Study of the dynamics of the local group using N-body cosmological simulations

Abstract

The Gaia satellite has been a revolution for the photometry and astrometry fields, providing a large amount of data (positions, parallaxes, proper motions) for the Local Group objects with a high accuracy never seen before. The goal of this work is to study the dynamics history of the Local Group galaxies from now to near to the time at the Big Bang using N-body simulations and taking advantage of the new proper motions measurements recently provided by Gaia. In order to obtain the 3D motion back in time of each Local Group galaxy, we have programmed an original N-body code in Fortran 90 which implements the Leapfrog algorithm which allows to solve numerically the equations of motion in classical mechanics for self-gravitating systems. We have done an exhaustive search in the literature to find the largest number of Local Group galaxies with updated measured proper motions and radial velocities. We have found a sample of 67 Local Group galaxies including the prominent members: the Milky Way, M31 and M33; and its dwarf satellites. We have transformed the right ascension, declination, heliocentric distance, line of sight velocity and proper motions obtained from the literature for all our sample of 67 galaxies into 6D phase-space coordinates in a Galactocentric reference system. We have run several N-body simulations with our code and our galaxy sample, and we have obtained the orbits back in time for 24 galaxies selected of the sample of 67 galaxies following two criteria: galaxies more distant than 50 kpc and with an error of their transverse velocity smaller than 50 km/s. Moreover, we have performed N-body simulations using only the Milky Way, M31 and M33 and we have compared the resulting orbits back in time. In addition, we have reviewed and described different important methods used to study some features of the dynamics of the Local Group, like the “Least Action Principle” or the “Timing Argument” which allows to estimate the mass of the Local Group