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Modeling the Alignment Profile of Satellite Galaxies in Clusters

Analyzing the halo and galaxy catalogs from the Millennium simulations at redshifts $z=0,\ 0.5,\ 1$, we determine the alignment profiles of cluster galaxies by measuring the average alignments between the major axes of the pseudo inertia tensors from all satellites within cluster's virial radius and from only those satellites within some smaller radius as a function of the top-hat scale difference. The alignment profiles quantify how well the satellite galaxies retain the memory of the external tidal fields after merging into their host clusters and how fast they lose the initial alignment tendency as the cluster's relaxation proceeds. It is found that the alignment profile drops faster at higher redshifts and on smaller mass scales. This result is consistent with the picture that the faster merging of the satellites and earlier onset of the nonlinear effect inside clusters tend to break the preferential alignments of the satellites with the external tidal fields. Modeling the alignment profile of cluster galaxies as a power-law of the density correlation coefficient that is independent of the power spectrum normalization ($σ_{8}$) and demonstrating that the density correlation coefficient varies sensitively with the density parameter ($Ω_{m}$) and neutrino mass fraction ($f_ν$), we suggest that the alignment profile of cluster galaxies might be useful for breaking the $Ω_{m}$-$σ_{8}$ and $f_ν$-$σ_{8}$ degeneracies.