Gravothermal Catastrophe and Negative Specific Heat of Self-Gravitating Systems

Hachisu, Izumi; Sugimoto, Daiichiro

doi:10.1143/ptp.60.123

Cited by 44 publications

(10 citation statements)

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“…Table 1 shows that both two quantities decrease as n increases. In the limit n → ∞(or q → 1), they asymptotically approach the well-known results of the isothermal sphere [1][2][3][5].…”

Section: Emden Solutionsupporting

confidence: 67%

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Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems

Taruya

Sakagami

2002

Physica A: Statistical Mechanics and its Applications

121

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We present a first physical application of Tsallis' generalized entropy to the thermodynamics of self-gravitating systems. The stellar system confined in a spherical cavity of radius r e exhibits an instability, so-called gravothermal catastrophe, which has been originally investigated by Antonov (Vest.Leningrad Gros.Univ. 7 (1962) 135) and Lynden-Bell & Wood (Mon.Not.R.Astron.Soc. 138 (1968) 495) on the basis of the maximum entropy principle for the phase-space distribution function. In contrast to previous analyses using the Boltzmann-Gibbs entropy, we apply the Tsallis-type generalized entropy to seek the equilibrium criteria. Then the distribution function of Vlassov-Poisson system can be reduced to the stellar polytrope system. Evaluating the second variation of Tsallis entropy and solving the zero eigenvalue problem explicitly, we find that the gravothermal instability appears in cases with polytrope index n > 5. The critical point characterizing the onset of instability are obtained, which exactly matches with the results derived from the standard turning-point analysis. The results give an important suggestion that the Tsallis' generalized entropy is indeed applicable and viable to the long-range nature of the self-gravitating system.

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Section: Emden Solutionsupporting

confidence: 67%

“…In our present analysis, standard definition of mean values is adopted for mass and energy (see eqs. [3][4]). Tsallis, Mendes and Plastino [17] recently showed that this choice yields undesirable divergence in some physical systems including Lévy random walk.…”

Section: Discussionmentioning

confidence: 99%

Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems

Taruya

Sakagami

2002

Physica A: Statistical Mechanics and its Applications

121

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“…With regard to Eq. (138), we are aware of Lynden-Bell and coauthors' crusade [59,89,90] in support of existence and physical plausibility of a negative heat capacity of the gas and the controversy it spawned in the literature [91][92][93][94][95]. However, we refrain from discussing virial-theorem applications and statistical-ensemble nonequivalence because it would take us far away from the mainstream of the present discourse and postpone the exposition of our viewpoint to future communications.…”

Section: State Equation (∂ E/∂s ) Vmgmentioning

confidence: 99%

Fluid statics of a self-gravitating perfect-gas isothermal sphere

Giordano

Amodio

Iavernaro

et al. 2019

European Journal of Mechanics - B/Fluids

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We open the paper with introductory considerations describing the motivations of our long-term research plan targeting gravitomagnetism, illustrating the fluid-dynamics numerical test case selected for that purpose, that is, a perfect-gas sphere contained in a solid shell located in empty space sufficiently away from other masses, and defining the main objective of this study: the determination of the gravitofluid-static field required as initial field (t = 0) in forthcoming fluid-dynamics calculations. The determination of the gravitofluid-static field requires the solution of the isothermalsphere Lane-Emden equation. We do not follow the habitual approach of the literature based on the prescription of the central density as boundary condition; we impose the gravitational field at the solid-shell internal wall. As the discourse develops, we point out differences and similarities between the literature's and our approach. We show that the nondimensional formulation of the problem hinges on a unique physical characteristic number that we call gravitational number because it gauges the self-gravity effects on the gas' fluid statics. We illustrate and discuss numerical results; some peculiarities, such as gravitational-number upper bound and multiple solutions, lead us to investigate the thermodynamics of the physical system, particularly entropy and energy, and preliminarily explore whether or not thermodynamic-stability reasons could provide justification for either selection or exclusion of multiple solutions. We close the paper with a summary of the present study in which we draw conclusions and describe future work.

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“…Thus, the central high-density region can evolve much faster than the rest of the system does. To give a clear understanding of the system, it will be helpful to consider the system in a spherical adiabatic wall [4,26,12].…”

Section: General N-body Problem and Stellar Systemsmentioning

confidence: 99%

“…Hachisu and Sugimoto [12] performed a stability analysis of the system by means of the perturbation equation, and found that the system is unstable against the redistribution of the heat if D > 709. In other words, if D > 709, the isothermal equilibrium state is unstable and would spontaneously develop a spatial structure if there is any small perturbation.…”

Section: General N-body Problem and Stellar Systemsmentioning

confidence: 99%

Do-it-yourself computational astronomy

Makino

2008

Jpn. J. Math.

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We overview our GRAPE (GRAvity PipE) and GRAPE-DR project to develop dedicated computers for astrophysical N-body simulations. The basic idea of GRAPE is to attach a custom-build computer dedicated to the calculation of gravitational interaction between particles to a general-purpose programmable computer. By this hybrid architecture, we can achieve both a wide range of applications and very high peak performance. GRAPE-6, completed in 2002, achieved the peak speed of 64 Tflops. The next machine, GRAPE-DR, will have the peak speed of 2 Pflops and will be completed in 2008.We discuss the physics of stellar systems, evolution of general-purpose high-performance computers, our GRAPE and GRAPE-DR projects and issues of numerical algorithms.

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Gravothermal Catastrophe and Negative Specific Heat of Self-Gravitating Systems

Cited by 44 publications

References 1 publication

Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems

Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems

Fluid statics of a self-gravitating perfect-gas isothermal sphere

Do-it-yourself computational astronomy

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