Fractal Properties of the Solar Neighborhood Based on the Geneva-Copenhagen Survey

This study analyzes the fractal properties of the space distribution of stars in the solar neighborhood, based on the Geneva-Copenhagen Survey data. We demonstrate the existence of dynamically weakly coupled stochastic fractal structures in the circumsolar stellar medium. The number of such structures in the real stellar medium on 3 to 20 pc scales significantly exceeds the number of similar structures in the corresponding simulated random distributions. The total number of fractal structures depends on their characteristic size – the scale factor (Mf). We demonstrate that the structuredness of the stellar medium increases with the scale factor reaching its maximum around Mf ~ 18 pc and has a minimum around Mf ~ 5 pc. For Mf = 5 pc, the number of fractal structures in the survey is equal to 688, while for Mf = 18−20 pc the corresponding number exceeds 4000, which differs by more than three standard deviations from the mean fractal dimension D for random distributions. Practically, no structures are observed in random distributions in this domain of fractal dimensions. The proportion of fractal structures with [Fe/H]> 0 increases slowly with increasing scale factor and the number of such structures remains in the interval from 170 to 900. On the whole, the number of structures with [Fe/H]< 0 varies with scale factor in the same way as the total number of structures, and lies in the interval from 530 (Mf = 5 pc) to 3200 (Mf = 20 pc). Such significant differences between the fractal properties of the real stellar medium and its random simulations are due to peculiar “gravitational viscosity” of the gravitating medium. The results reported may play an important part in the study of structural properties and dynamic processes in the Galaxy and in the investigation of relaxation processes in particular.