survival of the Patroclus-Menoetius binary system of Trojan asteroids that orbit along with Jupiter (Nesvorny et al., 2018)

  • The existence of collisional families in the asteroid belt that appear to be as old as the solar system (Delbo et al., 2019)

However, from the perspective of solar system formation models, timing the instability in conjunction with terrestrial planet formation is motivated by studies that show the fully formed terrestrial planets are unlikely to survive a late version of the Nice Model. This plot from Kaib & Chambers, 2016 shows the total number of terrestrial planets surviving in a large sample of late instability simulations. In the majority of outcomes, the terrestrial planets (typically Mercury or Mars) collide with one another, spiral in to the Sun, or are ejected from the solar system entirely.

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.

There are several advantage of using an early instability to abort Mars' growth:

1) This might explain why Mars' geologic formation time (inferred from isotopic dating of meteorites: Dauphas & Pourmand, 2011) is so much shorter than Earth's (1-10 Myr vs. 50-100 Myr; respectively).

2) The degree to which the instability limit's the final masses of Mars and the Asteroid Belt is related to the final giant planet orbits: namely the spacing between Jupiter and Saturn, and their eccentricities. In simulations of the event, the best matches to the inner solar system occur when the outer solar system is most closely replicated as well.

3) The Early Instability can work in conjunction with both the Grand Tack or Low Mass Asteroid Belt models.

4) The entire solar system's dynamical state can potentially be explained with a single event.

Figure Credit: Clement et al. (2018)


We are continually working to develop the model! Check back for more updates!