PNNL

Abstract

Halo abundance and structure play a central role for understating the small scale challenges of ?CDM cosmology. Without relying on a spherical or elliptical collapse model, we analytically derive the halo mass function and density profile based on the mass and energy cascade in dark matter flow. The hierarchical halo structure formation from gravitational collapse can be equivalent to a random walk process with a position-dependent waiting time tg. The inverse mass cascade leads to the random walk in halo mass space with tg?m-?r, where mr is the halo mass and ? is a halo geometry parameter. The corresponding Fokker-Planck solution gives rise to the analytical halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different ? for haloes below and above a critical mass scale m*h, i.e. a double-? mass function. Similarly, a double-? halo density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time tg?m-?r?r-?, where r is the halo size and mr?r5/3 from energy cascade. The Press-Schechter mass function and Einasto profile are just special cases of the proposed model. The small scale permanence can be identified due to the scale-independent rate of cascade, where halo density profiles of different halo mass and redshifts converge to the -4/3 scaling law (?h?r-4/3) on small scale. The halo number density scales with halo mass as ?m-1.9h, while halo mass density scales as ?m4/9h. Results are validated and compared against the large scale cosmological Illustris simulation. This new perspective provides a possible theory for the origin of halo mass function and density profile.