Origin of the power-law profile in a core-collapsing galactic globular-cluster model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912563009159168 |
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| author | Ito, Yuta |
| author_facet | Ito, Yuta |
| contents | Observed galactic globular clusters reveal power-law structural profiles in the inner halos around the core-collapse stage. However, the origin of the power-law has not been explained in an acceptable manner. The present paper applies the Buckingham's Pi theorem to the orbit-averaged Fokker-Plank (OAFP) model of equal masses to study the inner-halo structure of a core-collapsing isotropic star cluster. We first prove that an infinite OAFP model evolves self-similarly because of the principle of covariance. We then show that the inner halo must form a power-law profile in a finite OAFP model that has complete similarity so that the principle of covariance and conservation laws hold. The conventional assumption that inner halos are self-similar and stationary is unnecessary to explain the power-law profiles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Origin of the power-law profile in a core-collapsing galactic globular-cluster model Ito, Yuta Astrophysics of Galaxies Mathematical Physics Classical Physics Observed galactic globular clusters reveal power-law structural profiles in the inner halos around the core-collapse stage. However, the origin of the power-law has not been explained in an acceptable manner. The present paper applies the Buckingham's Pi theorem to the orbit-averaged Fokker-Plank (OAFP) model of equal masses to study the inner-halo structure of a core-collapsing isotropic star cluster. We first prove that an infinite OAFP model evolves self-similarly because of the principle of covariance. We then show that the inner halo must form a power-law profile in a finite OAFP model that has complete similarity so that the principle of covariance and conservation laws hold. The conventional assumption that inner halos are self-similar and stationary is unnecessary to explain the power-law profiles. |
| title | Origin of the power-law profile in a core-collapsing galactic globular-cluster model |
| topic | Astrophysics of Galaxies Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2509.00910 |