A coarse-grained field theory for density fluctuations and correlation functions of galaxies and clusters

作者：Zhang Y^*

来源：Astronomy & Astrophysics, 2007, 464(3): 811-814.

DOI：10.1051/0004-6361:20066436

• cosmology : large-scale structure of Universe
• cosmology : theory
• galaxies : clusters : general
• gravitation
• hydrodynamics
• instabilities

Aims. We aim to investigate the large- scale structure of the universe from a field- theoretical perspective, and to give a unifying understanding of several seemingly unrelated observed features of clusterings of galaxies and clusters, such as the dependence of clustering amplitude on mass and luminosity, the departure of the correlation function.( r) from the power law proportional to( r(0)/r)(1.7), the oscillatory behavior of zeta(cc)( r) for clusters on very large scales, and the scaling of r(0) with the mean separation d of clusters.
Methods. We present a coarse-grained field theory of density fluctuations for a Newtonian self-gravitating many-body system, apply it to a homogeneous Universe with small density fluctuations, and uniformly treat the clustering of all types of galactic objects in terms of the field of density fluctuations.
Results. The Jeans length lambda(0), a unique physical scale for a gravitating system, appears naturally as the characteristic scale underlying the large- scale structure. Under a Gaussian approximation the analytic expressions of Sigma(r) and P(k) are obtained. The correlation amplitude is proportional to the galactic mass zeta( r) proportional to m, and Sigma( r) departures from the power law (r(0)/ r)(1.7) around r similar to 20 h(-1) Mpc, and is oscillating over large scales similar to 100 h(-1) Mpc and damped to zero. The spectrum amplitude is inversely proportional to the galactic number density, P( k) proportional to 1/ n, and P(k). k(-2.2) in the range k similar or equal to ( 0.05 similar to 0.3) h Mpc(-1). The scaling r(0) proportional to d(0.3 similar to 0.5) holds quantitatively.
Conclusions. These preliminary analytic results under the Gaussian approximation already qualitatively explain these pronounced features of the observed large- scale structures. Yet on small scales the predicted clustering is insu. cient, and the peak of P( k) is too sharp. These deficiencies are due to neglecting higher order nonlinear e. ects, which need to be studied further.

• 出版日期2007-3