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The Effect of a Spiral Density Wave on the Galaxy′s Rotation Curve, as Applied to the Andromeda Galaxy (M31)

The rotational velocity curve, which is the circular velocity profile of the stars and gas in a spiral galaxy as a function of their distance from the galactic center, plays an important role in the kinematic and dynamic investigation of spiral galaxies. There are observations of approximately flat rotation curves (RC) at large distances that have introduced mass discrepancy between the theoretically derived RC and the observed one. In this paper, we derive a rotational velocity expression using a nonlinear spiral density wave solution for the surface mass density (SMD) within the disk. We show that the proposed nonlinear spiral solution is able to support the observed flat rotational velocity curve for large distances with no mass deficiency. The aim of the paper is to confirm the crucial importance of the mass distribution on the rotation curve profile. Although the model is limited by the fluid description of the galactic disk, it provides an improved rotational velocity expression and a rotation curve with no mass discrepancy in the outer part of the disk due to the inclusion of the spiral mass distribution. The disk mass has not been averaged within the exponential disk approximation, but it rather follows the observed spiral pattern given by the analytical solution of the nonlinear equation. The M31 galaxy has been chosen as the closest and well mapped spiral galaxy, similar in many aspects to our host galaxy, in order to apply a rotational velocity expression that accounts for nonlinear effects and derive RC. The obtained result can have a strong influence on large-scale gravity dynamics, as well.