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Astron. Astrophys. 343, 317-324 (1999)

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Lagrangian theory of structure formation in pressure-supported cosmological fluids

Susanne Adler and Thomas Buchert

Theoretische Physik, Ludwig-Maximilians-Universität, Theresienstrasse 37, D-80333 München, Germany

Received 1 July 1998 / Accepted 6 November 1998


The Lagrangian theory of structure formation in cosmological fluids, restricted to the matter model "dust", provides successful models of large-scale structure in the Universe in the laminar regime, i.e., where the fluid flow is single-streamed and "dust"-shells are smooth. Beyond the epoch of shell-crossing a qualitatively different behavior is expected, since in general anisotropic stresses powered by multi-stream forces arise in collisionless matter. In this paper we provide the basic framework for the modeling of pressure-supported fluids, restricting attention to isotropic stresses and to the cases where pressure can be given as a function of the density. We derive the governing set of Lagrangian evolution equations and study the resulting system using Lagrangian perturbation theory. We discuss the first-order equations and compare them to the Eulerian theory of gravitational instability, as well as to the case of plane-symmetric collapse. We obtain a construction rule that allows to derive first-order solutions of the Lagrangian theory from known first-order solutions of the Eulerian theory and so extend Zel'dovich's extrapolation idea into the multi-streamed regime. These solutions can be used to generalize current structure formation models in the spirit of the "adhesion approximation".

Key words: cosmology: large-scale structure of Universe – cosmology: theory – methods: analytical – instabilities – hydrodynamics – gravitation

Send offprint requests to: T. Buchert (buchert@stat.physik.uni-muenchen.de)

© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999