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Exact density-potential pairs from complex shifted axisymmetric systems

  • Ciotti, L.
  • Marinacci, F.
Publication Date
Apr 10, 2008
Submission Date
Apr 10, 2008
DOI: 10.1111/j.1365-2966.2008.13301.x
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In a previous paper the complex-shift method has been applied to self-gravitating spherical systems, producing new analytical axisymmetric density-potential pairs. We now extend the treatement to the Miyamoto-Nagai disc and to the Binney logarithmic halo, and we study the resulting axisymmetric and triaxial analytical density-potential pairs; we also show how to obtain the surface density of shifted systems from the complex-shift of the surface density of the parent model. In particular, the systems obtained from Miyamoto-Nagai discs can be used to describe disc galaxies with a peanut-shaped bulge or with a central triaxial bar, depending on the direction of the shift vector. By using a constructive method that can be applied to generic axisymmetric systems, we finally show that the Miyamoto-Nagai and the Satoh discs, and the Binney logarithmic halo, cannot be obtained from the complex-shift of any spherical parent distribution. As a by-product of this study we also found two new generating functions in closed form for even and odd Legendre polynomials, respectively.

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