Francisco-Shu Kitaura, Raul E. Angulo, Yehuda Hoffman, Stefan Gottl"ober
In this work we investigate the nonlinear and nonlocal relation between
cosmological density and peculiar velocity fields. Our goal is to provide an
algorithm for the reconstruction of the nonlinear velocity field from the fully
nonlinear density. We find that including the gravitational tidal field tensor
using second order Lagrangian perturbation theory (2LPT) based upon an estimate
of the linear component of the nonlinear density field significantly improves
the estimate of the cosmic flow in comparison to linear theory not only in the
low density, but also and more dramatically in the high density regions. In
particular we test two estimates of the linear component: the lognormal model
and the iterative Lagrangian linearisation. The present approach relies on a
rigorous higher order Lagrangian perturbation theory analysis which
incorporates a nonlocal relation. It does not require additional fitting from
simulations being in this sense parameter free, it is independent of
statistical-geometrical optimisation and it is straightforward and efficient to
compute. The method is demonstrated to yield an unbiased estimator of the
velocity field on scales >~5 h^{-1}Mpc with closely Gaussian distributed
errors. Moreover, the statistics of the divergence of the peculiar velocity
field is extremely well recovered showing a good agreement with the true one
from N-body simulations. The typical errors of about 10 km/s (1 sigma
confidence intervals) are reduced by more than 80% with respect to linear
theory in the scale range between 5 and 10 h^{-1}Mpc in high density regions
(delta>2). We also find that iterative Lagrangian linearisation is
significantly superior in the low density regime with respect to the lognormal
model.
View original:
http://arxiv.org/abs/1111.6629
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