Potential Theory in Astrophysics

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Potential Theory in Astrophysics

• Wu Yue, THCA

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General Results
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Gravitational Potential
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Poisson Equation
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Potential Energy
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Spherical Systems
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Spherical Systems
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Two Important Quantities
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Some Examples for Spherical Systems

• Point Mass

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Some Examples for Spherical Systems

• Homogeneous sphere

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Some Examples for Spherical Systems

• Isochrone potential

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Some Examples for Spherical Systems

• Modified Hubble profile

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Some Examples for Spherical Systems

• Power-law density profile

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Potential-Density Pairs for Flattened Systems

• Plummers model(1911)

• Kuzmins model(1956)(Toomres model 1)

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Potential-Density Pairs for Flattened Systems

• Miyamoto-Nagais model(1975)

• Toomres model n(1962)

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Potential-Density Pairs for Flattened Systems

• Logarithmic Potentials

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Poissons Equation in Very Flattened Systems

• The simple form of Poissons equation applies to
  almost any thin disk system

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Poissons Equation in Very Flattened Systems

• The solution of Poissons 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
  Poissons equation to find the vertical variation
  of

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Ellipsoidal Systems-Axisymmetric System

• Oblate Spheroidal Coordinates

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Ellipsoidal Systems-Axisymmetric System
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Ellipsoidal Systems-Axisymmetric System
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Ellipsoidal Systems-Axisymmetric System
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Ellipsoidal Systems-Axisymmetric System
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Multipole Expansion
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Multipole Expansion
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Multipole Expansions
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Multipole Expansions
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Multipole Expansions
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Potentials of Disks-Disks as Flattened Spheroids
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Potentials of Disks-Disks as Flattened Spheroids
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Disk Potentials via Bessel Functions
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Disk Potentials via Bessel Functions
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Disk Potentials via Bessel Functions
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Disk Potentials via Bessel Functions
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Disk Potentials via Bessel Functions
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Disk potential via logarithmic spirals
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Disk potential via logarithmic spirals
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Disk potential via logarithmic spirals
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Disk potential via logarithmic spirals
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Potential Energy Tensor
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Potential of Our Galaxy

• photometric method
• dynamical method