### Abstract

We discuss the systematic effects arising from the cosmological redshift space (geometric) distortion on the statistical analysis of the isodensity contour using high-redshift catalogs. In particular, we present a simple theoretical model for isodensity statistics in cosmological redshift space, as a generalization of earlier work by Matsubara. The statistical quantities considered here are the two- and three-dimensional genus of the isodensity contour, the surface area, the length of the contour intersecting with a plane, and the number of crossing points of the isodensity contour on a line. We give useful analytic formulae for the isodensity statistics, which take into account corrections from the geometric distortion, the nonlinear clustering, and the nonlinear velocity distortion phenomenologically. We then demonstrate how the geometric distortion and the nonlinear corrections alter the shapes of the statistical quantities on the basis of plausible cosmological models. Our results show that the nonlinear correction can be sensitive to a choice of the redshift-space coordinate as increasing the redshift. The low-dimensional quantities, such as the two-dimensional genus, systematically yield anisotropy due to the geometric and velocity distortions, and their angle-dependence shows a 10%-20% difference of amplitude. Sensitivities for typical high-redshift samples are estimated in an analytic manner, and the influence of the light-cone effect for the isodensity statistics is also discussed. A simple estimation suggests that the systematic effects of geometric and redshift-space distortions can become comparable to or even dominate the statistical error of deep cluster samples and future high-redshift galaxy surveys. These systematic effects might be a useful tool in probing the cosmological model of our universe.

Original language | English |
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Pages (from-to) | 528-546 |

Number of pages | 19 |

Journal | Astrophysical Journal |

Volume | 550 |

Issue number | 2 PART 1 |

DOIs | |

Publication status | Published - Apr 1 2001 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal*,

*550*(2 PART 1), 528-546. https://doi.org/10.1086/319795