Exact density-potential pairs from complex shifted axisymmetric systems

Abstract

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.

10 pages, 2 figures, MNRAS, accepted

References in corpus (16)

• The Nature of Boxy/Peanut-Shaped Bulges in Spiral Galaxies
• ESTABLISHING THE CONNECTION BETWEEN PEANUT-SHAPED BULGES AND GALACTIC BARS
• The Kinematic Signature of Face-On Peanut-Shaped Bulges
• Axisymmetric and triaxial MOND density-potential pairs
• Growth of a peanut shaped bulge via resonant trapping of stellar orbits in the vertical Inner Lindblad Resonances
• The energetics of flat and rotating early-type galaxies and their X-ray luminosity
• Superposition of Weyl solutions: The equilibrium forces
• A simple method to construct exact density-potential pairs from a homeoidal expansion
• Electromagnetic Magic: The Relativistically Rotating Disk
• Distributional Sources for Newman's Holomorphic Field
• Geodesics around Weyl-Bach's Ring Solution
• Exact density-potential pairs from the holomorphic Coulomb field
• The Relativistically Spinning Charged Sphere
• Simple pairs potential-density for flat rings
• On Multipolar Analytical Potentials for Galaxies
• Triaxial Analytical Potential-Density Pairs for Galaxies

Cited by in corpus (8)

• Spinning black holes with a separable Hamilton-Jacobi equation from a modified Newman-Janis algorithm
• Potential-density pairs for a family of finite disks
• Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures
• Orbital perturbations due to massive rings
• Fractional Derivative Approach to the Self-gravitation Equation
• Regular and chaotic orbits in axisymmetric stellar systems
• Relativistic ring models
• Analytical potential-density pairs from complex-shifted Kuzmin-Toomre discs