A Mathematical Model of Spiral Galaxy Disks and Arm Patterns

Author: He, Jin

Source: Astrophysics and Space Science, Volume 305, Number 2, October 2006 , pp. 197-203(7)

Publisher: Springer

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Abstract:

He (2003) described a preliminary mathematical model of spiral galaxy patterns that assumes light fluxes are arranged in equal ratios along two sides of orthogonal curvilinear coordinate lines. This ``ratio distribution'' is approximately equal to the gradient vector field of the logarithmic light distribution. An equal ratio along any coordinate line means that the gradient components associated with the local reference system of the coordinate lines depend on single curvilinear coordinate variables. A differential equation system which describes the distributions is given in He and Yang (2005). In the present paper a simpler solution to the equation system is found which can represent spiral galaxy disks. The resulting radial density profile of the disk model is exponential which is consistent with the known exponential law of spiral galaxy surface brightness. Spiral arms can be considered perturbation to the disk light in the same coordinate line direction. These arms are logarithmic. Therefore, the two astronomic facts, exponential disks and logarithmic arms, are connected by one coordinate system (λ, μ). He (2005a,b) show that the same method can be used to study light distributions of galaxy bars and ellipticals. A consistent description of all regular galaxy patterns is finally achieved.

Keywords: Methods: Analytic; Galaxies: Structure

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10509-006-9168-y

Affiliations: 1: Email: jin002@bama.ua.edu

Publication date: 2006-10-01