Fractal properties of the solar neighbourhood based on Geneva-Kopenhagen surveyстатья
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Аннотация:This study analyzes the fractal properties of the space distributionof stars in the solar neighborhood, based on the Geneva-Copenhagen Surveydata. We demonstrate the existence of dynamically weakly coupled stochasticfractal structures in the circumsolar stellar medium. The number of such structuresin the real stellar medium on 3 to 20 pc scales significantly exceeds thenumber of similar structures in the corresponding simulated random distributions.The total number of fractal structures depends on their characteristicsize – the scale factor (Mf). We demonstrate that the structuredness of thestellar medium increases with the scale factor reaching its maximum aroundMf ∼ 18 pc and has a minimum around Mf ∼ 5 pc. For Mf = 5 pc, the numberof fractal structures in the survey is equal to 688, while for Mf = 18−20 pcthe corresponding number exceeds 4000, which differs by more than three standarddeviations from the mean fractal dimension D for random distributions.Practically, no structures are observed in random distributions in this domainof fractal dimensions. The proportion of fractal structures with [Fe/H]> 0 increasesslowly with increasing scale factor and the number of such structuresremains in the interval from 170 to 900. On the whole, the number of structureswith [Fe/H]< 0 varies with scale factor in the same way as the totalnumber of structures, and lies in the interval from 530 (Mf = 5 pc) to 3200(Mf = 20 pc). Such significant differences between the fractal properties ofthe real stellar medium and its random simulations are due to peculiar “gravitationalviscosity” of the gravitating medium. The results reported may playan important part in the study of structural properties and dynamic processesin the Galaxy and in the investigation of relaxation processes in particular