Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion
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概要
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We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangiandescription of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure,given by a polytropic equation of state, using a perturbation method up to second order. This perturbativeapproach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of theinclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion.We obtain the first-order solutions in generic background universes and the second-order solutions in a widerrange of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein–deSitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions,we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how theevolution of inhomogeneities changes for the variation of the polytropic index.
- 2002-09-00
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