Some applications of Jacobi dynamics to the stellar evolution

DOI: 
10.1007/BF00643200
Publication date: 
01/07/1992
Main author: 
Quiroga R.J.
IAA authors: 
Claret A.
Authors: 
Quiroga R.J., Claret A.
Journal: 
Astrophysics and Space Science
Publication type: 
Article
Volume: 
193
Pages: 
185-200
Number: 
Abstract: 
This study compares computational results from stellar models and the evolutive behaviour of the stars, using elements of Jacobi dynamics. A linearized form of the Jacobi equation is used in order to analyze the dependency on the time of the coefficients α(t), β(t) of the inner structure of the stars. With these coefficients and the stellar radii R(t) one can define all the dynamical parameters: the potential energy Ep(t), the momentum of inertia I(t), the Jacobi function φ{symbol}(t), and the amount of action Ac(t), and the relations among them depending on the geometry of the problem. The computational models used here include pre-Main-Sequence stages and variations in the chemical composition X, Z. Since this is an introductory study, we only used the examples for 5 M⊙, 1 M⊙, and 0.6⊙. The results obtained are: (a) The Main Sequence represents a state of minimum action and potential energy where Ac(t) and Ep(t) are nearly invariant when compared to the variations of any other stellar parameter such as luminosity L(t), radius R(t), or the density ρ(t) on which depends α(t), β(t). (b) These parameters and the time of permanence of a star in the Main Sequence are, as expected, very sensitive to X, Z. But the parameters Ac, Ep remain minimum and nearly invariant in the Main Sequence. The contractive and expansive phases associated with the pre-and post-Main-Sequence stages are also analysed. The scenario is not fundamentally altered if one includes rotational effects, taking the possible upper limits from observed rotations in T Tauri stars. (c) As a test for the theoretical criteria used here (and as a by-product with further applications) one has that the effective dynamical density ρeff=α3ρ (mean stellar density) leads to an effective scale time for the thermal motions in the stellar interior Peff∝ ρeff-1/2 which is consistent with oscillation periods of pulsating stars not far from the Main Sequence such as δ Scuti and β Cephei. The possibilities of further studies about stellar evolution using Jacobi dynamics are discussed. © 1992 Kluwer Academic Publishers.
Database: 
WOK
SCOPUS
ADS
URL: 
https://ui.adsabs.harvard.edu/#abs/1992Ap&SS.193..185Q/abstract
ADS Bibcode: 
1992Ap&SS.193..185Q
Keywords: