Statistical properties of the spatial distribution of galaxies

Astrophysical Bulletin (Impact Factor: 0.87). 10/2009; 64(3):217-228. DOI: 10.1134/S199034130903002X
Source: arXiv


The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of
these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly applicable
to fractal structures only at the scale lengths from several average distances between the galaxies, and up to (10 − 20)%
of the radius of the largest sphere that fits completely inside the sample domain. Earlier the correlation methods were believed
to be applicable up to the entire radius of the sphere and the researchers did not take the above restriction into account
while finding the scale length corresponding to the transition to a uniform distribution. When an empirical formula is applied
for approximating the radial distributions in the samples confined by the limiting apparent magnitude, the deviation of the
true radial distribution from the approximating formula (but not the parameters of the best approximation) correlate with
fractal dimension. An analysis of the 2dF catalog yields a fractal dimension of 2.20 ± 0.25 on scale lengths from 2 to 20
Mpc, whereas no conclusive estimates can be derived by applying the conditional density method for larger scales due to the
inherent biases of the method. An analysis of the radial distributions of galaxies in the 2dF and 6dF catalogs revealed significant
irregularities on scale lengths of up to 70 Mpc. The magnitudes and sizes of these irregularities are consistent with the
fractal dimension estimate of D =2.1–2.4.

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