### Abstract

We write the correlation function of dark matter particles, ξ(r), as the sum of two terms -one which accounts for non-linear evolution, and dominates on small scales, and another which is essentially the term from linear theory, and dominates on large scales. We use models of the number and spatial distribution of haloes and halo density profiles to describe the non-linear term and its evolution. The result provides a good description of the evolution of ξ(r) in simulations. We then use this decomposition to provide simple and accurate models of how the single-particle velocity dispersion evolves with time, and how the first and second moments of the pairwise velocity distribution depend on scale. The key idea is to use the simple physics of linear theory on large scales, the simple physics of the virial theorem on small scales and our model for the correlation function to tell us how to weight the two types of contributions (linear and non-linear) to the pairwise velocity statistics. When incorporated into the streaming model, our results will allow a simple accurate description of redshift-space distortions over the entire range of linear to highly non-linear regimes.

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

Pages (from-to) | 1288-1302 |

Number of pages | 15 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 325 |

Issue number | 4 |

DOIs | |

State | Published - Aug 21 2001 |

### Fingerprint

### Keywords

- Cosmology: theory
- Dark matter
- Galaxies: clusters: general

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Monthly Notices of the Royal Astronomical Society*,

*325*(4), 1288-1302. https://doi.org/10.1046/j.1365-8711.2001.04222.x

**Linear and non-linear contributions to pairwise peculiar velocities.** / Sheth, Ravi K.; Hui, Lam; Diaferio, Antonaldo; Scoccimarro, Román.

Research output: Contribution to journal › Article

*Monthly Notices of the Royal Astronomical Society*, vol. 325, no. 4, pp. 1288-1302. https://doi.org/10.1046/j.1365-8711.2001.04222.x

}

TY - JOUR

T1 - Linear and non-linear contributions to pairwise peculiar velocities

AU - Sheth, Ravi K.

AU - Hui, Lam

AU - Diaferio, Antonaldo

AU - Scoccimarro, Román

PY - 2001/8/21

Y1 - 2001/8/21

N2 - We write the correlation function of dark matter particles, ξ(r), as the sum of two terms -one which accounts for non-linear evolution, and dominates on small scales, and another which is essentially the term from linear theory, and dominates on large scales. We use models of the number and spatial distribution of haloes and halo density profiles to describe the non-linear term and its evolution. The result provides a good description of the evolution of ξ(r) in simulations. We then use this decomposition to provide simple and accurate models of how the single-particle velocity dispersion evolves with time, and how the first and second moments of the pairwise velocity distribution depend on scale. The key idea is to use the simple physics of linear theory on large scales, the simple physics of the virial theorem on small scales and our model for the correlation function to tell us how to weight the two types of contributions (linear and non-linear) to the pairwise velocity statistics. When incorporated into the streaming model, our results will allow a simple accurate description of redshift-space distortions over the entire range of linear to highly non-linear regimes.

AB - We write the correlation function of dark matter particles, ξ(r), as the sum of two terms -one which accounts for non-linear evolution, and dominates on small scales, and another which is essentially the term from linear theory, and dominates on large scales. We use models of the number and spatial distribution of haloes and halo density profiles to describe the non-linear term and its evolution. The result provides a good description of the evolution of ξ(r) in simulations. We then use this decomposition to provide simple and accurate models of how the single-particle velocity dispersion evolves with time, and how the first and second moments of the pairwise velocity distribution depend on scale. The key idea is to use the simple physics of linear theory on large scales, the simple physics of the virial theorem on small scales and our model for the correlation function to tell us how to weight the two types of contributions (linear and non-linear) to the pairwise velocity statistics. When incorporated into the streaming model, our results will allow a simple accurate description of redshift-space distortions over the entire range of linear to highly non-linear regimes.

KW - Cosmology: theory

KW - Dark matter

KW - Galaxies: clusters: general

UR - http://www.scopus.com/inward/record.url?scp=0000203365&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000203365&partnerID=8YFLogxK

U2 - 10.1046/j.1365-8711.2001.04222.x

DO - 10.1046/j.1365-8711.2001.04222.x

M3 - Article

VL - 325

SP - 1288

EP - 1302

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 4

ER -