A simple model of spiral galaxies from geometric optics

Abstract

We propose a simple model of spiral galaxies based on the interference of gravitational waves. The interference is deduced from geometric optics analysis of the refractive index profiles that mimic the behavior of gravitational potentials −1/r and r2. We analyze the refractive index profiles, n(r)2 = a + b/r and n(r)2 = a + br2, because they are realistically shaped and yield closed form solutions. The two profiles yield similar physical results, showing that the physical interpretation is not dependent on the exact details of the profile. The first profile yields trajectories that can be elliptical, parabolic, or hyperbolic depending on the value of the constant a. The second profile yields square-root-elliptical trajectories. The elliptically shaped trajectories define spiral wavefronts of discrete circulating propagation modes. They are discrete when the gravitational wavelengths are comparable with the size of the galaxies. Stars tend to gather in the bright fringes of the stationary interferograms, largely independent of the motion of the individual stars, resulting in the spiral shapes of the galaxies. Using this modal approach, we obtain outlines of spiral galaxies with arbitrary number of arms and their spiral lengths. While this model does not capture all the complex physics of galaxies, it does provide a simple interpretation of the shapes so well-known from the astronomical observations.