On the observational bias of the Trojan swarms

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 = 11.5 mag. The L 5 swarm is 71% of the L 4 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 11.5−13 mag, 65% of new objects should have inclinations 15−40 • , while this inclination interval currently contains 49% of Trojans in the complete interval 9.5−11.5 mag. Trojans fainter than an absolute magnitude of 13 mag are also clearly biased in the ascending node at values coinciding with the Milky Way.

Creation, detection, and evolution of Jupiter Trojan families

“…1 further shows that it is foremost the small L 4 Trojans which contribute to the difference with the result by Dahlgren (1998). These largest Trojans have a steeper size distribution (Karlsson 2010;Shoemaker et al 1989) than the smaller Trojans and in this group the inclination is generally higher than for the smaller Trojans, thus more approaches with high velocity occur.…”

“…The integration length was chosen in order to keep the recorded position file at a reasonable size. Some of the Trojans in the MPC 2 http://www.cfa.harvard.edu/iau/lists/JupiterTrojans.html list might not be Trojans (Karlsson 2004(Karlsson , 2010. However, the number of non-Trojans is small and the orbital elements make them less likely to approach other objects in the sample.…”

“…In Fig. 2 I selected a sample of H ≤ 11.5 mag (white, 669 records), which is unbiased (Karlsson 2010) to compare with a nearly unbiased sample H ≤ 13 mag (black, 6986 records), and a sample of H ≤ 10.6 mag (grey, 122 records). The grey Table 2 Orbital elements of the target and approach directions of the projectile for the collision setup.…”

“…However, comparing the differences in absolute magnitudes from the previous section suggests that collisions within the known sample would likely result in small fragmented remnants, but using the intrinsic collision probability from Dahlgren (1998) indicates that this is unlikely to occur. In fact the Trojans with absolute magnitudes smaller than about H = 9.5 mag, where there is a change in size distribution (see, e.g., Karlsson 2010), is usually considered to have a primordial size distribution (de Elía & Brunini 2007;Marzari et al 1997). The number of projectiles are thus most likely biased by an incomplete small Trojan sample.…”

Photometric colors of the brightest members of the Jupiter L5 Trojan cloud

“…The sample includes objects; 71 of which are in the Greek camp and the remaining 42 in the Trojan camp. This initial cut-off of H ≤ 10 was chosen for two primary reasons: 1The known sample should be complete down to this limit (Szabó et al (2007), Karlsson (2010)), so we can be sure that our sample is unbiased and readily compared to other samples of similarly sized objects in other populations. (2) H = 10 results in a V apparent magnitude between 17 and 18 for Jupiter Trojans.…”