What influences Trojan Asteroid density?

I'm putting together a solar system for a story I'm working on, and in this solar system the most important planet is a particularly large Ice giant and its big moon nestled in the star's habitable zone (the sun is basically identical to ours).

I wanted to ask about Trojan Asteroids, I'm trying to understand what factors may influence a large pile up of big Asteroids at this planet's L4 and L5 lagrange points.

I understand that Jupiter has the most studied Trojan systems, some of the objects are quite large, in excess of 100 kilometers in diameter. Wikipedia tells me that there might be as many as a million Jupiter Trojans larger than one kilometer. Additionally Neptune probably has even more, and larger ones too. However Saturn and Uranus seem to have less than the other giant planets. Is Trojan density thus directly correlated with proximity to belts of small bodies, like the Asteroid and Kuiper belts? Is it affected by the size of the dominating body, or proximity to the sun? Would my Neptune like planet in the same position as earth be likely to have a significant collection of fairly large Trojans(about the size of Gaspra say), with or without an asteroid belt nearby?

posted over 9 years ago

Khwarezm‭

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