An Analysis of the Large Scale N-body Simulation using the Minkowski Functionals
msra(2004)
摘要
We analyze the Minkowski functionals with a large $N$-body simulation of a
standard $\Lambda$CDM model, focusing on transition scales between linear and
non-linear gravitational evolution. We numerically calculate the Minkowski
functionals with sufficient accuracies to investigate the transition scales,
10--$50\himpc$. The results are compared with analytic formulae of linear and
second-order perturbation theories. We first show that the skewness parameters
of the density fluctuations, which are important in second-order analytic
formulae of the Minkowski functionals, are in good agreement with the
perturbation theory. Considering relative differences between the Minkowski
functionals of the analytic formulae and that of the simulation data, we
evaluate accuracy levels of the predictions of the perturbation theory. When
the straightforward threshold $\nu$ by density value is used in Minkowski
functionals, the accuracy of the second-order perturbation theory is within 10%
for smoothing length $R > 15\himpc$, and within a several % for $R > 20\himpc$.
The accuracies of the linear theory are 2--5 times worse than that. When the
rescaled threshold by volume fraction, $\nu_{\rm f}$ is used, accuracies of
both linear and second-order theories are within a few % on all scales of
$10\himpc < R < 50\himpc$.
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关键词
astrophysics,perturbation theory,volume fraction,second order
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