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By examining the absolute magnitude (H) distributions (hereafter HD) of thecold and hot populations in the Kuiper belt and of the Trojans of Jupiter, wefind evidence that the Trojans have been captured from the outer part of theprimordial trans-Neptunian planetesimal disk. We develop a sketch model of theHDs in the inner and outer parts of the disk that is consistent with theobserved distributions and with the dynamical evolution scenario known as the`Nice model'. This leads us to predict that the HD of hot population shouldhave the same slope of the HD of the cold population for 6.5 < H < 9, both assteep as the slope of the Trojans' HD. Current data partially support thisprediction, but future observations are needed to clarify this issue. Becausethe HD of the Trojans rolls over at H~9 to a collisional equilibrium slope thatshould have been acquired when the Trojans were still embedded in theprimordial trans-Neptunian disk, our model implies that the same roll-overshould characterize the HDs of the Kuiper belt populations, in agreement withthe 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-Neptuniandisk imposed by the Nice model implies that it is unlikely that the coldpopulation formed beyond 35 AU.

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