Virial halo mass function in the $Planck$ cosmology

Abstract

We study halo mass functions with high-resolution $N$-body simulations under a $\Lambda$CDM cosmology. Our simulations adopt the cosmological model that is consistent with recent measurements of the cosmic microwave backgrounds with the $Planck$ satellite. We calibrate the halo mass functions for $10^{8.5} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$} M_\mathrm{vir} / (h^{-1}M_\odot) \lower.5ex\hbox{$\; \buildrel < \over \sim \;$} 10^{15.0 - 0.45 \, z}$, where $M_{\mathrm{vir}}$ is the virial spherical overdensity mass and redshift $z$ ranges from $0$ to $7$. The halo mass function in our simulations can be fitted by a four-parameter model over a wide range of halo masses and redshifts, while we require some redshift evolution of the fitting parameters. Our new fitting formula of the mass function has a 5\%-level precision except for the highest masses at $z\le 7$. Our model predicts that the analytic prediction in Sheth $\&$ Tormen would overestimate the halo abundance at $z=6$ with $M_{\mathrm{vir}}=10^{8.5-10}{h}^{-1}{M}_{\odot }$ by $20-30\%$. Our calibrated halo mass function provides a baseline model to constrain warm dark matter (WDM) by high-$z$ galaxy number counts. We compare a cumulative luminosity function of galaxies at $z=6$ with the total halo abundance based on our model and a recently proposed WDM correction. We find that WDM with its mass lighter than $2.71\mathrm{keV}$ is incompatible with the observed galaxy number density at a $2\sigma$ confidence level.

19 pages, 11 figures, 2 tables. Accepted for publication in ApJ

References in corpus (13)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Transients from Initial Conditions in Cosmological Simulations
• The halo mass function from the dark ages through the present day
• Dark Matter Substructure in Numerical Simulations: A Tale of Discreteness Noise, Runaway Instabilities, and Artificial Disruption
• The Halo Mass Function: High-Redshift Evolution and Universality
• What mass are the smallest protohalos?
• Effects of cold dark matter decoupling and pair annihilation on cosmological perturbations
• SubHaloes going Notts: The SubHalo-Finder Comparison Project
• The abundance of (not just) dark matter haloes
• The Effect of Gas Physics on the Halo Mass Function
• The properties of "dark" ΛCDM halos in the Local Group
• Ruling out 3 keV warm dark matter using 21 cm-EDGES data

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• Dark Matter in Fractional Gravity I: Astrophysical Tests on Galactic Scales
• Constraining Cosmological Parameters using the Cluster Mass-Richness Relation
• A Multi-messenger view of Cosmic Dawn: Conquering the Final Frontier
• A Stochastic Theory of the Hierarchical Clustering III. The Non-universality and Non-stationarity of the Halo Mass Function
• Distinguishing thermal histories of dark matter from structure formation