The fractal dimensions of the spatial distribution of young open clusters in the solar neighbourhood
Suffolk University Madrid Campus, C/ Viña 3, 28003 Madrid, Spain e-mail: raul@galaxy.suffolk.es
Received:
21
November
2005
Accepted:
26
January
2006
Context.Fractals are geometric objects with dimensionalities that are not integers. They play a fundamental role in the dynamics of chaotic systems. Observation of fractal structure in both the gas and the star-forming sites in galaxies suggests that the spatial distribution of young open clusters should follow a fractal pattern, too.
Aims.Here we investigate the fractal pattern of the distribution of young open clusters in the Solar Neighbourhood using a volume-limited sample from WEBDA and a multifractal analysis. By counting the number of objects inside spheres of different radii centred on clusters, we study the homogeneity of the distribution.
Methods.The fractal dimension D of the spatial distribution of a volume-limited sample of young open clusters is determined by analysing different moments of the count-in-cells. The spectrum of the Minkowski-Bouligand dimension of the distribution is studied as a function of the parameter q. The sample is corrected for dynamical effects.
Results.The Minkowski-Bouligand dimension varies with q in the
range 0.71–1.77, therefore the distribution of young open
clusters is fractal. We estimate that the average value of
the fractal dimension is 
for the
distribution of young open clusters studied.
Conclusions.The spatial distribution of young open clusters in the Solar Neighbourhood exhibits multifractal structure. The fractal dimension is time-dependent, increasing over time. The values found are consistent with the fractal dimension of star-forming sites in other spiral galaxies.
Key words: methods: statistical / stars: formation / open clusters and associations: general / solar neighbourhood
© ESO, 2006