Using the chi-square test to compare asteroid and laboratory reflectance spectra

Abstract: This study uses the Pearson's chi-square test to analyze the VNIR reflectance spectra of seven asteroids and look for spectral matches among approximately 11,000 laboratory spectra of meteoritic, terrestrial, synthetic, Apollo, and Luna samples. First, we use the chi-square method to analyze three well-studied asteroids - (4) Vesta, (6) Hebe, and (19) Fortuna - to establish the technique's reliability by attempting to confirm previously predicted spectral matches. The chi-square test is then applied to four other asteroids: the Mars trojans (5261) Eureka, (101429) 1998 VF31, (311999) 2007 NS2, and (385250) 2001 DH47. This study focuses on Mars trojans because of their undetermined origin and possible relationship to Mars. For asteroids that may have undergone space weathering, reddening effects are removed from the spectra to allow for a more accurate chi-square analysis. The top chi-square matches among the Mars trojans reveal significant spectral similarities with Martian meteorites and minerals found on Mars, supporting the hypothesis of a Martian origin for the analyzed Mars trojans. However, the possibility that these Mars trojans could be fragments of a disrupted differentiated body or bodies cannot be ruled out. We find that using the chi-square test with a large number of laboratory spectra is a very useful initial technique for identifying spectral analogs to asteroids.