470 Numerical simulations in cosmology
an intermediate case where both profiles provide equally good fits (similar to the
analysis of halo A).
Note that there seems to be real deviations in the parameters of halos of
the same mass. Halos B and D have the same virial radii and nearly the same
circular velocities, yet their concentrations are different by 30%. We find the
same differences in estimates ofC 1 / 5 concentrations, which do not depend on the
specifics of an analytic fit. The central slope at around 1 kpc also changes from
halo to halo.
15.4.4.3 Summary
In this section we have given a review of some of the internal properties of DM
halos focusing mostly on their profiles and concentrations. Our results are mostly
based on simulations done with the ART code, which is capable of handling
particles with different masses, variable force and time resolution. In runs with the
highest resolution, the code achieved (formal) dynamical range of 2^17 =131 072
with 500 000 steps for particles at the highest level of resolution.
Our conclusions regarding the convergence of the profiles differ from those
of Mooreet al(1998). If we take into account only the radii, at which we believe
the numerical effects (the force resolution, the resolution of initial perturbations
and two-body scattering) to be small, then we find that the slope and amplitude
of the density do not change when we change the force and mass resolution. This
result is consistent with what was found in simulations of the ‘Santa Barbara’
cluster (Frenket al1999): at a fixedresolvedscale the results do not change as
the resolution increases. For the ART code the results converged at four times
the formal force resolution and more than 200 particles. These convergence
limits very likely depend on the particular code used and on the duration of the
integration.
We reproduce Mooreet al’s results regarding convergence and the results
from Kravtsovet al(1998) regarding shallow central profiles, but only when
we considered points inside unresolved scales. We conclude that those results
followed from an overly optimistic interpretation of the numerical accuracy of the
simulations.
For the galaxy-size halos considered in this section with massesMvir =
7 × 1011 h−^1 M to 2× 1012 h−^1 M and concentrationsC=9–17 both the NFW
profile,ρ∝r−^1 ( 1 +r)−^2 , and the Mooreet alprofile,ρ∝r−^1.^5 ( 1 +r^1.^5 )−^1 ,
give good fits with an accuracy of about 10% for radii not smaller than 1% of the
virial radius. None of the profiles is significantly better than the other.
Halos with the same mass may have different profiles. No matter what profile
is used—NFW or Mooreet al—there is no universal profile: halo mass does not
yet define the density profile. Nevertheless, the universal profile is an extremely
useful notion which should be interpreted as the general trendC(M)of halos with
a larger mass to have a lower concentration. Deviations from the generalC(M)
are real and significant (Bullocket al2001). It is not yet clear but it seems very