Standard planet-formation models have been unable to reconstruct the distributions of the Solar System's small, rocky planets and asteroids in the same simulation. A new analysis suggests that it cannot be done.
About 4.5 billion years ago, the Solar System formed in a disk of gas and dust particles that surrounded the newly born Sun1. The 'giant' planets (Jupiter, Saturn, Uranus and Neptune) formed first, within the few million years of the disk's lifetime. Closer to the Sun, the small, rocky 'terrestrial' planets (Mercury, Venus, Earth and Mars) took tens of million years to form, by collisions of numerous smaller objects generated in the disk. Myriad small bodies formed the asteroid belt between the orbits of Mars and Jupiter. Despite decades of attempts, no computational realization of standard formation theories has reproduced the mass and orbital distribution of both the terrestrial planets and the asteroids. Writing in the Monthly Notices of the Royal Astronomical Society, Izidoro et al.2 show that this is not possible.
In the standard scenario of terrestrial-planet formation, planetary building blocks are segregated into two mass categories: a few tens of large planetary embryos, and several thousand small planetesimals from which embryos also grew while gas was still around. The embryos are roughly the size of Mars, whereas planetesimals are at most a few hundred kilometres across. All of these objects follow circular, co-planar orbits, and their number density decreases slowly with distance from the Sun. They are also gravitationally perturbed by the giant planets, whose orbits have remained roughly unaltered since they began to form. As the system evolves, the strong gravitational pull that embryos receive from the giant planets and from each other deforms the embryos' orbits, which begin to cross. A cascade of collisions follows, forming planets as the embryos merge and collect planetesimals. Leftover planetesimals become asteroids.
Such simulations produce a small number of planets and a belt of leftovers that are broadly similar to the present Solar System, on reasonable timescales (see ref. 3, for example). Yet despite improvements, the detailed mass and orbital distribution of the inner Solar System are exceedingly difficult to reproduce. In the real Solar System, Venus and Earth are comparable in mass, and they orbit between the smaller Mercury and Mars (Fig. 1a). But standard models suffer from the 'Mars problem': in place of Mars, another planet forms that is comparable in size to Earth, and additional Mars-sized embryos can get stuck in the asteroid belt.
Although planets follow nearly circular, co-planar orbits, asteroid orbits are much more elliptical, and can be inclined to the ecliptic (Earth's mean orbital plane) by as much as 30°. Only part of this 'excitation' is explained by gravitational perturbations from the planets acting over the lifetime of the Solar System. If embryos had got stuck in the primordial belt, as suggested by standard simulations, this could have excited asteroid inclinations. But the embryos would have had to have decamped quickly, otherwise the asteroid belt would look very different today.
Building a huge 'Mars' and trapping massive embryos in the asteroid belt might not occur if most embryos are initially gathered within the orbit of Mars — that is, if a steep density profile develops in the early Solar System. This could occur if solid material in the gas disk accumulates near the Sun so that embryo formation is favoured in this region4. In their work, Izidoro et al. modelled the steep-profile scenario and compared it with other density profiles, but did not detail how this accumulation occurred.
Their main result is that, no matter what the density profile, it is impossible both to solve the Mars problem and to build a correctly structured asteroid belt (Fig. 1b, c). Steep density profiles reproduce the terrestrial planets fairly well, unlike shallow profiles. But asteroid excitation follows the opposite trend: steeper density profiles give much lower inclination excitations, because of the lack of embryos in the belt. Once the terrestrial planets have formed, leftover planetesimals cannot excite each other enough to produce the observed structure of the asteroid belt, because their gravity is weak. Perturbations from the giant planets cannot do the job either, even if they change their orbits abruptly later in the Solar System's evolution, as modern models predict (see ref. 5, for example). So the asteroid belt must have been both depleted of mass and excited before the terrestrial planets began to assemble.
Standard formation models don't consider the fact that giant planets can substantially change their orbits while forming in the disk. An intricate migration pattern of the giants has been reported6 to produce a mass distribution that solves the Mars problem and generates an asteroid belt broadly similar to the observed one. As Izidoro et al. point out, this is the only known model that is compatible with their results, although it assumes a match between the growth and migration-time profiles of Jupiter and Saturn that has not been reproduced in simulations.
Planet-formation models have, in fact, been undergoing revision since it was realized that trillions of small pebbles in gas disks can spiral onto planetesimals as the pebbles drift towards the Sun, causing planetesimals to grow swiftly into embryos7. Pebble accretion, combined with gravitational self-stirring, has been shown to produce the giant planets within the short lifetime of the disk8 — the first time that this has been achieved in a model. More-recent work9 suggests that the same process might explain the structure of the inner Solar System, without the need for giant-planet migration. However, this accretion model also depends sensitively on largely unknown physical properties of both the gas disk and the growing bodies.
Izidoro et al. do not offer a final model of terrestrial-planet formation. But their work convincingly demonstrates that standard models cannot satisfy major constraints on the process, the toughest of which is set by asteroids. Even if their simulations were refined, it is unlikely that this general result would change. Planetary scientists should now focus on whether the intricate structure of the inner Solar System can be adequately explained by non-standard accretion models, or whether it simply represents the heritage of a preceding phase of extensive giant-planet migration6.