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Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas

  • B. Semelin
  • H. J. de Vega
  • N. Sánchez
  • F. Combes
Part of the NATO Science Series book series (ASIC, volume 562)

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≤rR, (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

Stationary Point Renormalization Group Equation Vertex Function Effective Coupling Perturbative Series 
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.

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References

  1. [1] H. J. de Vega, N. Sánchez and F. Combes, Nature, 383, 56 (1996). Phys. Rev. D54, 6008 (1996).ADSCrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • B. Semelin
    • 2
    • 4
  • H. J. de Vega
    • 1
    • 3
  • N. Sánchez
    • 2
    • 4
  • F. Combes
    • 2
    • 4
  1. 1.Laboratoire de Physique Théorique et Hautes EnergiesUniversité Paris VIParis, Cedex 05FRANCE
  2. 2.Observatoire de ParisDemirmParisFRANCE
  3. 3.Laboratoire Associé au CNRS UMRFrance
  4. 4.Observatoire de Paris et École Normale SupérieureFrance

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