Rotational curves decomposition of spiral galaxies using least square non-linear regression

Abstract

Dark Matter mass distribution is studied in a Cold Dark Matter Universe using Navarro–Frenk–White density profile for Dark Matter (DM) in spiral galaxies. An equation for a complete rotation curve (RC) is obtained by combining the individual RC equations for the bulge, disk and DM halo. The equation is further used for fitting and decomposition of the RCs of 34 spiral galaxies using a Least Square non-linear algorithm in MATLAB. The free parameters’ values are recorded, \(\chi ^2\) values and masses of each component are calculated. 32 of 34 galaxies yield a \(\chi ^2\) value between 1 and 2 validating the algorithm for the purpose of RC decomposition and the exceptions are discussed. We also present the rotational velocity dataset for the bulge, disk and DM halo for all galaxies (https://adhitya-spas.github.io/Database/).