By examining the absolute magnitude (H) distributions (hereafter HD) of the cold and hot populations in the Kuiper belt and of the Trojans of Jupiter, we find evidence that the Trojans have been captured from the outer part of the primordial trans-Neptunian planetesimal disk. We develop a sketch model of the HDs in the inner and outer parts of the disk that is consistent with the observed distributions and with the dynamical evolution scenario known as the `Nice model'. This leads us to predict that the HD of hot population should have the same slope of the HD of the cold population for 6.5 < H < 9, both as steep as the slope of the Trojans' HD. Current data partially support this prediction, but future observations are needed to clarify this issue. Because the HD of the Trojans rolls over at H~9 to a collisional equilibrium slope that should have been acquired when the Trojans were still embedded in the primordial trans-Neptunian disk, our model implies that the same roll-over should characterize the HDs of the Kuiper belt populations, in agreement with the results of Bernstein et al. (2004) and Fuentes and Holman (2008). Finally, we show that the constraint on the total mass of the primordial trans-Neptunian disk imposed by the Nice model implies that it is unlikely that the cold population formed beyond 35 AU.
Deep Dive into Considerations on the magnitude distributions of the Kuiper belt and of the Jupiter Trojans.
By examining the absolute magnitude (H) distributions (hereafter HD) of the cold and hot populations in the Kuiper belt and of the Trojans of Jupiter, we find evidence that the Trojans have been captured from the outer part of the primordial trans-Neptunian planetesimal disk. We develop a sketch model of the HDs in the inner and outer parts of the disk that is consistent with the observed distributions and with the dynamical evolution scenario known as the `Nice model’. This leads us to predict that the HD of hot population should have the same slope of the HD of the cold population for 6.5 < H < 9, both as steep as the slope of the Trojans’ HD. Current data partially support this prediction, but future observations are needed to clarify this issue. Because the HD of the Trojans rolls over at H~9 to a collisional equilibrium slope that should have been acquired when the Trojans were still embedded in the primordial trans-Neptunian disk, our model implies that the same roll-over should
Models have recently proposed that the Jovian Trojan asteroids and the Kuiper belt objects share a common origin -they formed in a massive primordial disk that stretched from roughly 15 to ∼ 30 AU and were transported to their current locations during the phase of orbital migration of the giant planets (Morbidelli et al. 2005;Levison et al. 2008).
This connection is a main result of the so-called Nice model (Tsiganis et al., 2005;Gomes et al., 2005). In the Nice model, the giant planets are assumed to have formed in a compact configuration (all were located between 5-15 AU) and be surrounded by a ∼ 35M ⊕ planetesimal disk that extended to about 30 AU. It introduced the idea that Jupiter and Saturn were so close in the past that they had to migrate across their mutual 1:2 resonance. This led to a violent, but temporary phase of instability in the dynamics of the four outer planets. The gravitational interaction between the ice giants and the planetesimals damped the orbits of these planets -leading them to evolve onto their current orbits.
As a result, however, ∼ 35M ⊕ of planetesimals were scattered throughout the Solar System. Some were then captured into stable orbits by the migrating planets. In particular, as Jupiter and Saturn passed through various resonances with one another, a small number of planetesimals would have been captured into the Trojans regions of Jupiter. Morbidelli et al. (2005) showed that this process quantitatively reproduces both the number and the orbital element distribution of the observed Trojan swarms. Another example can be found in the trans-Neptunian region, which, according to Levison et al. (2008;L08 hereafter), was populated during the high-eccentricity phase of Neptune. The simulations in L08 are the most successful to date at reproducing the observed characteristics of the Kuiper belt.
If the above argument is correct, then there should be a genetic link between the Trojan asteroids of Jupiter and the Kuiper belt objects (hereafter KBOs), which should be detectable by studying their physical characteristics. Perhaps the most significant physical property of a population is its size-distribution, or equivalently, for a size-independent albedo, its absolute magnitude (H) distribution (hereafter HD). In particular, if the Trojan and Kuiper belt populations are related they should have similar HDs. This assumes that they have not undergone significant collisional evolution since they were emplaced in their current orbits. Levison et al. (2008b) has shown that this is a reasonable assumption for the Trojans. The fact that, as we show below, the HDs of the Trojans and the Kuiper belt are consistent with one another argues that this is a reasonable assumption for the Kuiper belt as well -at least at the sizes we are concerned with here. Thus, the goal of this paper is to study the HDs of the Trojans and the Kuiper belt to search for any genetic link.
Before we proceed, however, we need to discuss the structure of the Kuiper belt in more detail. The Kuiper belt has very intriguing properties that show that the primordial disk of trans-Neptunian planetesimals was drastically sculpted by a variety of dynamical processes.
A characteristic of particular relevance here is the co-existence of cold and hot populations (defined by having inclination respectively smaller and larger than 4.5 degrees; Brown, 2001) with different physical properties (Levison and Stern, 2001;Tegler andRomanishin, 2000, 2003;Doressoundiram et al., 2001Doressoundiram et al., , 2005;;Trujillo and Brown, 2002;Bernstein et al., 2004, B04 hereafter;Elliot et al., 2005;see however Pexinho et al., 2008 for a proposed alternative inclination divide between populations of different color properties). Levison and Stern (2001) showed that all of the largest KBOs are found in the hot population. This led them to suggest that the hot population formed closer to the Sun (where large objects would form more quickly) than the cold population, and were transported outward as the orbits of the planets evolved (see Gomes, 2003). The difference in the size-distributions was confirmed by B04, who showed that the HD for the hot population is shallower at the bright end than that of the cold.
L08 explained the differences between the hot and cold populations in the context of the Nice model by showing that the cold population is derived almost exclusively from the outer part of the disk, while the hot population samples the full disk more evenly. Thus they concluded that the different HDs of the cold and the hot populations at the bright end can be explained if the HD was not uniform throughout the original planetesimal disk; instead, the outer part of the disk had a steep HD and the inner part had a shallow HD and contained the largest objects.
Studies of the collisional accretion and erosion of planetesimals (e.g. Kenyon and Bromley, 2004) show that a small-body population should have a cumulative size distribution that c
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