Spatial density fluctuations and selection effects in galaxy redshift surveys

One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determining the shape of the correlation function, its possible evolution with redshift and the size and amplitude of large scale structures. Different selection effects, inevitably entering in any observation, introduce important constraints in the measurement of correlations. In the context of galaxy redshift surveys selection effects can be caused by observational techniques and strategies and by implicit assumptions used in the data analysis. Generally all these effects are taken into account by using pair-counting algorithms to measure two-point correlations. We review these methods stressing that they are based on the a-priori assumption that galaxy distribution is spatially homogeneous inside a given sample. We show that, when this assumption is not satisfied by the data, results of the correlation analysis are affected by finite size effects. In order to quantify these effects, we introduce a new method based on the computation of the gradient of galaxy counts along tiny cylinders. We show, by using artificial homogeneous and inhomogeneous point distributions, that this method identifies redshift dependent selection effects and disentangles them from the presence of large scale density fluctuations. We then apply this new method to several redshift catalogs and we find evidence that galaxy distribution, in those samples where selection effects are small enough, is characterized by power-law correlations with exponent gamma = 0.9 up to 20 Mpc/h followed by a change of slope that, in the range 20-100 Mpc/h, corresponds to a power-law exponent gamma - 0.25. Whether a crossover to spatial uniformity occurs at similar to 100 Mpc/h or larger scales cannot be clarified by the present data.