Sub-structure of Dark-Matter Halos Lecture Sub-structure of Dark-Matter Halos

N-body simulation of Halo Formation

Origin of Halo Density Profile? =1 2 3 r ρ Varying slope -α Navarro & Taylor: r Hayashi, Navarro et al.

Phase-Space Density Vlasov eq. Poisson eq. Distribution function of f: V(f)df = volume of phase space occupied by f in the range (f,f+df)

Measuring f(x,v) using an adaptive “grid” Delaunay Tesselation particle i Arad, Dekel & Klypin

PDF of Phase-Space Density v∝f-2.5 V(f) f Arad, Dekel & Klypin

Dwarf v(f) f

Dwarf v(f) f

Cluster v(f) f

PDF of Phase-Space Density V(f) 109Mʘ 1012Mʘ 1015Mʘ f Arad, Dekel & Klypin

V(f) related to ρ(r)? if e.g., spherical & isotropic

Halo Phase-Space Density Real Density Phase-Space Density

Halo Phase-Space Density Real Density Phase-Space Density

Profiles in Real Space and Phase Space f(r) ρ(r) radius radius

Is v(f)∝f-2.5 determined by substructure? ΛCDM No short waves Moore et al. Real-Space Density

Phase-Space density ΛCDM No short waves

Phase-Space Density Profile ΛCDM No short waves f(r) f(r) radius radius

Same power law v(f)? no short waves v∝f-3.2 ΛCDM v∝f-2.5 v(f) f

Additive Contribution of Subhalos v∝f-2.5 each subhalo is not a power law

The Two Most Massive Subhalos v∝f-2.5

Background Halo – Subhalos Removed The background halo is steeper v∝f-3 v∝f-2.5 leftover substructure

Background Halo real space phase space

Adding up Sub-halos ρ(r)→v(f) f-2 halo mass function: v∝f-2.5 v(f) from a universal density profile ρ(r)→v(f) f-2.8 f-2 v∝f-2.5 halo mass function: sum of halos f v(f) Scaling of halos: f subs/host Boylan-Kolchin, Ma, Arad, Dekel f

Tentative Conclusions In hierarchical clustering, robust PDF: v(f)∝f-2.5 doesn’t depend on power-spectrum slope, or on method of simulation The power-law v(f) is driven by substructure. How exactly? Yet to be understood ! Phase-space density is a unique tool for studying substructure and its evolution Adding up small CDM halos leads to v(f)∝f-2.5 ? How robust? How dependent on subhalo density profile and mass function?

Satellite merging into a halo apo 0 peri 1 apo 1 apo 2 apo 3 final Dekel, Devor & Hetzroni 2003