Dust arcs in the region of Jupiter's Trojan asteroids

Aims. The surfaces of the Trojan asteroids are steadily bombarded by interplanetary micrometeoroids, which releases ejecta of small dust particles. These particles form the faint dust arcs that are associated with asteroid clouds. Here we analyze the particle dynamics and structure of the arc in the region of the $L_4$ Trojan asteroids. Methods. We calculate the total cross section of the $L_4$ Trojan asteroids and the production rate of dust particles. The motion of the particles is perturbed by a variety of forces. We simulate the dynamical evolution of the dust particles, and explore the overall features of the Trojan dust arc. Results. The simulations show that the arc is mainly composed of grains in the size range 4-10 microns. Compared to the $L_4$ Trojan asteroids, the dust arc is distributed more widely in the azimuthal direction, extending to a range of [30,120] degrees relative to Jupiter. The peak number density does not develop at $L_4$. There exist two peaks that are azimuthally displaced from $L_4$.