466 Numerical simulations in cosmology
Figure 15.20.Fits of the NFW and Mooreet alhalo profiles to the profile of halo A 1
(bottom panel). Thetop panelshows the fractional deviations of the analytic fits from the
numerical profile. Note that both analytical profiles fit the numerical profile equally well:
fractional deviations are smaller than 20% over almost three decades in the radius.
In order to judge which profile provides a better description of the simulated
profiles we fitted the NFW and Mooreet alanalytical profiles. Figure 15.20
presents the results of the fits and shows that both profiles fit the numerical profile
equally well: fractional deviations of the fitted profiles from the numerical one are
smaller than 20% over almost three decades in the radius. It is thus clear that the
fact that the numerical profile has a slope steeper than−1 at the scale of∼ 0. 01 rvir
does not mean that a good fit of the NFW profile (or even analytical profiles with
shallower asymptotic slopes) cannot be obtained.
There is certainly a certain degree of degeneracy in fitting various analytic
profiles to the numerical results. Figure 15.21 illustrates this further by showing
results of fitting profiles (full curves) of the formρ(r) ∝ (r/r 0 )−γ[ 1 +
(r/r 0 )α]−(β−α)/γ tothe same(halo A 1 ) simulated halo profile shown as full