### Abstract

The halo mass function, encoding the comoving number density of dark matter halos of a given mass, plays a key role in understanding the formation and evolution of galaxies. As such, it is a key goal of current and future deep optical surveys to constrain the mass function down to mass scales that typically host L_{∗} galaxies. Motivated by the proven accuracy of PressSchechter-type mass functions, we introduce a related but purely empirical form consistent with standard formulae to better than 4% in the medium-mass regime, 10^{10}-10^{13} h^{-1} M_{⊙}. In particular, our form consists of four parameters, each of which has a simple interpretation, and can be directly related to parameters of the galaxy distribution, such as L_{∗}. Using this form within a hierarchical Bayesian likelihood model, we show how individual mass-measurement errors can be successfully included in a typical analysis, while accounting for Eddington bias. We apply our form to a question of survey design in the context of a semi-realistic data model, illustrating how it can be used to obtain optimal balance between survey depth and angular coverage for constraints on mass function parameters. Open-source Python and R codes to apply our new form are provided at http://mrpy.readthedocs.org and https://cran.r-project.org/web/packages/tggd/index.html respectively.

Language | English |
---|---|

Article number | 5 |

Journal | Astrophysical Journal |

Volume | 855 |

Issue number | 1 |

DOIs | |

State | Published - 1 Mar 2018 |

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*Astrophysical Journal*,

*855*(1), [5]. DOI: 10.3847/1538-4357/aaa552

}

*Astrophysical Journal*, vol. 855, no. 1, 5. DOI: 10.3847/1538-4357/aaa552

**An Empirical Mass Function Distribution.** / Murray, S. G.; Robotham, A. S.G.; Power, C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An Empirical Mass Function Distribution

AU - Murray,S. G.

AU - Robotham,A. S.G.

AU - Power,C.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - The halo mass function, encoding the comoving number density of dark matter halos of a given mass, plays a key role in understanding the formation and evolution of galaxies. As such, it is a key goal of current and future deep optical surveys to constrain the mass function down to mass scales that typically host L∗ galaxies. Motivated by the proven accuracy of PressSchechter-type mass functions, we introduce a related but purely empirical form consistent with standard formulae to better than 4% in the medium-mass regime, 1010-1013 h-1 M⊙. In particular, our form consists of four parameters, each of which has a simple interpretation, and can be directly related to parameters of the galaxy distribution, such as L∗. Using this form within a hierarchical Bayesian likelihood model, we show how individual mass-measurement errors can be successfully included in a typical analysis, while accounting for Eddington bias. We apply our form to a question of survey design in the context of a semi-realistic data model, illustrating how it can be used to obtain optimal balance between survey depth and angular coverage for constraints on mass function parameters. Open-source Python and R codes to apply our new form are provided at http://mrpy.readthedocs.org and https://cran.r-project.org/web/packages/tggd/index.html respectively.

AB - The halo mass function, encoding the comoving number density of dark matter halos of a given mass, plays a key role in understanding the formation and evolution of galaxies. As such, it is a key goal of current and future deep optical surveys to constrain the mass function down to mass scales that typically host L∗ galaxies. Motivated by the proven accuracy of PressSchechter-type mass functions, we introduce a related but purely empirical form consistent with standard formulae to better than 4% in the medium-mass regime, 1010-1013 h-1 M⊙. In particular, our form consists of four parameters, each of which has a simple interpretation, and can be directly related to parameters of the galaxy distribution, such as L∗. Using this form within a hierarchical Bayesian likelihood model, we show how individual mass-measurement errors can be successfully included in a typical analysis, while accounting for Eddington bias. We apply our form to a question of survey design in the context of a semi-realistic data model, illustrating how it can be used to obtain optimal balance between survey depth and angular coverage for constraints on mass function parameters. Open-source Python and R codes to apply our new form are provided at http://mrpy.readthedocs.org and https://cran.r-project.org/web/packages/tggd/index.html respectively.

KW - dark matter

KW - galaxies: halos

KW - methods: analytical

KW - methods: statistical

UR - http://www.scopus.com/inward/record.url?scp=85044042024&partnerID=8YFLogxK

U2 - 10.3847/1538-4357/aaa552

DO - 10.3847/1538-4357/aaa552

M3 - Article

VL - 855

JO - The Astrophysical Journal

T2 - The Astrophysical Journal

JF - The Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 5

ER -