Potential-density pairs for flat galaxies

Statistics – Computation

Scientific paper

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Computational Astrophysics, Density Distribution, Galactic Structure, Spiral Galaxies, Astronomical Models, Ellipticity, Galactic Rotation, Integral Equations

Scientific paper

Consideration is given to the potential-density pairs of an infinite number of families of nonaxisymmetric disks. The families are all generated by superposing a class of exactly elliptical surface density distributions, which are designated as elliptic disks. For any chosen short-axis surface density profile, an integral equation for the weight-function, which describes the superposition of the elliptic disks, is solved by Stieltjes transform methods to yield the potential-density pair of the constructed disks as quadratures. All the families of disks are shown to satisfy generalized Kuzmin formulas relating the surface density at a general point to the surface density on the short axis. The physical properties of the models as well as the scale-free limit are described.

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