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Potential Theory in Astrophysics

Potential Theory in Astrophysics. Wu Yue, THCA. General Results. Gravitational Potential. Poisson Equation. Potential Energy. Spherical Systems. Spherical Systems. Two Important Quantities. Some Examples for Spherical Systems. Point Mass. Some Examples for Spherical Systems.

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Potential Theory in Astrophysics

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  1. Potential Theory in Astrophysics Wu Yue, THCA

  2. General Results

  3. Gravitational Potential

  4. Poisson Equation

  5. Potential Energy

  6. Spherical Systems

  7. Spherical Systems

  8. Two Important Quantities

  9. Some Examples for Spherical Systems • Point Mass

  10. Some Examples for Spherical Systems • Homogeneous sphere

  11. Some Examples for Spherical Systems • Isochrone potential

  12. Some Examples for Spherical Systems • Modified Hubble profile

  13. Some Examples for Spherical Systems • Power-law density profile

  14. Potential-Density Pairs for Flattened Systems • Plummer’s model(1911) • Kuzmin’s model(1956)(Toomre’s model 1)

  15. Potential-Density Pairs for Flattened Systems • Miyamoto-Nagai’s model(1975) • Toomre’s model n(1962)

  16. Potential-Density Pairs for Flattened Systems • Logarithmic Potentials

  17. Poisson’s Equation in Very Flattened Systems • The simple form of Poisson’s equation applies to almost any thin disk system

  18. Poisson’s Equation in Very Flattened Systems • The solution of Poisson’s equation in a thin disk can be decomposed into two steps • (i) Approximate the thin disk as a surface density layer of zero thickness and determine the potential in the plane of the disk • (ii)At each radius R solve the simple form of Poisson’s equation to find the vertical variation of

  19. Ellipsoidal Systems-Axisymmetric System • Oblate Spheroidal Coordinates

  20. Ellipsoidal Systems-Axisymmetric System

  21. Ellipsoidal Systems-Axisymmetric System

  22. Ellipsoidal Systems-Axisymmetric System

  23. Ellipsoidal Systems-Axisymmetric System

  24. Multipole Expansion

  25. Multipole Expansion

  26. Multipole Expansions

  27. Multipole Expansions

  28. Multipole Expansions

  29. Potentials of Disks-Disks as Flattened Spheroids

  30. Potentials of Disks-Disks as Flattened Spheroids

  31. Disk Potentials via Bessel Functions

  32. Disk Potentials via Bessel Functions

  33. Disk Potentials via Bessel Functions

  34. Disk Potentials via Bessel Functions

  35. Disk Potentials via Bessel Functions

  36. Disk potential via logarithmic spirals

  37. Disk potential via logarithmic spirals

  38. Disk potential via logarithmic spirals

  39. Disk potential via logarithmic spirals

  40. Potential Energy Tensor

  41. Potential of Our Galaxy • photometric method • dynamical method

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