Fractal structures and scaling laws in the universe. Statistical mechanics of the self-gravitating gas

✍ Scribed by H.J. De Vega; N. Sánchez; F. Combes

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 968 KB
• Volume: 10
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(98)00194-5

✦ Synopsis

Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10e4pc till 100~~. Secondly, the galaxy distribution has been observed to be fractal in scales up to hundreds of Mpc. We give here a short review of the statistical mechanical (and field theoretical) approach developed by us for the cold interstellar medium (ISM) and large structure of'the universe. We consider a non-relativistic self-gravitating gas in thermal equilibrium at temperature T inside a volume I'. The statistical mechanics of such system has special features and, as is known, the thermodynamical limit does not exist in its customary form. Moreover, the treatments through microcanonical, canonical and grand canonical ensembles yield different results. We present here for the first time the equation of state for the self-gravitating gas in the canonical ensemble. We find that it has the form p = [NT/V]/(q), where p is the pressure, N is the number of