Using the chi-square test to determine if Mars trojans are fragments of Mars

Spectroscopy is crucial for understanding the compositional and evolutionary history of asteroids. This study uses Pearson's χ-square test to analyze the visible and near-infrared reflectance spectra of seven asteroids by comparing their spectra against approximately 11,000 laboratory spectra of meteoritic, terrestrial, synthetic, Apollo, and Luna samples. The chi-square test is initially applied to three well-studied asteroids - (4) Vesta, (6) Hebe, and (19) Fortuna - to validate the technique's reliability and successfully confirms previously predicted spectral matches. Subsequently, the method investigates the spectra of four Mars trojans - (5261) Eureka, (101429) 1998 VF₃₁, (311999) 2007 NS₂, and (385250) 2001 DH₄₇ - due to their undetermined origin and potential relationship with Mars. To account for space weathering, some spectra are de-reddened before the chi-square test is applied. Our results showed significant spectral similarities between the observed Mars Trojans and minerals found on Mars, supporting the hypothesis of a Martian origin for these trojans. However, the possibility that these Mars trojans could be fragments of a disrupted differentiated body or bodies cannot be ruled out. The study underscores the effectiveness of the chi-square test in identifying spectral analogs and providing a robust method for initially analyzing asteroid spectra.