Considerations on the magnitude distributions of the Kuiper belt and of the Jupiter Trojans

TL;DR

This study analyzes the magnitude distributions of Kuiper belt objects and Jupiter Trojans, proposing a model consistent with the Nice model that suggests Trojans originated from the outer trans-Neptunian disk and predicts similar size distribution features.

Contribution

It develops a sketch model of magnitude distributions that links Kuiper belt and Trojan populations, supporting a common origin and providing testable predictions.

Findings

Trojan and Kuiper belt populations share similar magnitude distribution slopes.

The magnitude distribution of Trojans shows a rollover at H~9, indicating collisional equilibrium.

The primordial trans-Neptunian disk likely did not extend beyond 35 AU.

Abstract

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.