An Empirical Mass Function Distribution

S. G. Murray, A. S.G. Robotham, C. Power

Research output: Contribution to journalArticle

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, 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.

LanguageEnglish
Article number5
JournalAstrophysical Journal
Volume855
Issue number1
DOIs
Publication statusPublished - 1 Mar 2018

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distribution functions
galaxies
halos
mass media
survey design
distribution
dark matter
coding
parameter

Cite this

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

In: Astrophysical Journal, Vol. 855, No. 1, 5, 01.03.2018.

Research output: Contribution to journalArticle

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