An Empirical Mass Function Distribution
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 t...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Institute of Physics Publishing
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/67207 |
| _version_ | 1848761504319406080 |
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| author | Murray, Steven Robotham, A. Power, C. |
| author_facet | Murray, Steven Robotham, A. Power, C. |
| author_sort | Murray, Steven |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T10:32:43Z |
| format | Journal Article |
| id | curtin-20.500.11937-67207 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:32:43Z |
| publishDate | 2018 |
| publisher | Institute of Physics Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-672072018-09-21T01:56:35Z An Empirical Mass Function Distribution Murray, Steven Robotham, A. Power, C. 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. 2018 Journal Article http://hdl.handle.net/20.500.11937/67207 10.3847/1538-4357/aaa552 Institute of Physics Publishing fulltext |
| spellingShingle | Murray, Steven Robotham, A. Power, C. An Empirical Mass Function Distribution |
| title | An Empirical Mass Function Distribution |
| title_full | An Empirical Mass Function Distribution |
| title_fullStr | An Empirical Mass Function Distribution |
| title_full_unstemmed | An Empirical Mass Function Distribution |
| title_short | An Empirical Mass Function Distribution |
| title_sort | empirical mass function distribution |
| url | http://hdl.handle.net/20.500.11937/67207 |