Terrestrial Planet Formation and the Small-Mars problem

The majority of my work concerns the formation of the Sun's four terrestrial planets: Mercury, Venus, Earth and Mars. The giant planets (Jupiter, Saturn, Uranus and Neptune) must form first because their gaseous envelopes imply that they formed while still imbedded in the primordial gas disk (which dissipates 10-100 times faster in proto-planetary disks than the amount of time isotopic dating tells us it took the Earth to form). My research investigates how the early dynamical evolution of the newly formed outer planets can shape the still-forming terrestrial planets. It turns out that an orbital instability between the giant planets (the Nice Model) can explain many of the peculiar aspects about the inner solar system (see my page on the Early Instability Scenario). These include the low mass of Mars, the size and structure of the Asteroid Belt and the shapes of the inner planets' orbits. Below is a video of a successful simulation of this scenario from Clement et al. (2018). The x axis shows the semi-major axis of the planets (distance from the sun). The y axis plots the orbital eccentricity (the degree to which the orbit is elliptical or non-circular). The size of each dot is proportional to the mass of the object in the simulation, and the color is related to the amount of water and volatiles the object contains. The 5 black dots represent the giant planets (Jupiter, Saturn, Uranus, Neptune and an additional primordial Ice Giant that is ejected). The terrestrial planets grow out of a disk of 1100 initial small, asteroid-like bodies. The objects exterior to the giant planets represent the primordial Kuiper Belt (a disk of comets outside of Neptune's orbit that includes Pluto). When the instability ensues, the extra ice giant is ejected, and the outer section of the terrestrial disk is substantially depleted. This limits the mass of the Asteroid Belt, and prevents a planet from forming in the belt. Furthermore, Mars stops accreting other large embryos after the instability, while Earth and Venus continue to grow. This is consistent with the geological ages of Earth and Mars inferred from isotopic dating (Mars is thought to have finished forming within 1-10 million years, while Earth is believed to have taken around 100 million years to fully form).

The original simulations presented in Clement et al. (2018) assume that objects perfectly merge in every collision. Though this is standard practice in the field of dynamical astronomy, it is still a significant oversimplification of the various complex collisional processes that actually shaped the solar system. In reality, when things collide they can bounce off each other without actually merging, totally merge, fragment in to smaller pieces, or mostly merge but still eject some small fragments. In Clement et al. (2019b), we used a new code that includes the effects of collisional fragmentation to study how the process can affect our early instability model. The video below shows the results of such a simulation (this one begins with 2 extra primordial Ice Giants). In this video, however, the collisional fragments that get produces are color coded black. The presence of these additional particles tends to have a damping effect on the orbits of the growing planets (particularity Earth and Venus). This prevents their orbital eccentricities and inclinations from getting too high; a common problem in simulations of terrestrial planet formation in the solar system. Furthermore, collisional grinding is particularity effective at stopping planets from growing in the Asteroid Belt.

Terrestrial planet formation simulations are inherently biased by the assumptions made about the initial conditions in the terrestrial-forming disk. I have recently worked to refine our understand of the conditions and structures that gave rise to the terrestrial planets. In Clement et al. (2020b) we addressed this by performing high resolution, GPU-accelerated simulations of terrestrial embryo formation starting from ~100 km objects in the primordial gas disk. We found that embryos emerging from the primordial gas at a given radial distance already have masses similar to the largest objects at the same semi-major axis in the modern solar system. Thus, Earth and Venus attain half of their modern mass, Mars-massed embryos form in the Mars region, and Ceres-massed objects are prevalent throughout the asteroid belt. Our results represent a paradigm shift for terrestrial formation models: rather than a hundred or so embryos accreting over hundreds of giant impacts, our work suggests that a dozen embryos experience just a handful of massive impacts as they continue to accrete small bodies over hundreds of Myr. In Clement et al. (2021d) we verified the success off these initial conditions and the 2:1 Jupiter-Saturn resonance version of the Nice Model within the Early Instability framework.