Table B.1.
Total energy for the most commonly used spherical models.
Model | ρ(r) or I(R) | Etot |
---|---|---|
Dehnen or γ | ![]() |
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β | ![]() |
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Veltmann | ![]() |
![]() |
Einasto | ![]() |
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Sérsic | ![]() |
![]() |
Plummer | ![]() |
![]() |
Hénon’s isochrone | ![]() |
![]() |
Hernquist | ![]() |
![]() |
Jaffe | ![]() |
![]() |
Perfect sphere | ![]() |
![]() |
Constant density | ![]() |
![]() |
Exponential | ![]() |
![]() |
Gaussian | ![]() |
![]() |
Constant intensity | ![]() |
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Notes. The upper half of the table, above the horizontal line, contains a number of popular one-parameter families of spherical models. The bottom half, below the horizontal line, lists a number of well-known specific models. The first column is the name of the model (or one-parameter family of models), the second column corresponds to either the density ρ(r) or the surface brightness I(R), depending on the most natural way to define the model. The third column is the total energy Etot. Everything is expressed in normalised units, i.e., the gravitational constant, total mass, the mass-to-light ratio, and the scale length are set to one.
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