Distributions of Constant Directional Derivatives and a Model of Spiral Galaxy Arms |
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| Authors: | Jin He |
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| Institution: | (1) Department of Physics and Astronomy, the University of Alabama, Tuscaloosa, AL35487 |
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| Abstract: | Image analysis of over one hundred nearby galaxies (He, 2003) indicates that for any spiral galaxy image of small inclination there is evidence of two orthogonalsets of iso-ratio curves in different scales which, like curvilinear coordinate lines, expand over different galaxy components. This result sets a constraint on galaxy patterns and a general model equation which carries this constraint is given in its geometric form in He (2003). In the current paper the author reformulates the geometric equation into one quasilinearsystem of 3 partial differential equations with 3 dependents (the tangent direction of one set of iso-ratio curves and the two ratio profiles along the two sets of iso-ratio curves respectively). With one profile assumed to be a nonzero constant, there are two dependents and the system of two partial differential equations is a hyperbolic one. The author uses the standard method of characteristics and the boundary condition of ideal arms which are found by setting the above constant to be zero, to solve the hyperbolic system. This provides one analytic method to model galaxy patterns. Its varying parameters will be useful for galacticarm classification and for investigation of galaxy structure. |
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| Keywords: | methods: nonlinear science galaxies: structure |
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