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Fractal Dimensions and Scaling Laws in the Interstellar Medium and Galaxy Distributions: a new Field Theory Approach | H. J. de Vega
; N. Sánchez
; F. Combes
; | Date: |
13 Dec 1997 | Subject: | astro-ph cond-mat gr-qc hep-ph hep-th | Abstract: | We develop a field theoretical approach to the cold interstellar medium (ISM) and large structure of the universe. We show that a non-relativistic self- gravitating gas in thermal equilibrium with variable number of atoms or fragments is exactly equivalent to a field theory of a scalar field phi(x) with exponential self-interaction. We analyze this field theory perturbatively and non-perturbatively through the renormalization group(RG).We show scaling behaviour (critical) for a continuous range of the physical parameters as the temperature. We derive in this framework the scaling relation M(R) sim R^{d_H} for the mass on a region of size R, and Delta v sim R^frac12(d_H -1) for the velocity dispersion. For the density-density correlations we find a power-law behaviour for large distances sim |r_1 - r_2|^{2D - 6}.The fractal dimension D turns to be related with the critical exponent
u by D = 1/
u. Mean field theory yields
u = 1/2, D = 2. Both the Ising and the mean field values are compatible with the present ISM observational data:1.4leq D leq 2. We develop a field theoretical approach to the galaxy distribution considering a gas of self-gravitating masses on the FRW background, in quasi-thermal equi- librium. We show that it exhibits scaling behaviour by RG methods. The galaxy correlations are computed without assuming homogeneity. We find <
ho({vec r_0})
ho({vec r_0} + {vec r}) > sim r^{D-3} $. The theory allows to compute the three and higher density correlators without any assumption.We find that the connected N-points density scales as r_1^{N(D-3)}, when $ r_1 >> r_i, 2leq i leq N $. There are no free parameters in this theory. | Source: | arXiv, astro-ph/9801115 | Services: | Forum | Review | PDF | Favorites |
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