The Method of a Two-Point Conditional Column Density for Estimating the Fractal Dimension of the Galaxy Distribution

We suggest a new method for estimating the fractal dimension of the spatial distribution of galaxies, the method of selected cylinders. We show the capabilities of this method by constructing a two-point conditional column density for galaxies with known redshifts from the LEDA database. The fractal dimension of a sample of LEDA and EDR SDSS galaxies has been estimated to be D = 2.1 for cylinder lengths of 200 Mpc. Amajor advantage of the suggested method is that it allows scales comparable to the catalog depth to be analyzed for galaxy surveys in the form of conical sectors and small fields in the sky.Comment: 9 pages, 8 figure

Properties of Quasar-Galaxy Associations and Gravitational Mesolensing by Halo Objects

A new catalog of 8382 close quasar-galaxy pairs is presented. The catalog was composed using published catalogs of quasars and active galactic nuclei containing 11358 objects, as well as the LEDA catalog of galaxies, which contains on the order of 100 thousand objects. The search for pairs was carried out in such a way that the linear distance between the galaxy and projected quasar does not exceed 150kpc. Based on these new data, the dependence of the number of pairs on a=z_G/z_Q is analysed, where z_G and z_Q are the redshifts of the galaxy and quasar, respectively, revealing an excess of pairs with a<0.1 and a>0.9. This means that the galaxies in pairs are preferably located close to either the observer or the quasar and avoid intermediate distances along the line of sight to the quasar. Computer simulations demonstrate that it is not possible to explain this number of pairs with the observed distribution in a as the result of chance positional coincidences with a uniform spatial distribution of galaxies. Data on globular clusters show that the excess of pairs with a0.9 is consistent with the hypothesis that we are observing distant compact objects that are strongly gravitationally lensed by transparent lenses with a King mass distribution located in the halos of nearby galaxies. The Hubble diagram for galaxies and quasars is presented. Observational tests of the mesolensing hypothesis are formulated.Comment: 11 pages, 7 figure

Globular Clusters as Candidates for Gravitational Lenses to Explain Quasar-Galaxy Associations

We argue that globular clusters (GCs) are good candidates for gravitational lenses in explaining quasar-galaxy associations. The catalog of associations (Bukhmastova 2001) compiled from the LEDA catalog of galaxies (Paturel 1997) and from the catalog of quasars (Veron-Cetty and Veron 1998) is used. Based on the new catalog containing 8382 pairs, we show that one might expect an increased number of GCs around irregular galaxies of types 9 and 10 from the hypothesis that distant compact sources are gravitationally lensed by GCs in the halos of foreground galaxies. The King model is used to determine the central surface densities of 135 GCs in the Milky Way. The distribution of GCs in central surface density was found to be lognormal.Comment: 22 pages, 4 figure

The Non-Uniform Distribution of Galaxies from Data of the SDSS DR7 Survey

We have analyzed the spatial distribution of galaxies from the release of the Sloan Digital Sky Survey of galactic redshifts (SDSS DR7), applying the complete correlation function (conditional density), two-point conditional density (cylinder), and radial density methods. Our analysis demonstrates that the conditional density has a power-law form for scales lengths 0.5-30 Mpc/h, with the power-law corresponding to the fractal dimension D = 2.2+-0.2; for scale lengths in excess of 30 Mpc/h, it enters an essentially flat regime, as is expected for a uniform distribution of galaxies. However, in the analysis applying the cylinder method, the power-law character with D = 2.0+-0.3 persists to scale lengths of 70 Mpc/h. The radial density method reveals inhomogeneities in the spatial distribution of galaxies on scales of 200 Mpc/h with a density contrast of two, confirming that translation invariance is violated in the distribution of galaxies to 300 Mpc/h, with the sampling depth of the SDSS galaxies being 600 Mpc/h.Comment: 22 page