Density Profiles and Substructure of Dark Matter Halos: Converging Results at Ultra‐High Numerical Resolution

Abstract

Can dissipationless N-body simulations be used to reliably determine the structural and substructure properties of dark matter halos? A large simulation of a galaxy cluster in a cold dark matter universe is used to increase the force and mass resolution of current "high resolution simulations" by almost an order of magnitude to examine the convergence of the important physical quantities. The cluster contains ∼ 5 million particles within the final virial radius, R vir ≃ 2 Mpc (with H 0 = 50 Km s −1 Mpc −1 ), and is simulated using a force resolution of 1.0 kpc (≡ 0.05% of R vir ); the final virial mass is 4.3 10 14 M ⊙ , equivalent to a circular velocity v circ ≡ (GM/R) 1/2 ≃ 1000 km s −1 at the virial radius. The central density profile has a logarithmic slope of -1.5, identical to lower resolution studies of the same halo, indicating that the profiles measured from simulations of this resolution have converged to the "physical" limit down to scales of a few kpc (∼ 0.2% of R vir ). Also the abundance and properties of substructure are consistent with those derived from lower resolution runs; from small to large galaxy scales (v circ > 100 km s −1 , m > 10 11 M ⊙ ), the circular velocity function and the mass function of substructures can be approximated by power laws with slopes ∼ −4 and ∼ −2 respectively. At the current resolution, overmerging -a numerical effect that leads to structureless virialized halos in low-resolution N -body simulations -seems to be globally unimportant for substructure halos with circular velocities v circ > 100 km s −1 (∼ 10% of the cluster's v circ ). We can identify subhalos orbiting in the very central region of the cluster (R ∼ < 100 kpc) and we can trace most of the cluster progenitors from high redshift to the present. The object at the cluster center (the dark matter analog of a cD galaxy) is assembled between z = 3 and z = 1 from the merging of a dozen halos with v circ ∼ > 300 km s −1 . Tidal stripping and halo-halo collisions decrease the mean circular velocity of the substructure halos by ≈ 20% over a 5 billion year period. We use the sample of 2000 substructure halos to explore the possibility of biases using galactic tracers in clusters: the velocity dispersions of the halos globally agree with the dark matter within ∼ < 10%, but the halos are spatially anti-biased, and in the very central region of the cluster (R/R vir < 0.3), they show positive velocity bias (b v ≡ σ v3D,halos /σ v3D,DM ≃ 1.2-1.3); however, this effect appears to depend on numerical resolution.

The Galactic center as a dark matter gamma-ray source

“…Dynamical measurements show that dark matter is, in the Galactic center region, just a subdominant component with respect to baryonic matter, but lack the Table 2 Values of J(0) ∆Ω [29]) as the galactocentric distance r → 0. The corresponding values of J , and hence of N χ are listed in the second column of Table 2 assuming, as commonly done, that the dark matter density at the Sun's galactocentric distance is equal to 0.3 GeV cm −3 .…”

Detecting the dark matter annihilation at the ground EAS detectors

“…The index of the central cusp at about 1.5 is also favored by following higher resolution simulations [42]. For the Moore profile we have r s = r −2 /0.63.…”

“…Taking the power index of the differential mass function smaller than -2 makes the fraction of the total mass enclosed in subhalos insensitive to the mass of the minimal subhalo we take. The mass fraction of subhalos estimated in the literature is around between 5 percent to 20 percent [16,17,35]. In this work we will always take the differential index of −1.9 and the mass fraction of substructures as 10 percent.…”

The Galactic center as a dark matter gamma-ray source

“…Dynamical measurements show that dark matter is, in the Galactic center region, just a subdominant component with respect to baryonic matter, but lack the [29]) as the galactocentric distance r → 0. The corresponding values of J , and hence of N χ are listed in the second column of Table 2 assuming, as commonly done, that the dark matter density at the Sun's galactocentric distance is equal to 0.3 GeV cm −3 .…”