SIMBAD references

We study the mass-density distribution of Newtonian self-gravitating systems. Modeling the system as a fluid in hydrostatical equilibrium, we obtain from first principles the field equation and its solution of the correlation function ξ(r) of the mass-density fluctuation itself. We apply this to studies of the large-scale structure of the Universe within a small redshift range. The equation shows that ξ(r) depends on the point mass m and the Jeans wavelength scale λ₀, which are different for galaxies and clusters. It explains several long-standing prominent features of the observed clustering: that the profile of ξ_cc(r) of clusters is similar to ξ_gg(r) of galaxies, but with a higher amplitude and a longer correlation length, and that the correlation length increases with the mean separation between clusters as a universal scaling r₀≃0.4d. Our solution ξ(r) also shows that the observed power-law correlation function of galaxies ξ_gg(r)≃(r₀/r)^1.7 is only valid in a range 1<r<10 h^–1Mpc. At larger scales the solution ξ(r) breaks below the power law and goes to zero around ∼50 h^–1Mpc, just as observational data have demonstrated. With a set of fixed model parameters, the solutions ξ_gg(r) for galaxies, the corresponding power spectrum, and ξ_cc(r) for clusters, simultaneously agree with the observational data from the major surveys of galaxies and clusters.