Principal Component Analysis of Dynamically Distinct D-Type Asteroids

Document Type

Conference Proceeding

Publication Date


Publication Title

American Astronomical Society, Department of Planetary Sciences


Principal Component Analysis (PCA), a common statistically based classification technique, has been used to classify asteroids into broad spectral categories. In some cases, a spectral superclass considered in isolation may undergo sub-classification (e.g. S-type subclasses). Since D-type asteroids populate at least three distinct dynamical regions in the asteroid belt -- namely Hilda, L4 Trojans and L5 Trojans, and since the recently-developed "Nice” model (Morbidelli et al. 2005. Nature 435, 462; Levison et al. 2008, ACM 2008 abstract #8156) hypothesizes that these regions may share a common origin, examining the appropriateness of a D-type sub-classification scheme is warranted. Toward this end, we performed PCA on the D-type L4, L5, and Hilda asteroids. Our PCA was based on the Sloan Digital Sky Survey broadband colors (u - g, g - r, r - i, and i - z) of 31 L4, 24 L5, and 32 Hilda asteroids with radii ranging from approximately 5 to 45 km. PCA showed 90.2% of the variance in the spectra could be condensed into the first two principal components, PC1 and PC2, with the first and second component accounting for 50.7% and 39.4% respectively. No significant clustering is observed on a PC1 vs. PC2 plot suggesting the D-type L4, L5, and Hilda asteroids do not form three independent groups, but rather are spectrally indistinguishable. We performed several statistical analyses of the means and variances of the principal components to test the validity of this conclusion. No statistically significant difference in the means among the three groups was found, nor was there any such difference in the variances, although the statistic comparing the L4 Trojans and Hildas was close to the critical value. Further measurements of colors of both large and small Trojans and Hildas will let us continue to investigate the spectral diversity of these objects.