Solving the Bernoulli-Zel'dovich equation

Details Solving the Bernoulli-Zel'dovich equation Solving the Bernoulli-Zel'dovich equation

Apr 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...407....1l&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 407, no. 1, p. 1-4.

Astronomy and Astrophysics

Astrophysics

10

Bernoulli Theorem, Cosmology, Gravitational Fields, Universe, Astronomical Models, Lagrange Coordinates, Reconstruction

Scientific paper

The Zel'dovich approximation is very efficient in reconstructing the initial conditions (in the form of a displacement field, a deformation tensor, or the corresponding potential) from observational data, usually proper velocities. Recently it has been shown that this problem reduces to a differential equation for the velocity potential, the Bernouilli-Zel'dovich equation, and numerical methods were proposed to solve it. Here I derive an analytical solution to this equation which allows reconstruction without any numerical integration (except a spatial integration of the present velocity field which is the first step of any procedure). This allows the reconstruction of the initial potential at Lagrangian positions. I also propose an approximation which makes this method even more direct, allowing the reconstruction of the initial potential (Lagrangian or Eulerian) at Eulerian positions.

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