Mixed fractal models for the distribution of galaxies.

The ability of fractal models to reproduce the observed distribution of galaxies is explored. Mixed models, made of fractal density fluctuations superposed on a Poisson background, are needed in order to explain the observed large scale cutoff of the number counts probabilities and the power-law behavior of the correlation functions. The distribution of IRAS galaxies is well fitted by a model in which the Poisson component is five times larger than the fractal component, of dimension 1.6. A similar mixed fractal model is built for visible galaxies in the Southern Sky Survey, taking into account some dynamic aspects of clusters. The best fit is obtained for a mixed model in which the Poisson component is as large as the fractal component, of dimension 2. The fit is however not good at large scales. These results illustrate the complexity of the matter distribution in the Universe, and prove the necessity of considering multifractal models. They also suggest that the multifractallity is confined only to small scales.