Title: STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, andmore » the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.« less

Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States)

Publication Date:

OSTI Identifier:

22518574

Resource Type:

Journal Article

Resource Relation:

Journal Name: Astrophysical Journal; Journal Volume: 820; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CONTINUITY EQUATIONS; COSMOLOGY; DECOUPLING; DENSITY; DIAGRAMS; FLUID MECHANICS; FLUIDS; LAGRANGIAN FUNCTION; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; NONLUMINOUS MATTER; PROBABILITY DENSITY FUNCTIONS; TENSORS; TRANSPORT THEORY; UNIVERSE