The relationship between the shape of SPARC rotation curves to the galactic mass model: a chi-square test of independence

Abstract

Rotation curves of galaxies are strongly related to dark matter and baryonic matter. The gravitational attraction of baryonic matter, e.g., stars and gas, is the dominant force in the inner regions of galaxies, and its distribution determines the shape of the inner rotation curve. In contrast, the outer regions of galaxies are dominated by the gravitational force of dark matter, which is thought to be distributed in a spherical halo around a galaxy. Since the ratio of rotational speed in the inner regions and maximum rotational speed (η rot) is related to the shape of the galaxy rotation curve, it might be a significant association between this ratio and each combination of matters, or the mass models. Specifically, for dark matter, we assume the Navarro-Frenk-White (NFW) profile. This study explores the use of SPARC data (Spitzer Photometry and Accurate Rotation Curves) and categorizes shapes of galaxy rotation curves according to η rot. For mass models, we classify galaxies by considering the reduced chi-square of the best-fit parameter of each model. To determine whether there is a significant association between η rot and the mass models, we utilize the chi-square test of independence. The study suggests with a 95% confidence level that there is no relation between the mass models and η rot.