Local approximations in the weakly nonlinear regime and the density-velocity relation

Details Local approximations in the weakly nonlinear regime and the density-velocity relation Local approximations in the weakly nonlinear regime and the density-velocity relation

Aug 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003basbr..23...55m&link_type=abstract

Boletim da Sociedade Astronômica Brasileira (ISSN 0101-3440), vol.23, no.1, p.55-56

Astronomy and Astrophysics

Astronomy

Scientific paper

We develop a perturbative study of a set of approximations aimed to the description of the nonlinear evolution of large-scale structure. We include in our analysis all four local approximations know to be exact for planar, cylindrical, and spherical symmetries (Makler et al. 2001). We have shown that they are exact up to second order in the density contrast. They are also extremely accurate at third order, in the region of initial conditions that can be parameterized by a homogeneous ellipsoid. By means these approximations, we derive a local expression relating the density with the velocity divergence up to third order. This relation is useful for comparisons between the cosmic density and peculiar velocity fields, and could be readily incorporated into reconstruction methods of the matter distribution such as POTENT. Our expression includes a new shear term that was absent in previous approaches. Omitting such a term produces a systematic effect leading to an underestimation of the density. Finally, we compute the higher order moments of the density distribution and use the result to show that no diagonal local approximation can be exact beyond second order. This work motivates further tests of the accuracy of the local approximations with generic initial conditions, and in particular of the newly proposed density-velocity relation.

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