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Hierarchical Object Formation in the Peculiar Velocity Field.pdf

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Hierarchical Object Formation in the Peculiar Velocity Field

a r X i v : a s t r o - p h / 0 5 0 8 0 6 9 v 3 2 0 A p r 2 0 0 7 HIERARCHICAL OBJECT FORMATION IN THE PECULIAR VELOCITY FIELD1 HIDEAKI MOURI Meteorological Research Institute, Nagamine, Tsukuba 305-0052, Japan and YOSHIAKI TANIGUCHI Astronomical Institute, Graduate School of Science, Tohoku University, Aoba, Sendai 980-8578, Japan; tani@astr.tohoku.ac.jp ABSTRACT Using the initial peculiar-velocity field, we analytically study the hierarchical formation of gravitationally bound objects. The field is smoothed over a scale that corresponds to the mass of a given class of objects. Through the Zel’dovich approximation, the smoothed field determines how the objects cluster together to form a new class of more massive objects. The standard cosmological parameters lead to the evolution of primordial clouds with ≤ 106M⊙ → galaxies with 1012M⊙ → clusters of galaxies with 1015M⊙ → superclusters of galaxies with 1016M⊙. The epochs obtained for the formation of these classes of objects are consistent with observations. Subject headings: cosmology: theory — galaxies: formation — large scale struc- ture of universe 1. INTRODUCTION For the formation of gravitationally bound objects such as galaxies and clusters of galaxies, the current paradigm is hierarchical formation based on the cold dark matter model. The cold dark matter induces significant small-scale fluctuations in the initial field. Since 1This version corrects errors in equations (19), (20), (22), and (25) and Figures 2a and 3 of the published version (ApJ, 634, 20 [2005]). The errors are also corrected in the erratum (ApJ, 659, 1792 [2007]). – 2 – the first objects arise from these initial fluctuations, they are not so massive. They merge with one another via gravitational clustering in a hierarchy, evolving successively into more massive objects. We analytically discuss some statistical properties of this hierarchical object formation via the gravitational clustering. The existing analytical studies are based on