Three-Dimensional Stationary Spherically Symmetric Stellar Dynamic Models Depending on the Local Energy

Batt, J.; Joern, E. und Skubachevskii, A. L. (2022): Three-Dimensional Stationary Spherically Symmetric Stellar Dynamic Models Depending on the Local Energy. In: Computational Mathematics and Mathematical Physics, Bd. 62, Nr. 9: S. 1455-1485

Abstract

The stellar dynamic models considered here deal with triples (f, rho,U) of three functions: the distribution function f = f(r,u), the local density rho = rho(r), and the Newtonian potential U = U(r), where r := vertical bar x vertical bar, u := vertical bar v vertical bar ((x,v) is an element of R(3)xR(3) are the space-velocity coordinates), and f is a function q of the local energy E = U(r) + u(2)/2. Our first result is an answer to the following question: Given a (positive) function p = p(r) on a bounded interval [0,R], how can one recognize p as the local density of a stellar dynamic model of the given type (inverse problem)? If this is the case, we say that p is extendable (to a complete stellar dynamic model). Assuming that p is strictly decreasing we reveal the connection between p and F, which appears in the nonlinear integral equation p=FU[p] and the solvability of Eddingtons equation between F and q (Theorem 4.1). Second, we investigate the following question (direct problem): Which q induce distribution functions f of the form f = q(-E(r,u) - E-0) of a stellar dynamic model? This leads to the investigation of the nonlinear equation p=FU[p] in an approximative and constructive way by mainly numerical methods.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0965-5425
• Sprache: Englisch