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    An Empirical Mass Function Distribution

    265666.pdf (1.418Mb)
    Access Status
    Open access
    Authors
    Murray, Steven
    Robotham, A.
    Power, C.
    Date
    2018
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Murray, S. and Robotham, A. and Power, C. 2018. An Empirical Mass Function Distribution. Astrophysical Journal. 855 (1): Article No 5.
    Source Title
    Astrophysical Journal
    DOI
    10.3847/1538-4357/aaa552
    ISSN
    0004-637X
    School
    Curtin Institute of Radio Astronomy (Physics)
    Remarks

    Copyright © 2018 The American Astronomical Society. All rights reserved.

    URI
    http://hdl.handle.net/20.500.11937/67207
    Collection
    • Curtin Research Publications
    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 ${L}_{\star }$ galaxies. Motivated by the proven accuracy of Press–Schechter-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}\mbox{--}{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 ${L}_{\star }$. 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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