# Could Hot Jupiter systems sustain Trojans?

My understanding is that there is a gravitationally stable region between the Sun and Mercury where asteroids could - in theory - orbit for long periods without being perturbed. However these hypothetical vulcanoids are seemingly non-existent; it being likely that their orbits decay through other means besides the influence of a planet, such as the Yarkovsky effect. We also have trojan asteroids, which share the orbits of planets such as Jupiter but spend their time in the leading and trailing Lagrange Points, keeping their orbits stable.

If a Hot Jupiter such as 51 Pegasi b were to host trojan asteroids, would their proximity to the planet allow their orbits to remain stable for longer, or would their orbits decay regardless? If a Hot Jupiter migrated inwards towards its star, is it more likely to have swept away any possible trojans?

• Small point, and more of a pet peeve of mine than a correction, but "stable for longer" are you talking years or orbital periods. The orbital periods obviously get considerably shorter as the orbiting objects get closer to the star. It seems to me that orbital stability should be counted in number of orbits, not in amount of time. (Maybe I should make that a separate question). – userLTK Mar 9 '18 at 19:49
• I'd say 'long period' meaning as long as the planet has been around, or at least from the time the hot jupiter settles into its current orbit to the present. – user10106 Mar 12 '18 at 8:38

As for the actual formation and capture of such a Trojan, Beauge' et al. (2007) modeled the inward migration of a massive planet, with its semi-major axis decaying over a time scale of $10^5 - 10^7~\mathrm{yr}$. Their results suggest that a Trojan satellite with a tadpole orbit close to $L_4$ will be maintained during the migration.