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Dark matter halo mass functions and density profiles from mass and energy cascade
Halo abundance and structure play a central role for modeling structure formation and evolution. Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of −4/3) based on the mass and energy cascade theory in dar...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Nature Publishing Group UK
2023
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10545740/ https://www.ncbi.nlm.nih.gov/pubmed/37783702 http://dx.doi.org/10.1038/s41598-023-42958-6 |
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author | Xu, Zhijie (Jay) |
author_facet | Xu, Zhijie (Jay) |
author_sort | Xu, Zhijie (Jay) |
collection | PubMed |
description | Halo abundance and structure play a central role for modeling structure formation and evolution. Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of −4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time [Formula: see text] . First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with [Formula: see text] , where [Formula: see text] is the halo mass and [Formula: see text] is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different [Formula: see text] for haloes below and above a critical mass scale [Formula: see text] , i.e. a double-[Formula: see text] halo mass function. Second, a double-[Formula: see text] density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time [Formula: see text] , where [Formula: see text] is the gravitational potential and r is the particle distance to halo center. Theory predicts [Formula: see text] that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the [Formula: see text] scaling law ([Formula: see text] ) on small scales. Theory predicts the halo number density scales with halo mass as [Formula: see text] , while the halo mass density scales as [Formula: see text] . Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles. |
format | Online Article Text |
id | pubmed-10545740 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-105457402023-10-04 Dark matter halo mass functions and density profiles from mass and energy cascade Xu, Zhijie (Jay) Sci Rep Article Halo abundance and structure play a central role for modeling structure formation and evolution. Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of −4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time [Formula: see text] . First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with [Formula: see text] , where [Formula: see text] is the halo mass and [Formula: see text] is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different [Formula: see text] for haloes below and above a critical mass scale [Formula: see text] , i.e. a double-[Formula: see text] halo mass function. Second, a double-[Formula: see text] density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time [Formula: see text] , where [Formula: see text] is the gravitational potential and r is the particle distance to halo center. Theory predicts [Formula: see text] that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the [Formula: see text] scaling law ([Formula: see text] ) on small scales. Theory predicts the halo number density scales with halo mass as [Formula: see text] , while the halo mass density scales as [Formula: see text] . Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles. Nature Publishing Group UK 2023-10-02 /pmc/articles/PMC10545740/ /pubmed/37783702 http://dx.doi.org/10.1038/s41598-023-42958-6 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Xu, Zhijie (Jay) Dark matter halo mass functions and density profiles from mass and energy cascade |
title | Dark matter halo mass functions and density profiles from mass and energy cascade |
title_full | Dark matter halo mass functions and density profiles from mass and energy cascade |
title_fullStr | Dark matter halo mass functions and density profiles from mass and energy cascade |
title_full_unstemmed | Dark matter halo mass functions and density profiles from mass and energy cascade |
title_short | Dark matter halo mass functions and density profiles from mass and energy cascade |
title_sort | dark matter halo mass functions and density profiles from mass and energy cascade |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10545740/ https://www.ncbi.nlm.nih.gov/pubmed/37783702 http://dx.doi.org/10.1038/s41598-023-42958-6 |
work_keys_str_mv | AT xuzhijiejay darkmatterhalomassfunctionsanddensityprofilesfrommassandenergycascade |