On the observational bias of the Trojan swarms

TLDR: In this article, the authors investigate whether the Trojans swarms are observationally biased and place a completion limit on their absolute magnitude, which is known to be H = 11.5mag.

Abstract: Aims. I investigate whether the Trojan swarms are observationally biased and place a completion limit on their absolute magnitude. Methods. Observations including Trojans from a number of observation sites are cross-checked with orbital integration of known Trojans and a set of fictitious Trojan orbits. Results. The completion limit for the Trojans swarms can be set to be H = 11.5mag.TheL 5 swarm is 71% of the L4 size down to this limit. It is not likely that any existing set of orbital elements can have escaped detections. However, parts of the orbital element space, especially in the inclination, are biased for Trojans fainter than the completion limit. In the absolute magnitude interval 11.5−13mag, 65% of new objects should have inclinations 15−40 ◦ , while this inclination interval currently contains 49% of Trojans in the complete interval 9.5−11.5mag. Trojans fainter than an absolute magnitude of 13mag are also clearly biased in the ascending node at values coinciding with the Milky Way.