Field equation of the correlation function of mass-density fluctuations for self-gravitating systems
Department of Astronomy, Key Laboratory for Researches in Galaxies and Cosmology, University of Science and Technology of China, Hefei, Anhui 230026, PR China
e-mail: firstname.lastname@example.org; email@example.com
Received: 28 November 2014
Accepted: 1 July 2015
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 ξcc(r) of clusters is similar to ξgg(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 ξgg(r) ≃ (r0/r)1.7 is only valid in a range 1 <r< 10h-1 Mpc. At larger scales the solution ξ(r) breaks below the power law and goes to zero around ~50 h-1 Mpc, just as observational data have demonstrated. With a set of fixed model parameters, the solutions ξgg(r) for galaxies, the corresponding power spectrum, and ξcc(r) for clusters, simultaneously agree with the observational data from the major surveys of galaxies and clusters.
Key words: galaxies: clusters: general / large-scale structure of Universe / gravitation / cosmology: theory
© ESO, 2015