### Abstract

Our heuristic understanding of the abundance of dark matter halos centers around the concept of a density threshold, or "barrier," for gravitational collapse. If one adopts the ansatz that regions of the linearly evolved density field smoothed on mass scale M with an overdensity that exceeds the barrier will undergo gravitational collapse into halos of mass M, the corresponding abundance of such halos can be estimated simply as a fraction of the mass density satisfying the collapse criterion divided by the mass M. The key ingredient of this ansatz is therefore the functional form of the collapse barrier as a function of mass M or, equivalently, of the variance σ^{2}(M). Several such barriers based on the spherical, Zel'dovich, and ellipsoidal collapse models have been extensively discussed. Using large-scale cosmological simulations, we show that the relation between the linear overdensity and the mass variance for regions that collapse to form halos by the present epoch resembles expectations from dynamical models of ellipsoidal collapse. However, we also show that using such a collapse barrier with the excursion set ansatz predicts a halo mass function inconsistent with that measured directly in cosmological simulations. This inconsistency demonstrates a failure of the excursion set ansatz as a physical model for halo collapse. We discuss implications of our results for understanding the collapse epoch for halos as a function of mass, and avenues for improving consistency between analytical models for the collapse epoch and the results of cosmological simulations.

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

Pages (from-to) | 636-652 |

Number of pages | 17 |

Journal | Astrophysical Journal |

Volume | 696 |

Issue number | 1 |

DOIs | |

State | Published - May 1 2009 |

Externally published | Yes |

### Fingerprint

### Keywords

- Dark matter
- Galaxies: formation
- Galaxies: halos
- Methods: N-body simulations

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Astrophysical Journal*,

*696*(1), 636-652. https://doi.org/10.1088/0004-637X/696/1/636

**Collapse barriers and halo abundance : Testing the excursion set ansatz.** / Robertson, Brant E; Kravtsov, Andrey V.; Tinker, Jeremy; Zentner, Andrew R.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 696, no. 1, pp. 636-652. https://doi.org/10.1088/0004-637X/696/1/636

}

TY - JOUR

T1 - Collapse barriers and halo abundance

T2 - Testing the excursion set ansatz

AU - Robertson, Brant E

AU - Kravtsov, Andrey V.

AU - Tinker, Jeremy

AU - Zentner, Andrew R.

PY - 2009/5/1

Y1 - 2009/5/1

N2 - Our heuristic understanding of the abundance of dark matter halos centers around the concept of a density threshold, or "barrier," for gravitational collapse. If one adopts the ansatz that regions of the linearly evolved density field smoothed on mass scale M with an overdensity that exceeds the barrier will undergo gravitational collapse into halos of mass M, the corresponding abundance of such halos can be estimated simply as a fraction of the mass density satisfying the collapse criterion divided by the mass M. The key ingredient of this ansatz is therefore the functional form of the collapse barrier as a function of mass M or, equivalently, of the variance σ2(M). Several such barriers based on the spherical, Zel'dovich, and ellipsoidal collapse models have been extensively discussed. Using large-scale cosmological simulations, we show that the relation between the linear overdensity and the mass variance for regions that collapse to form halos by the present epoch resembles expectations from dynamical models of ellipsoidal collapse. However, we also show that using such a collapse barrier with the excursion set ansatz predicts a halo mass function inconsistent with that measured directly in cosmological simulations. This inconsistency demonstrates a failure of the excursion set ansatz as a physical model for halo collapse. We discuss implications of our results for understanding the collapse epoch for halos as a function of mass, and avenues for improving consistency between analytical models for the collapse epoch and the results of cosmological simulations.

AB - Our heuristic understanding of the abundance of dark matter halos centers around the concept of a density threshold, or "barrier," for gravitational collapse. If one adopts the ansatz that regions of the linearly evolved density field smoothed on mass scale M with an overdensity that exceeds the barrier will undergo gravitational collapse into halos of mass M, the corresponding abundance of such halos can be estimated simply as a fraction of the mass density satisfying the collapse criterion divided by the mass M. The key ingredient of this ansatz is therefore the functional form of the collapse barrier as a function of mass M or, equivalently, of the variance σ2(M). Several such barriers based on the spherical, Zel'dovich, and ellipsoidal collapse models have been extensively discussed. Using large-scale cosmological simulations, we show that the relation between the linear overdensity and the mass variance for regions that collapse to form halos by the present epoch resembles expectations from dynamical models of ellipsoidal collapse. However, we also show that using such a collapse barrier with the excursion set ansatz predicts a halo mass function inconsistent with that measured directly in cosmological simulations. This inconsistency demonstrates a failure of the excursion set ansatz as a physical model for halo collapse. We discuss implications of our results for understanding the collapse epoch for halos as a function of mass, and avenues for improving consistency between analytical models for the collapse epoch and the results of cosmological simulations.

KW - Dark matter

KW - Galaxies: formation

KW - Galaxies: halos

KW - Methods: N-body simulations

UR - http://www.scopus.com/inward/record.url?scp=70350685301&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350685301&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/696/1/636

DO - 10.1088/0004-637X/696/1/636

M3 - Article

AN - SCOPUS:70350685301

VL - 696

SP - 636

EP - 652

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

ER -