IS DARK-MATTER IN SPIRAL GALAXIES COLD GAS .2. FRACTAL MODELS AND STAR NONFORMATION

In a companion paper (Paper 1) we have proposed a new candidate to acc ount for the dark matter around spiral galaxies: cold H-2 gas in a fra ctal structure, supported by rotation, and concomitant with the HI dis c. We have shown that this hypothesis is compatible with dynamical and observational constraints about disc galaxies, and explains several c onspiracies and paradoxes, since the dark matter is then in a form of fresh gas able to produce stars. In this paper we attempt to describe the physical conditions leading to a fractal state of cold gas in oute r galaxy discs. Gas cloud models taking into account the recently disc losed fractal structure of cold gas are set up, showing that large err ors in the classical gas mass determination based on smooth cloud mode ls can easily follow if the gas is in reality fractal. Indeed the rang e of possible column densities is then much larger, including 5 or mor e decades of surface densities, instead of 2 for smooth cloud models. Thus fractal clouds must present both optically thin and optically thi ck clumps in any single wavelength observations. The observed fractal dimension of the cold ISM suggests that mass underestimates by a facto r 10 or more are typical. Due to its low temperature (around 3 K), and its condensed fractal structure, together with its low metallicity, t he outer gas would be almost invisible for usual detectors. We conside r the paradox of the persistence of cold kans unstable gas in outer di scs, far from important heating sources, yet not forming stars or Jupi ters. Following Rees (1976), we determine the smallest clump distribut ion that can persist in a collisional and almost isothermal fragmentin g cold gas. At 3 K these elementary cloudlets are predicted to have a radius of about 30 AU, and have a mass of the order of a Jupiter. Thei r average density and column density are 10(9) cm-3 and 10(24) cm-2. T hey are gravitationally bound, and their line of sight thermal width i s about 0.1 km s-1. Their frequent collisions prevent them from formin g Jupiters or stars and the near isothermality of the fractal nearly s uppresses energy dissipation. At higher temperature, especially above H-2 dissociation, the collision rate in the fractal decreases, favouri ng star formation. It turns out that the smallest density condensation s, called ''clumpuscules'' offer favourable conditions for containing H-2 in both vapour and solid phases. However it is unknown whether eno ugh condensations sites such as dust exist in the outer discs to permi t the freezing of H-2. It is expected that the large sublimation energ y prevents much H-2 to become solid, but a small amount of H-2 ice gra ins is a crucial factor for a good coupling between gas and the 3 K ba ckground. Many of the general arguments presented here about fractals can be applied to other inhomogeneous structures, such as the hot gas in galaxy clusters. The clumpuscules presented here might be the form of matter in which cooling flows in clusters seem to disappear.