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We present the results of a visible spectroscopic and photometric survey of Jupiter Trojans belonging to different dynamical families carried out at the ESO-NTT telescope. We obtained data on 47 objects, 23 belonging to the L5 swarm and 24 to the L4 one. These data together with those already published by Fornasier et al. (2004a) and Dotto et al. (2006), constitute a total sample of visible spectra for 80 objects. The survey allows us to investigate six families (Aneas, Anchises, Misenus, Phereclos, Sarpedon, Panthoos) in the L5 cloud and four L4 families (Eurybates, Menelaus, 1986 WD and 1986 TS6). The sample that we measured is dominated by D--type asteroids, with the exception of the Eurybates family in the L4 swarm, where there is a dominance of C- and P-type asteroids. All the spectra that we obtained are featureless with the exception of some Eurybates members, where a drop--off of the reflectance is detected shortward of 5200 A. Similar features are seen in main belt C-type asteroids and commonly attributed to the intervalence charge transfer transition in oxidized iron. Our sample comprises fainter and smaller Trojans as compared to the literatures data and allows us to investigate the properties of objects with estimated diameter smaller than 40--50 km. The analysis of the spectral slopes and colors versus the estimated diameters shows that the blue and red objects have indistinguishable size distribution. We perform a statistical investigation of the Trojanss spectra property distributions as a function of their orbital and physical parameters, and in comparison with other classes of minor bodies in the outer Solar System. Trojans at lower inclination appear significantly bluer than those at higher inclination, but this effect is strongly driven by the Eurybates family.
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