Abstract
The self-gravitating thermal gas (non-relativistic particles of mass m at temperature T) is exactly equivalent to a field theory with a single scalar field ϕ(x) and exponential self-interaction. We build up perturbation theory around a space dependent stationary point ϕ0(r) in a finite size domain σ≤r≤R, (σ << R which is relevant for astrophysical applications (inter stellar medium, galaxy distributions). We compute the correlations of the gravitational potential (ϕ) and of the density and find that they scale; the density correlator scales as r −2. A rich structure emerges in the two-point correlators from the ϕ fluctuations around ϕ0(r). The n-point correlators are explicitly computed to the one loop level. The relevant effective coupling turns out to be λ=4π G m 2/(T R. The renormalization group equations (RGE) for the n-point correlatorare derived and the RG flow for the effective coupling λ(τ), τ=ln(R/σ), explicitly obtained. A novel dependence on τ emerges here. λ(τ) vanishes each time τ approaches discrete values \( \tau = \tau _n = 2\pi n/\sqrt 7 - 0,n = 0,1,2, \ldots \). Such RG stable behaviour [λ(τ) decreasing with increasing τ] is here connected with low density self-similar fractal structures fitting one into another. For sizes smaller than the points τ n , RG unstable behaviour appears which we connect to Jeans' unstable behaviour, growing density and fragmentation. Remarkably, we get a hierarchy of scales and Jeans lengths following the geometric progression \( R_n = R_0 e^{2\pi n/\sqrt 7 } = R_0 [10.749087 \ldots ]^n \). A hierarchy of this type is expected for non-spherical geometries, with a ratio different from \( e^{2n/\sqrt 7 } \).
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
[1] H. J. de Vega, N. Sánchez and F. Combes, Nature, 383, 56 (1996). Phys. Rev. D54, 6008 (1996).
[2] H. J. de Vega, N. Sánchez and F. Combes, Astrophys. Journal, 500, 8 (1998). H..J. de Vega. N. Sánchez and F. Combes, in ‘Current Topics in Astrofundarnental Physics: Primordial Cosmology’, NATO ASI at Erice, N. Sánchez and A. Zichichi editors, vol 511, Kluwer, 1998.
[3] H..J. de Vega, N. Sánchez and F. Combe, ‘Fractal Structures and Scaling Laws in the Universe: Statistical Mechanics of t he Self-Gravitating Gas’, ast ro-ph/ 98070·18, to appear in the special issue of the ‘Journal of Chaos, Solitons and Fractals’:’ superstrings, M, F, S… theory’, M. S El Naschie and C. Castro, Editors.
[4] S. Chandrasekhar, ‘An Introduction to the Study of Stellar Structure’, Chicago Univ. Press, 1939.
[5] See for example. W. C. Saslaw, ‘Gravitational Physics of stellar and galactic systems’, Cambridge Univ. Press, 1987.
[6] C. Itzykson and J. M. Drouffe, «Théorie Statistique des Champs”, Inter/CNRS, 1989, Paris.
[7] see for example, S. Coleman, Aspects of Symmetry, Selected Erice Lectures Cambridge Uuiv. Press, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Semelin, B., de Vega, H.J., Sánchez, N., Combes, F. (2001). Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas. In: Sánchez, N.G. (eds) Current Topics in Astrofundamental Physics: The Cosmic Microwave Background. NATO Science Series, vol 562. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0748-1_22
Download citation
DOI: https://doi.org/10.1007/978-94-010-0748-1_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6856-4
Online ISBN: 978-94-010-0748-1
eBook Packages: Springer Book Archive