Abstract
We develop a field theoretical approach to the cold interstellar medium (ISM). We show that a nonrelativistic self-gravitating gas in thermal equilibrium with a variable number of atoms or fragments is exactly equivalent to a field theory of a single scalar field with an exponential self-interaction. We analyze this field theory perturbatively and nonperturbatively through the renormalization group approach. We show a scaling behavior (critical) for a continuous range of the temperature and of the other physical parameters. We derive in this framework the scaling relation for the mass on a region of size , and for the velocity dispersion where . For the density-density correlations we find a power-law behavior for large distances . The fractal dimension turns out to be related with the critical exponent of the correlation lenght by . The renormalization group approach for a single component scalar field in three dimensions states that the long-distance critical behavior is governed by the (nonperturbative) Ising fixed point. The corresponding values of the scaling exponents are , , and . Mean field theory yields for the scaling exponents , , and . Both the Ising and the mean field values are compatible with the present ISM observational data: , . As typical in critical phenomena, the scaling behavior and critical exponents of the ISM can be obtained without dealing with the dynamical (time-dependent) behavior.
- Received 10 May 1996
DOI:https://doi.org/10.1103/PhysRevD.54.6008
©1996 American Physical Society