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Media type:
E-Article
Title:
Exploring the dynamics of collisionless spherical stellar systems using the matrix method: Insights from the dilation mode
Contributor:
Polyachenko, Evgeny V.;
Shukhman, Ilia G.
Published:
EDP Sciences, 2024
Published in:
Astronomy & Astrophysics, 684 (2024), Seite A58
Language:
Not determined
DOI:
10.1051/0004-6361/202348556
ISSN:
0004-6361;
1432-0746
Origination:
Footnote:
Description:
<jats:p><jats:italic>Context.</jats:italic> Analytical solutions to the perturbed equations that govern self-gravitating collisionless stellar systems are crucial for both code testing and theoretical insights. For spheres, a solution has been known for years that corresponds to the entire object’s shift from the origin. We recently introduced a new exact stationary solution, relevant for models with a single length parameter. This solution, referred to as the scale-invariant or dilation mode, has led to insights regarding the concept of perturbation energy within the linear theory framework.</jats:p>
<jats:p><jats:italic>Aims.</jats:italic> Our aim is to use Hénon’s isochrone model as an example to verify the ability of the standard matrix method to successfully predict the existence of a dilation mode, and to explore its potential application as a test disturbance.</jats:p>
<jats:p><jats:italic>Methods.</jats:italic> We used the standard matrix method for radial perturbations and applied Clutton-Brock potential-density pairs to determine the properties of the perturbations.</jats:p>
<jats:p><jats:italic>Results.</jats:italic> In this particular case of stationary radial perturbations, the typical relationship between the perturbations of the distribution function and the potential fails. This discrepancy poses a challenge when attempting to use the dilation mode as a test. When using Clutton-Brock pairs with the matrix method, a mass conservation equation as an additional equation to the ordinary set of linear equations is required. With this added equation, it’s possible to obtain the needed test: identical vanishing of the determinant of this modified set of equations with an increasing number of included basis functions.</jats:p>