Spiral structure of the galactic disk and its influence on the rotational velocity curve

Abstract

The most spiral galaxies have a flat rotational velocity curve, according to the different observational techniques used in several wavelengths domain. In this work, we show that non-linear terms are able to balance the dispersive effect of the wave, thus reviving the observed rotational curve profiles without inclusion of any other but baryonic matter concentrated in the bulge and disk. In order to prove that the considered model is able to restore a flat rotational curve, Milky Way has been chosen as the best mapped galaxy to apply on. Using the gravitational N-body simulations with up to $10^7$ particles, we test this dynamical model in the case of the Milky Way with two different approaches. Within the direct approach, as an input condition in the simulation runs we set the spiral surface density distribution which is previously obtained as an explicit solution to non-linear Schrödinger equation (instead of a widely used exponential disk approximation). In the evolutionary approach, we initialize the runs with different initial mass and rotational velocity distributions, in order to capture the natural formation of spiral arms, and to determine their role in the disk evolution. In both cases we are able to reproduce the stable and non-expanding disk structures at the simulation end times of $\sim10^9$ years, with no halo inclusion. Although the given model doesn't take into account the velocity dispersion of stars and finite disk thickness, the results presented here still imply that non-linear effects can significantly alter the amount of dark matter which is required to keep the galactic disk in stable configuration.