The Double Distribution
of Dark Matter Halos

How does the process of structure formation depend on the properties of the environment of forming structures? Does the mass function of structures in filaments differ from the mass function in filament knots? How does the state of the material surrounding and accreted by a collapsed object depend on the mass of the object and how does it evolve with time?

To seek analytical insight to such environment-related questions, we have extended the Press-Schechter mass function to include information on the environment of collapsed structures as well as their mass. We have used the random walk formalism to derive a double distribution of the number density of cosmic structures with respect to both mass and overdensity (or underdensity) of the local environment of each structure, defining the "local environment" in a mass-dependent way.

Some of the most exciting results are that at any redshift, and for each mass, there is a most probable "environment", which becomes more overdense with increasing structure mass. At the present epoch in the concordance universe, the most probable environment is a modest underdensity, for all objects below about 10¹⁴ solar masses ; thus, underdensities are preferentially populated by low-mass objects. The fraction of mass in underdensities increases with time, and in the concordance cosmology the present underdense mass fraction in objetcs of M > 10¹² solar masses is about 40%. These trends can be understood in terms of hierarchical clustering in which overdense regions are the site of vigorous merging that clears out low-mass objects, which then find their last refuge in underdensities.

Reference: Pavlidou, V., & Fields, B. D. 2005, PhysRevD, 71, 043510
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