We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It is shown that a critical angular momentum λc (or, in the canonical language, a critical angular velocity ωc) exists, such that for λ < λc the system's behaviour is qualitatively similar to that of a non-rotating gas, with a high energy disordered phase and a low energy collapsed phase ending with Antonov's limit, below which there is no equilibrium state. For λ > λc, instead, the low-energy phase is characterized by the formation of two dense clusters (a "binary star"). Remarkably, no Antonov limit is found for λ > λc. The thermodynamics of the system (phase diagram, caloric curves, local stability) is analyzed and compared with the recently-obtained picture emerging from a different type of statistics which forbids particle overlapping. © 2003 Elsevier Science B.V. All rights reserved.
The Antonov problem for rotating systems / De Martino, A.; Votyakov, E. V.; Gross, D. H. E.. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - 654:3(2003), pp. 427-444. [10.1016/S0550-3213(03)00050-6]
The Antonov problem for rotating systems
De Martino A.;
2003
Abstract
We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It is shown that a critical angular momentum λc (or, in the canonical language, a critical angular velocity ωc) exists, such that for λ < λc the system's behaviour is qualitatively similar to that of a non-rotating gas, with a high energy disordered phase and a low energy collapsed phase ending with Antonov's limit, below which there is no equilibrium state. For λ > λc, instead, the low-energy phase is characterized by the formation of two dense clusters (a "binary star"). Remarkably, no Antonov limit is found for λ > λc. The thermodynamics of the system (phase diagram, caloric curves, local stability) is analyzed and compared with the recently-obtained picture emerging from a different type of statistics which forbids particle overlapping. © 2003 Elsevier Science B.V. All rights reserved.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2976732