A Stochastic Theory of the Hierarchical Clustering I. Halo Mass Function

Abstract

We present a new theory for the hierarchical clustering of dark matter (DM) halos based on stochastic differential equations, that constitutes a change of perspective with respect to existing frameworks (e.g., the excursion set approach); this work is specifically focused on the halo mass function. First, we present a stochastic differential equation that describes fluctuations in the mass growth of DM halos, as driven by a multiplicative white (Gaussian) noise dependent on the spherical collapse threshold and on the power spectrum of DM perturbations. We demonstrate that such a noise yields an average drift of the halo population toward larger masses, that quantitatively renders the standard hierarchical clustering. Then, we solve the Fokker-Planck equation associated to the stochastic dynamics, and obtain the Press & Schechter mass function as a (stationary) solution. Moreover, generalizing our treatment to a mass-dependent collapse threshold, we obtain an exact analytic solution capable of fitting remarkably well the N-body mass function over a wide range in mass and redshift. All in all, the new perspective offered by the theory presented here can contribute to better understand the gravitational dynamics leading to the formation, evolution and statistics of DM halos across cosmic times.

arXiv comment12 pages, 3 figures. Accepted by ApJ

References in corpus (36)

• Large scale bias and the peak background split
• Hierarchical Galaxy Formation
• Toward a halo mass function for precision cosmology: the limits of universality
• Mass function of dark matter halos
• An analytic model for the spatial clustering of dark matter haloes
• An excursion set model of hierarchical clustering: Ellipsoidal collapse and the moving barrier
• The Connection between Galaxies and their Dark Matter Halos
• Theoretical Challenges in Galaxy Formation
• Precision Determination of the Mass Function of Dark Matter Halos
• A hierarchy of voids: Much ado about nothing
• Accurate universal models for the mass accretion histories and concentrations of dark matter halos
• Dark matter and cosmic structure
• How to Plant a Merger Tree
• Generating Dark Matter Halo Merger Trees
• The halo mass function through the cosmic ages
• The Current Status of Galaxy Formation
• Simulating the Universe with MICE: The abundance of massive clusters
• Mass Function Predictions Beyond LCDM
• The abundance of voids and the excursion set formalism
• Merger Rates of Dark-Matter Haloes
• The Halo Mass Function from Excursion Set Theory. II. The Diffusing Barrier
• Generating Merger Trees for Dark Matter Haloes: A Comparison of Methods
• One step beyond: The excursion set approach with correlated steps
• An improved model for the formation times of dark matter haloes
• The forest of merger history trees associated with the formation of dark matter halos
• Self-Consistent Theory of Halo Mergers
• On Random Walks with a General Moving Barrier
• Toward a Universal Formulation of the Halo Mass Function
• How to Grow a Healthy Merger Tree
• Halo abundances and counts-in-cells: The excursion set approach with correlated steps
• Constraining the halo mass function with observations
• Statistics of Dark Matter Halos from the Excursion Set Approach
• The halo mass function of late-type galaxies from HI kinematics
• The halo mass function in alternative dark matter models
• Towards a Model-Independent Measurement of the Halo Mass Function with Observables
• Universality of the halo mass function in screened gravity theories

Cited by in corpus (6)

• Dark Matter in Fractional Gravity I: Astrophysical Tests on Galactic Scales
• Tomography-based observational measurements of the halo mass function via the submillimeter magnification bias
• A Stochastic Theory of the Hierarchical Clustering II. Halo progenitor mass function and large-scale bias
• Massive Black Hole Mergers
• 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