Modelling the mass accretion histories of dark matter haloes using a Gamma formalism

Antonios Katsianis; Xiaohu Yang; Matthew Fong; Jie Wang

doi:10.1093/mnras/stad1498

paper

Modelling the mass accretion histories of dark matter haloes using a Gamma formalism

arXiv:2305.17772 · doi:10.1093/mnras/stad1498

Abstract

We present a physical model of the Mass Accretion Histories (MAH) of haloes in concordance with the {\it observed} cosmic star formation rate density (CSFRD). We model the MAHs of dark matter haloes using a Gamma ( $Γ$ ) functional form: $M_{h} (T) = \frac{M _{0}}{f _{0}} \times \frac{γ ( α _{h} , β _{h} \times ( T - T h ))}{Γ ( α _{h} )}$ , where $M_{0}$ is the halo mass at present time, $T$ is time, $α_{h}$ and $β_{h}$ are parameters we explore, $f_{0}$ is the percentage of the mass of the halo at z = 0 with respect to the final mass of the halo achieved at $T = \infty$ . We use the MAHs of haloes obtained from cosmological simulations and analytical models to constrain our model. $f_{0}$ can be described by a power-law ( $f_{0} = 1 - c \times M_{0}^{d}$ ). Haloes with small masses have already on average attained most of their final masses. The average $< f_{0} >$ of haloes in the Universe is $> 0.95$ pointing to the direction that the cosmic MAH/CSFRD is saturated at our era. The average $< β_{h} >$ parameter (the depletion rate of the available dark matter for halo growth) is related to the dynamical timescales of haloes. The $α$ parameter is a power-law index of $M_{0}$ and represents the early growth a halo experiences before the expansion of the Universe starts to slow it down. Finally, $T_{h}$ (the time that marks the co-evolution/growth of galaxies and haloes after the Big Bang) is found to be 150-300 million years.

18 pages, 8 figures, Accepted at MNRAS

Modelling the mass accretion histories of dark matter haloes using a Gamma formalism

Abstract

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