The Halo Mass Function from Excursion Set Theory. II. The Diffusing Barrier

Abstract

In excursion set theory the computation of the halo mass function is mapped into a first-passage time process in the presence of a barrier, which in the spherical collapse model is a constant and in the ellipsoidal collapse model is a fixed function of the variance of the smoothed density field. However, N-body simulations show that dark matter halos grow through a mixture of smooth accretion, violent encounters and fragmentations, and modeling halo collapse as spherical, or even as ellipsoidal, is a significant oversimplification. We propose that some of the physical complications inherent to a realistic description of halo formation can be included in the excursion set theory framework, at least at an effective level, by taking into account that the critical value for collapse is not a fixed constant ${\delta }_c$, as in the spherical collapse model, nor a fixed function of the variance $\sigma$ of the smoothed density field, as in the ellipsoidal collapse model, but rather is itself a stochastic variable, whose scatter reflects a number of complicated aspects of the underlying dynamics. Solving the first-passage time problem in the presence of a diffusing barrier we find that the exponential factor in the Press-Schechter mass function changes from $\exp \{-{\delta }_c^2/2{\sigma }^2\}$ to $\exp \{-a{\delta }_c^2/2{\sigma }^2\}$, where $a=1/(1+D_B)$ and $D_B$ is the diffusion coefficient of the barrier. The numerical value of $D_B$, and therefore the corresponding value of $a$, depends among other things on the algorithm used for identifying halos. We discuss the physical origin of the stochasticity of the barrier and we compare with the mass function found in N-body simulations, for the same halo definition.[Abridged]

7 pages, 5 figures. v3: significant conceptual improvements. More detailed comparison with N-body simulations. References added

References in corpus (12)

• Toward a halo mass function for precision cosmology: the limits of universality
• The halo mass function from the dark ages through the present day
• Halo Assembly Bias in Hierarchical Structure Formation
• The Excursion Set Theory of Halo Mass Functions, Halo Clustering, and Halo Growth
• The Halo Mass Function: High-Redshift Evolution and Universality
• Halo mass function and scale-dependent bias from N-body simulations with non-Gaussian initial conditions
• Large-scale non-Gaussian mass function and halo bias: tests on N-body simulations
• Collapse Barriers and Halo Abundance: Testing the Excursion Set Ansatz
• The Structure of Halos: Implications for Group and Cluster Cosmology
• Environmental dependence in the ellipsoidal collapse model
• Why does the clustering of haloes depend on their formation history
• The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances

Cited by in corpus (92)

• Formation of Galaxy Clusters
• Large-Scale Galaxy Bias
• The Phenomenology of Right Handed Neutrinos
• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity
• One step beyond: The excursion set approach with correlated steps
• The Halo Mass Function from Excursion Set Theory. III. Non-Gaussian Fluctuations
• Excursion set peaks: a self-consistent model of dark halo abundances and clustering
• High-Redshift Galaxies from Early JWST Observations: Constraints on Dark Energy Models
• Spherical collapse and halo mass function in f(R) theories
• Nonlinear structure formation in Nonlocal Gravity
• On the Primordial Black Hole Mass Function for Broad Spectra
• Primordial Black Holes from Broad Spectra: Abundance and Clustering
• Modelling Void Abundance in Modified Gravity
• Primordial non-Gaussianity in the large scale structure of the Universe
• Toward a Universal Formulation of the Halo Mass Function
• A double take on early and interacting dark energy from JWST
• Cluster abundance in chameleon $f(R)$ gravity I: toward an accurate halo mass function prediction
• Spherical collapse of dark energy with an arbitrary sound speed
• Caught in the cosmic web: Environmental effect on halo concentrations, shape, and spin
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Halo abundances and counts-in-cells: The excursion set approach with correlated steps
• Voids in Modified Gravity Reloaded: Eulerian Void Assignment
• The clustering of galaxies and galaxy clusters: constraints on primordial non-Gaussianity from future wide-field surveys
• Excursion Set Halo Mass Function and Bias in a Stochastic Barrier Model of Ellipsoidal Collapse
• Joint halo mass function for modified gravity and massive neutrinos I: simulations and cosmological forecasts
• The Bias and Mass Function of Dark Matter Halos in Non-Markovian Extension of the Excursion Set Theory
• A high precision semi-analytic mass function
• Imprints of primordial non-Gaussianity on the number counts of cosmic shear peaks
• The Imprint of f(R) Gravity on Non-Linear Structure Formation
• Excursion Set Theory for generic moving barriers and non-Gaussian initial conditions
• An Improved Calculation of the Non-Gaussian Halo Mass Function
• Excursion Sets and Non-Gaussian Void Statistics
• A Study of High-Order Non-Gaussianity with Applications to Massive Clusters and Large Voids
• Estimating f_NL and g_NL from Massive High-Redshift Galaxy Clusters
• Testing spherical evolution for modelling void abundances
• Excursion set theory for modified gravity: Eulerian versus Lagrangian environments
• The importance of stepping up in the excursion set approach
• Self-consistency of the Excursion Set Approach
• Conditional Probabilities in the Excursion Set Theory. Generic Barriers and non-Gaussian Initial Conditions
• Measuring nonlocal Lagrangian peak bias
• Large Scale Anisotropic Bias from Primordial non-Gaussianity
• Computation of the Halo Mass Function Using Physical Collapse Parameters: Application to Non-Standard Cosmologies
• The Halo Void (Dust) Model of Large Scale Structure
• Statistics of Dark Matter Halos from the Excursion Set Approach
• Primordial Non-Gaussianity Estimation using 21 cm Tomography from the Epoch of Reionization
• The Effect of Local non-Gaussianity on the Matter Bispectrum at Small Scales
• Non-Gaussianity and Excursion Set Theory: Halo Bias
• Stochastic bias in multi-dimensional excursion set approaches
• Primordial Non-Gaussianity and Reionization
• Fixing a Rigorous Formalism for the Accurate Analytic Derivation of Halo Properties
• The scale-dependent signature of primordial non-Gaussianity in the large-scale structure of cosmic reionization
• Non-Gaussian Halo Mass Function and Non-Spherical Halo Collapse: Theory vs. Simulations
• Halo statistics in non-Gaussian cosmologies: the collapsed fraction, conditional mass function, and halo bias from the path-integral excursion set method
• Small scale structures in coupled scalar field dark matter
• Small-scale clustering of Primordial Black Holes: cloud-in-cloud and exclusion effects
• The effects of primordial non-Gaussianity on giant-arc statistics
• Alignments of the Galaxies in and around the Virgo Cluster with the Local Velocity Shear
• The Extreme Tail of the Non-Gaussian Mass Function
• Primordial Bispectrum and Trispectrum Contributions to the Non-Gaussian Excursion Set Halo Mass Function with Diffusive Drifting Barrier
• Isotropic extragalactic flux from dark matter annihilations: lessons from interacting dark matter scenarios
• Peaks and dips in Gaussian random fields: a new algorithm for the shear eigenvalues, and the excursion set theory
• A Stochastic Theory of the Hierarchical Clustering I. Halo Mass Function
• Excursion Set Theory for Correlated Random Walks
• Fingerprints of Anomalous Primordial Universe on the Abundance of Large Scale Structures
• Matrix Formalism of Excursion Set Theory: A new approach to statistics of dark matter halo counting
• An Extended Zel'dovich Model for the Halo Mass Function
• Imprint of primordial non-Gaussianity on dark matter halo profiles
• Choose to smooth: Gaussian streaming with the truncated Zel'dovich approximation
• Dark matter halo assembly bias: environmental dependence in the non-Markovian excursion set theory
• A Stochastic Theory of the Hierarchical Clustering II. Halo progenitor mass function and large-scale bias
• Scale-dependent bias from an inflationary bispectrum: the effect of a stochastic moving barrier
• Constraining the Neutrino Mass with the Drifting Coefficient of the Field Cluster Mass Function
• Tidal shear and the consistency of microscopic Lagrangian halo approaches
• Non-linear matter power spectrum without screening dynamics modelling in $f(R)$ gravity
• Breaking the Dark Degeneracy with the Drifting Coefficient of the Field Cluster Mass Function
• The Diffusion Coefficient of the Splashback Mass Function as a Probe of Cosmology
• Mass assembly history of dark matter halos in the light of $H_0$ tension
• Evolution of the Deterministic Collapse Barrier of the Field Clusters as a Probe of Cosmology
• Accurate halo mass functions from the simplest excursion set theory
• Voids and Halos in Voids statistics as a probe of the Expansion History of the Universe
• Stochasticity in halo formation and the excursion set approach
• Statistical Properties of Supercluster-Like Filaments from Cosmological Simulations
• The Splashback Mass Function in the Presence of Massive Neutrinos
• The Effect of Primordial Anti-Biasing on the Local Measurement of the Key Cosmological Parameters
• Statistical Decoupling of Lagrangian Fluid Parcel in Newtonian Cosmology
• Towards cosmology with Void Lensing: how to find voids sensitive to weak-lensing and numerically interpret them
• The Extended Zel'dovich Mass Functions of Clusters and Isolated Clusters in the Presence of Primordial Non-Gaussianity
• A revisited Correction to the Halo Mass Function for local-type Primordial non-Gaussianity
• Kinematic effects of the velocity fluctuations for dark halos population in LCDM model
• Segmenting proto-halos with vision transformers
• Luminosity Function of Galaxies in Voids: A Modification Inspired by Excursion Set Theory