Distribution functions for spheroids
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910235626569728 |
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| author | Binney, James |
| author_facet | Binney, James |
| contents | Galaxy models comprising several components (including dark matter) that are bound by the self-consistently generated gravitational field are readily constructed from distribution functions (DFs) that are analytic functions of the action integrals J. We explain why such models have unphysical velocity distributions unless the DFs of hot components satisfy certain conditions as J_ϕ-> 0. We show how DFs for both isotropic and radially biased spherical systems can be constructed with specified f(J). We show how to construct DFs for flattened systems with significant velocity anisotropy. Construction of self-consistent models rather than populations that are confined by an external potential leads to the conclusion that radially-biased spherical systems are generically unstable to quadrupolar perturbations. Chaos is likely key to maintenance of these constraints during adiabatic disc growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23127 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distribution functions for spheroids Binney, James Astrophysics of Galaxies Galaxy models comprising several components (including dark matter) that are bound by the self-consistently generated gravitational field are readily constructed from distribution functions (DFs) that are analytic functions of the action integrals J. We explain why such models have unphysical velocity distributions unless the DFs of hot components satisfy certain conditions as J_ϕ-> 0. We show how DFs for both isotropic and radially biased spherical systems can be constructed with specified f(J). We show how to construct DFs for flattened systems with significant velocity anisotropy. Construction of self-consistent models rather than populations that are confined by an external potential leads to the conclusion that radially-biased spherical systems are generically unstable to quadrupolar perturbations. Chaos is likely key to maintenance of these constraints during adiabatic disc growth. |
| title | Distribution functions for spheroids |
| topic | Astrophysics of Galaxies |
| url | https://arxiv.org/abs/2602.23127 |