New model for asteroid belt formation is described

Researchers have published an article in The Astrophysical Journal suggesting that asteroids between the orbits of Mars and Jupiter are evidence of a chaotic phase in our Solar System's infancy.

By Peter Moon  |  Agência FAPESP – In 1801, while looking for a planet he believed to exist between the orbits of Mars and Jupiter, Italian priest and astronomer Giuseppe Piazzi (1746-1826) discovered Ceres, a dwarf planet with a diameter of almost 1,000 km.

Ceres is the largest object in the asteroid belt, which is estimated to contain between 1.1 and 1.9 million asteroids with a diameter of more than 1 km, as well as millions of smaller asteroids. For more than 200 years, astronomers have been puzzling over how the asteroid belt formed and why there are no planets between Mars and Jupiter.

Despite the enormous amount of data assembled during two centuries of research on the asteroid belt, not least thanks to the various space probes sent there, no consensus has yet been reached on how it formed. 

Among the new hypotheses that continue to be raised is the chaotic model, which was recently described in an article in The Astrophysical Journal. Its authors are Brazilian astronomers André Izidoro and Othon Winter, both affiliated with the Orbital Dynamics & Planetology Group at São Paulo State University (UNESP), Guaratinguetá campus, in collaboration with colleagues in France and the United States. The research was supported by FAPESP through a Thematic Grant and a Young Investigator Grant.

The planets in the Solar System are divided into two categories: the inner planets (Mercury, Venus, Earth and Mars), called rocky or terrestrial planets; and the outer planets (Jupiter, Saturn, Uranus and Neptune), called gas giants.

The main asteroid belt lies between the two groups. Its hundreds of thousands of objects are scattered in a wide variety of orbits ranging between 1.8 and 3.2 astronomical units from the Sun. One AU corresponds to the average distance between Earth and the Sun.

“The gas giants, such as Jupiter and Saturn, were the first to form, when the Solar System was at most 10 million years old,” said Izidoro, whose research project “Planetary formation and dynamics: from the Solar System to exoplanets” is supported by FAPESP through its Young Investigators in Emerging Centers Program.

According to Izidoro, the gas giants were formed by accretion of gas in the solar nebula, the cloud of gas and dust left over from the Sun’s formation in the proto-solar system.

Earth was formed when there was no more gas available because all matter in the nebula either had been sucked in by the Sun or by the gas giants or had dissipated or been driven far off by intense radiation from the newborn Sun. “It’s estimated that the Earth formed when the Sun was between 30 and 150 million years old. The asteroid belt formed earlier than Earth, but the asteroids reached their current distribution during the history of the Solar System,” Izidoro said.

“To explain the chaos model, we have to start by saying that the main model of the Solar System’s formation used today is the Grand Tack.” The name is a reference to tacking or coming about, a sailing maneuver that consists of turning the bow of the boat into the wind and back again in a zigzag motion.

The Grand Tack model proposes that after its formation at 3.5 AU Jupiter migrated inward to 1.5 AU and then reversed course and migrated outward owing to the influence of Saturn, the second-largest planet in the Solar System.

As Saturn incorporated gas and grew in size, it also migrated toward the Sun and then moved away again. Jupiter and Saturn are thought to have performed this zigzag duet as Saturn met Jupiter on its course toward the Sun.

The Grand Tack by Jupiter and Saturn had two consequences, one for Mars and the other for the formation of the asteroid belt.

Jupiter (and Saturn) absorbed most of the matter available between Mars’s orbit and the asteroid belt. That explains why Mars, which formed later, only reached one-tenth of Earth’s mass. 

In the case of the asteroid belt, Jupiter’s gravitational influence had more drastic consequences. Only a small fraction of the original matter survived in the region of the asteroid belt – not enough to form a planet, but an amount consistent with what is observed today. In addition, the belt’s distribution in this model is fairly similar to that of the actual asteroids.

Computer simulation

When astronomers observe the cloud of interstellar gas and dust that gave rise to the solar nebula in the Milky Way, they try to work out how the giant planets formed.

“The Grand Tack is widely accepted. It’s a solid theory and is supported by astronomical observation. However, that doesn’t mean it’s right or that the asteroid belt formed as predicted by the model,” Izidoro said.

“The Grand Tack isn’t the only model that explains the formation of the asteroid belt. Our chaos model is also viable,” said Winter, Full Professor in the Mathematics Department of UNESP’s Engineering School and principal investigator for the Thematic Project “Orbital dynamics of minor bodies”.

The difference between the two models resides in their estimates of the amount of raw material available in the regions of Mars and the asteroid belt. The Grand Tack assumes there was a great deal of matter in these regions and that this matter was removed by Jupiter and Saturn during a dramatic migration episode.

The chaos model developed by Izidoro and Winter assumes there was practically no matter at all in these regions, dispensing with the need for such intense migration by Jupiter toward the Sun. 

Studies in astronomy use both astronomical observations and computer simulations. The latter are made by compiling and running programs that simulate the behavior of the celestial bodies to be studied in accordance with the laws of physics and the variables to be tested.

“Astronomical studies involve dozens or hundreds of different simulations. In our case, they all produced unsatisfactory results, failing to reproduce the Solar System as we know it – all except one, that is,” Winter recalled.

The only positive result of the chaotic model, the one that matches the actual Solar System as it is observed, was obtained by chance. This happened when the orbits of Jupiter and Saturn were slightly changed in the simulation variables but kept at the same resonance. 

Two planets are in resonance when their orbital periods are related by a ratio of two small integers, such as 1, 2, 3, and 4. In this specific case, the configuration was such that for every orbit of Saturn, Jupiter orbited almost (but not quite) twice around the Sun. The simulation predicted a slight vibration in the orbits of Jupiter and Saturn.

“The vibration was tiny, too small to move the planets out of resonance but sufficient to alter the balance of the system. This is the source of the chaos that gives the model its name,” Winter said.

The simulation calculated the orbits of Jupiter and Saturn not as perfect ellipses but with tiny differences in both the shape of the ellipse and its fluctuation with regard to the plane of the Solar System. This minimal condition was sufficient to change all the behavior of the asteroids in the main belt.

“The difference between the results of this simulation, in which Jupiter and Saturn had chaotic orbits, and those in which they didn’t was striking,” Izidoro said.

“The simulation resulted in an inner Solar System with a small Mars, equivalent in mass to its actual mass, and an asteroid belt with a very similar distribution of bodies to the observed distribution. In our model, the asteroid distribution reached its current status at some time during the infancy of the Solar System – during its first 700 million years,” Izidoro said.

“In the chaotic model, Jupiter and Saturn probably migrated somewhat toward the Sun but much less than in the Grand Tack model. They never reached 5.1 AU according to our conception.”

The new model developed by the Brazilians to describe the asteroid belt’s formation is plausible and reproduces the Solar System that we know. But is this hypothesis the final answer to the question?

“We can’t say that yet,” Winter said. “Both models, Chaos and Grand Tack, are valid a priori, but either could be disproved at any time if it fails to reproduce results consistent with the reality we observe.

“Our model has certain advantages over the Grand Tack, which is a handsome model but very complex. It [Grand Tack] only works if the Solar System disk satisfies a number of specific conditions, whereas our chaos model fits more commonplace situations that have been observed, such as the fact that the planets come into resonance.

“The chaotic model is simpler. In science, the simplest answers are usually the ones that lead to the solution of a problem.”

The article “The asteroid belt as a relic from a chaotic early Solar System” (doi: https://doi.org/10.3847/1538-4357/833/1/40) by André Izidoro, Sean N. Raymond, Arnaud Pierens, Alessandro Morbidelli, Othon C. Winter and David Nesvorny can be read by subscribers to The Astrophysical Journal at iopscience.iop.org/article/10.3847/1538-4357/833/1/40.