Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2010-07-07
ApJ, 724, 285 (2010)
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
14 pages, lots of interesting figures. This version supersedes the ApJ version. Fitting formulae corrected
Scientific paper
10.1088/0004-637X/724/1/285
The statistical meaning of the local non-Gaussianity parameters f_NL and g_NL is examined in detail. Their relations to the skewness and the kurtosis of the probability distribution of density fluctuations are shown to obey simple fitting formulae, accurate on galaxy-cluster scales. We argue that the knowledge of f_NL and g_NL is insufficient for reconstructing a well-defined distribution of density fluctuations. However, by weakening the statistical significance of f_NL and g_NL, it is possible to reconstruct a well-defined pdf by using a truncated Edgeworth series. We give some general guidelines on the use of such a series, noting in particular that 1) the Edgeworth series cannot represent models with nonzero f_NL, unless g_NL is nonzero also, 2) the series cannot represent models with g_NL<0, unless some higher-order non-Gaussianities are known. Finally, we apply the Edgeworth series to calculate the effects of g_NL on the abundances of massive clusters and large voids. We show that the abundance of voids may generally be more sensitive to high-order non-Gaussianities than the cluster abundance.
Chongchitnan Sirichai
Silk Joseph
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