Correlation functions in 2D and 3D as descriptors of the cosmic web
  Aims. Our goal is to find the relation between the two-point correlation
functions (CFs) of projected and spatial density fields of galaxies in the
context of the cosmic web. Methods. To investigate relations between spatial
(3D) and projected (2D) CFs of galaxies we used density fields of two
simulations: a $\Lambda$-dominated cold dark matter (LCDM) model with known
particle data, and the Millennium simulation with know data on simulated
galaxies. We compare 3D and 2D correlation functions. In the 2D case, we use
samples of various thickness to find the dependence of 2D CFs on the thickness
of samples. We also compare 3D CFs in real and redshift space. Results. The
dominant elements of the cosmic web are clusters and filaments, separated by
voids filling most of the volume. In individual 2D sheets, the positions of
clusters and filaments do not coincide. As a result, in projection, the
clusters and filaments fill in 2D voids. This leads to a decrease in the
amplitudes of CFs (and power spectra) in projection. For this reason, the
amplitudes of 2D CFs are lower than the amplitudes of 3D correlation functions:
the thicker the 2D sample, the greater the difference. Conclusions. Spatial CFs
of galaxies contain valuable information about the geometrical properties of
the cosmic web that cannot be found from projected CFs.
