Preprint Article Version 1 This version is not peer-reviewed

Simplification of Galactic Dynamic equations

Version 1 : Received: 27 February 2020 / Approved: 27 February 2020 / Online: 27 February 2020 (16:10:59 CET)

How to cite: Gu, Y. Simplification of Galactic Dynamic equations. Preprints 2020, 2020020412 (doi: 10.20944/preprints202002.0412.v1). Gu, Y. Simplification of Galactic Dynamic equations. Preprints 2020, 2020020412 (doi: 10.20944/preprints202002.0412.v1).

Abstract

Most fully developed galaxies have vivid spiral structure, but the formation and evolution of spiral structure is still a mystery that is not fully understood in astrophysics. We find that the currently used equations of galactic dynamics contain some unreasonable components. In this paper, the following three working assumptions are introduced to simplify the galactic structural equations. 1. In the research of large-scale structure, the retarded potential of the gravitational field should be taken into account. The propagating time of the gravitational field from center to border is longer than the revolution periods of the stars near the center of galaxy. Newton's gravitational potential is unreasonable for such case, and the weak field and low velocity approximation of Einstein's field equation should be adopted. 2. The stars in a fully developed galaxy should be zero-pressure and inviscid fluid, and the equation of motion is different from that of ordinary continuum mechanics. Stars move along geodesics. 3. The structure of the galaxy is only related to the total mass density distribution. The equation of state of dark halo is different from that of ordinary luminous interstellar matter, so their trajectories are also very different. Dark halo and ordinary matter in galaxy are automatically separated. The total mass density distribution can be presupposed according to the observation data, and then it can be determined by comparing the solution of the equations with the observed data. These assumptions and treatments are supported by theory and observation. The variables of the equations of simplified galactic dynamics are separated from each other, and the equations are well-posed and can be solved according to a definite procedure. Therefore, this simplified dynamic equation system provides a more reasonable and practical framework for the further study of galactic structure, and can solve many practical problems. Besides, it is closely related to the study of dark energy and dark matter.

Subject Areas

Galactic dynamics; Spiral structure; Bared spiral structure; Density wave; Gravitational retarded potential

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