Generalized Schwarzschild's method

Details Generalized Schwarzschild's method Generalized Schwarzschild's method

2010-07-25

arxiv.org/abs/1007.4298v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

14 pages, 7 Figures, Submitted to MNRAS

Scientific paper

We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions to continuous ones. In contrast to Schwarzschild's method, FEM produces a continuous distribution function (DF) and satisfies the intra element continuity and Jeans equations. The method employs two finite-element meshes, one in configuration space and one in action space. The DF is represented by its values at the nodes of the action-space mesh and by interpolating functions inside the elements. The Galerkin projection of all equations that involve the DF leads to a linear system of equations, which can be solved for the nodal values of the DF using linear or quadratic programming, or other optimization methods. We illustrate the superior performance of FEM by constructing ergodic and anisotropic equilibrium DFs for spherical stellar systems (Hernquist models). We also show that explicitly constraining the DF by the Jeans equations leads to smoother and/or more accurate solutions with both Schwarzschild's method and FEM.

Affiliated with

Also associated with

No associations

Rating

Generalized Schwarzschild's method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Schwarzschild's method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Schwarzschild's method will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-467052