### Abstract

We study the evolution of the cluster correlation function and its richness dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with Ω_{m} = 0.3 and, for comparison, a tilted Ω_{m} = 1 model (TSCDM) are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high-redshift clusters are clustered more strongly (on a comoving scale) than low-redshift clusters of the same mass. The increased correlation with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation scale versus cluster mean separation relation, R_{0}-d, is found to be, remarkably, independent of redshift to z ≲ 2 for LCDM and z ≲ 1 for TSCDM for a fixed correlation function slope and a cluster mass within a fixed comoving radius. The nonevolving R_{0}-d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters, so that the R_{0}-d relation remains essentially unchanged. For LCDM, this relation is R_{0}(Z) ≃ 2.6[d(z}]^{1/2} for z ≲ 2 in comoving h^{-1} Mpc scales. The TSCDM model has smaller correlation scales, as expected. Evolution in the relation is seen at z ≳ 2 for LCDM and z ≳ 1 for TSCDM, where the amplitude of the relations declines. The evolution of the R_{0}-d relation from z ∼ 0 to z ∼ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ∼ 0 and provide precise determination of cosmological parameters.

Original language | English (US) |
---|---|

Pages (from-to) | 1-6 |

Number of pages | 6 |

Journal | Astrophysical Journal |

Volume | 603 |

Issue number | 1 I |

DOIs | |

State | Published - Mar 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*603*(1 I), 1-6. https://doi.org/10.1086/381386

}

*Astrophysical Journal*, vol. 603, no. 1 I, pp. 1-6. https://doi.org/10.1086/381386

**Evolution of the cluster correlation function.** / Bahcall, Neta; Lei, H. A O; Bode, Paul; Dong, Feng.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Evolution of the cluster correlation function

AU - Bahcall, Neta

AU - Lei, H. A O

AU - Bode, Paul

AU - Dong, Feng

PY - 2004/3/1

Y1 - 2004/3/1

N2 - We study the evolution of the cluster correlation function and its richness dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with Ωm = 0.3 and, for comparison, a tilted Ωm = 1 model (TSCDM) are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high-redshift clusters are clustered more strongly (on a comoving scale) than low-redshift clusters of the same mass. The increased correlation with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation scale versus cluster mean separation relation, R0-d, is found to be, remarkably, independent of redshift to z ≲ 2 for LCDM and z ≲ 1 for TSCDM for a fixed correlation function slope and a cluster mass within a fixed comoving radius. The nonevolving R0-d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters, so that the R0-d relation remains essentially unchanged. For LCDM, this relation is R0(Z) ≃ 2.6[d(z}]1/2 for z ≲ 2 in comoving h-1 Mpc scales. The TSCDM model has smaller correlation scales, as expected. Evolution in the relation is seen at z ≳ 2 for LCDM and z ≳ 1 for TSCDM, where the amplitude of the relations declines. The evolution of the R0-d relation from z ∼ 0 to z ∼ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ∼ 0 and provide precise determination of cosmological parameters.

AB - We study the evolution of the cluster correlation function and its richness dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with Ωm = 0.3 and, for comparison, a tilted Ωm = 1 model (TSCDM) are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high-redshift clusters are clustered more strongly (on a comoving scale) than low-redshift clusters of the same mass. The increased correlation with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation scale versus cluster mean separation relation, R0-d, is found to be, remarkably, independent of redshift to z ≲ 2 for LCDM and z ≲ 1 for TSCDM for a fixed correlation function slope and a cluster mass within a fixed comoving radius. The nonevolving R0-d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters, so that the R0-d relation remains essentially unchanged. For LCDM, this relation is R0(Z) ≃ 2.6[d(z}]1/2 for z ≲ 2 in comoving h-1 Mpc scales. The TSCDM model has smaller correlation scales, as expected. Evolution in the relation is seen at z ≳ 2 for LCDM and z ≳ 1 for TSCDM, where the amplitude of the relations declines. The evolution of the R0-d relation from z ∼ 0 to z ∼ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ∼ 0 and provide precise determination of cosmological parameters.

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U2 - https://doi.org/10.1086/381386

DO - https://doi.org/10.1086/381386

M3 - Article

VL - 603

SP - 1

EP - 6

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1 I

ER -