Conditional Mass Functions and Merger Rates of Dark Matter Halos in the Ellipsoidal Collapse Model

Abstract

Analytic models based on spherical and ellipsoidal gravitational collapse have been used to derive the mass functions of dark matter halos and their progenitors (the conditional mass function). The ellipsoidal model generally provides a better match to simulation results, but there has been no simple analytic expression in this model for the conditional mass function that is accurate for small time steps, a limit that is important for generating halo merger trees and computing halo merger rates. We remedy the situation by deriving accurate analytic formulae for the first-crossing distribution, the conditional mass function, and the halo merger rate in the ellipsoidal collapse model in the limit of small look-back times. We show that our formulae provide a closer match to the Millennium simulation results than those in the spherical collapse model and the ellipsoidal model of Sheth & Tormen (2002).

5 pages, 3 figures, accepted by MNRAS letters

References in corpus (4)

• Generating Dark Matter Halo Merger Trees
• The Nearly Universal Merger Rate of Dark Matter Haloes in Lambda-CDM Cosmology
• Constructing Merger Trees that Mimic N-Body Simulations
• The statistical properties of LCDM halo formation

Cited by in corpus (21)

• Merger Rates of Dark-Matter Haloes
• Generating Merger Trees for Dark Matter Haloes: A Comparison of Methods
• Coming of Age in the Dark Sector: How Dark Matter Haloes grow their Gravitational Potential Wells
• Simulating Subhalos at High Redshift: Merger Rates, Counts, and Types
• H_2 Suppression with Shocking Inflows: Testing a Pathway for Supermassive Black Hole Formation
• A high precision semi-analytic mass function
• The effect of baryonic streaming motions on the formation of the first supermassive black holes
• Massive black hole and Population III galaxy formation in over-massive dark matter halos with violent merger histories
• Universal Merger Histories of Dark-Matter Haloes
• The Density Contrast of the Shapley Supercluster
• Mass accretion rates of clusters of galaxies: CIRS and HeCS
• The Universal Specific Merger Rate of Dark Matter Halos
• Merger history trees of dark matter haloes in moving barrier models
• GECO: Galaxy Evolution COde - A new semi-analytical model of galaxy formation
• Galaxy cluster mass accretion rates from IllustrisTNG
• An IllustrisTNG View of the Caustic Technique for Galaxy Cluster Mass Estimation
• Starlight from JWST: Implications for star formation and dark matter models
• Dark matter halo assembly bias: environmental dependence in the non-Markovian excursion set theory
• Mass accretion rates of the HectoMAP clusters of galaxies
• Massive Black Hole Mergers
• A Conditional Abundance Matching Method of Extending Simulated Halo Merger Trees to Resolve Low-Mass Progenitors and Sub-halos