FRACTAL DIMENSIONS AND SCALING LAWS IN THE INTERSTELLAR-MEDIUM - A NEW FIELD-THEORY APPROACH

We develop a field theoretical approach to the cold interstellar mediu m (ISM). We show that a nonrelativistic self-gravitating gas in therma l equilibrium with a variable number of atoms or fragments is exactly equivalent to a field theory of a single scalar field phi((x) over rig ht arrow) with an exponential self-interaction. We analyze this field theory perturbatively and nonperturbatively through the renormalizatio n group approach. We show a scaling behavior (critical) for a continuo us range of the temperature and of the other physical parameters. We d erive in this framework the scaling relation Delta M(R)similar to R(dH ) for the mass on a region of size R, and Delta v similar to R(q) for the velocity dispersion where q = 1/2(d(H) - 1). For the density-densi ty correlations we find a power-law behavior for large distances simil ar to\(r) over right arrow(1)-(r) over right arrow(2)\(2dH-6). The fra ctal dimension d(H) turns out to be related with the critical exponent v of the correlation length by d(H)=1/nu. The renormalization group a pproach for a single component scalar field in three dimensions states that the long-distance critical behavior is governed by the (nonpertu rbative) Ising fixed point. The corresponding values of the scaling ex ponents are nu=0.631..., d(H)=1.585..., and q = 0.293.... Mean field t heory yields for the scaling exponents nu = 1/2, d(H)=2, and q = 1/2. Both the Ising and the mean field values are compatible with the prese nt ISM observational data: 1.4 less than or equal to d(H) less than or equal to 2, 0.3 less than or equal to q less than or equal to 0.6. As typical in critical phenomena, the scaling behavior and critical expo nents of the ISM can be obtained without dealing with the dynamical (O ne-dependent) behavior.