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Register a new userDynamical evolution of the inner asteroid belt
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Stanley F. Dermott
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A determination of the dynamical evolution of the asteroid belt is difficult because the asteroid belt has evolved since the time of asteroid formation through mechanisms that include: (1) catastrophic collisions, (2) rotational disruption, (3) chaotic orbital evolution and (4) orbital evolution driven by Yarkovsky radiation forces. The timescales of these loss mechanisms are uncertain and there is a need for more observational constraints. In the inner main belt, the mean size of the non-family asteroids increases with increasing inclination. Here, we use that observation to show that all inner main belt asteroids originate from either the known families or from ghost families, that is, old families with dispersed orbital elements. We estimate that the average age of the asteroids in the ghost families is a factor of 1/3 less than the Yarkovsky orbital evolution timescale. However, this orbital evolution timescale is a long-term average that must allow for the collisional evolution of the asteroids and for stochastic changes in their spin directions. By applying these constraints on the orbital evolution timescales to the evolution of the size-frequency distribution of the Vesta asteroid family, we estimate that the age of this family is greater than 1.3 $Gyr$ and could be comparable with the age of the solar system. By estimating the number of ghost families, we calculate that the number of asteroids that are the root sources of the meteorites and the near-Earth asteroids that originate from the inner main belt is about 20.
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The asteroid belt was dynamically shaped during and after planet formation. Despite representing a broad ring of stable orbits, the belt contains less than one one-thousandth of an Earth mass. The asteroid orbits are dynamically excited with a wide range in eccentricity and inclination and their compositions are diverse, with a general trend toward dry objects in the inner belt and more water-rich objects in the outer belt. Here we review models of the asteroid belts origins and dynamical history. The classical view is that the belt was born with several Earth masses in planetesimals, then strongly depleted. However, it is possible that very few planetesimals ever formed in the asteroid region and that the belts story is one of implantation rather than depletion. A number of processes may have implanted asteroids from different regions of the Solar System, dynamically removed them, and excited their orbits. During the gaseous disk phase these include the effects of giant planet growth and migration and sweeping secular resonances. After the gaseous disk phase these include scattering from resident planetary embryos, chaos in the giant planets orbits, the giant planet instability, and long-term dynamical evolution. Different global models for Solar System formation imply contrasting dynamical histories of the asteroid belt. Vesta and Ceres may have been implanted from opposite regions of the Solar System -- Ceres from the Jupiter-Saturn region and Vesta from the terrestrial planet region -- and could therefore represent very different formation conditions.
The asteroid belt is an open window on the history of the Solar System, as it preserves records of both its formation process and its secular evolution. The progenitors of the present-day asteroids formed in the Solar Nebula almost contemporary to the giant planets. The actual process producing the first generation of asteroids is uncertain, strongly depending on the physical characteristics of the Solar Nebula, and the different scenarios produce very diverse initial size-frequency distributions. In this work we investigate the implications of the formation of Jupiter, plausibly the first giant planet to form, on the evolution of the primordial asteroid belt. The formation of Jupiter triggered a short but intense period of primordial bombardment, previously unaccounted for, which caused an early phase of enhanced collisional evolution in the asteroid belt. Our results indicate that this Jovian Early Bombardment caused the erosion or the disruption of bodies smaller than a threshold size, which strongly depends on the size-frequency distribution of the primordial planetesimals. If the asteroid belt was dominated by planetesimals less than 100 km in diameter, the primordial bombardment would have caused the erosion of bodies smaller than 200 km in diameter. If the asteroid belt was instead dominated by larger planetesimals, the bombardment would have resulted in the destruction of bodies as big as 500 km.
We have observed the lightcurves of 13 V-type asteroids ((1933) Tinchen, (2011) Veteraniya, (2508) Alupka, (3657) Ermolova, (3900) Knezevic, (4005) Dyagilev, (4383) Suruga, (4434) Nikulin, (4796) Lewis, (6331) 1992 $mathrm{FZ_{1}}$, (8645) 1998 TN, (10285) Renemichelsen, and (10320) Reiland). Using these observations we determined the rotational rates of the asteroids, with the exception of Nikulin and Renemichelsen. The distribution of rotational rates of 59 V-type asteroids in the inner main belt, including 29 members of the Vesta family that are regarded as ejecta from the asteroid (4) Vesta, is inconsistent with the best-fit Maxwellian distribution. This inconsistency may be due to the effect of thermal radiation Yarkovsky--OKeefe--Radzievskii--Paddack (YORP) torques, and implies that the collision event that formed V-type asteroids is sub-billion to several billion years in age.
The asteroid belt contains less than a thousandth of Earths mass and is radially segregated, with S-types dominating the inner belt and C-types the outer belt. It is generally assumed that the belt formed with far more mass and was later strongly depleted. Here we show that the present-day asteroid belt is consistent with having formed empty, without any planetesimals between Mars and Jupiters present-day orbits. This is consistent with models in which drifting dust is concentrated into an isolated annulus of terrestrial planetesimals. Gravitational scattering during terrestrial planet formation causes radial spreading, transporting planetesimals from inside 1-1.5 AU out to the belt. Several times the total current mass in S-types is implanted, with a preference for the inner main belt. C-types are implanted from the outside, as the giant planets gas accretion destabilizes nearby planetesimals and injects a fraction into the asteroid belt, preferentially in the outer main belt. These implantation mechanisms are simple byproducts of terrestrial- and giant planet formation. The asteroid belt may thus represent a repository for planetary leftovers that accreted across the Solar System but not in the belt itself.
Polluted white dwarfs are generally accreting terrestrial-like material that may originate from a debris belt like the asteroid belt in the solar system. The fraction of white dwarfs that are polluted drops off significantly for white dwarfs with masses $M_{rm WD}gtrsim 0.8,rm M_odot$. This implies that asteroid belts and planetary systems around main-sequence stars with mass $M_{rm MS}gtrsim 3,rm M_odot$ may not form because of the intense radiation from the star. This is in agreement with current debris disc and exoplanet observations. The fraction of white dwarfs that show pollution also drops off significantly for low mass white dwarfs $(M_{rm WD}lesssim 0.55,rm M_odot)$. However, the low-mass white dwarfs that do show pollution are not currently accreting but have accreted in the past. We suggest that asteroid belts around main sequence stars with masses $M_{rm MS}lesssim 2,rm M_odot$ are not likely to survive the stellar evolution process. The destruction likely occurs during the AGB phase and could be the result of interactions of the asteroids with the stellar wind, the high radiation or, for the lowest mass stars that have an unusually close-in asteroid belt, scattering during the tidal orbital decay of the inner planetary system.
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