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Most fully developed galaxies have a vivid spiral structure, but theformation and evolution of the spiral structure are still an enigma inastrophysics. In this paper, according to the standard Newtonian gravitationaltheory and some observational facts, we derive an idealized model for spiralgalaxy, and give a natural explanation to the spiral structure. We solve someanalytic solutions to a spiral galaxy, and obtain manifest relations betweendensity and speed. From the solution we get some interesting results: (I) Thespiral pattern is a stationary or static structure of density wave, and thebarred galaxy globally rotate around an axis at tiny angular speed. (II) Allstars in the disc of a barred spiral galaxy move in almost circular orbits.(III) In the spiral arms, the speed of stars takes minimum and the stellardensity takes maximum. (IV) The mass-energy density of the dark halo iscompensatory for that of the disc, namely, it takes minimum in the spiral arms.This phenomenon might reflect the complicated stream lines of the dark halo.

Stationary Spiral Structure and Collective Motion of the Stars in a Spiral Galaxy