Dark matter halos 459Figure 15.16.Velocity functions for isolated halos (squares) and for halos in groups and
clusters. Halos with mass less than 10^13 h−^1 M are used for the plots. (After Sigadet al
2000.)
15.4.3.2 Correlation between characteristic density and radius
The halo density profiles are approximated by the NFW profile:
ρ=ρ 0
(r/r 0 )[ 1 +r/r 0 ]^2. (15.18)
Kravtsovet al(1999) found the correlation between the two parameters of halos:
ρ 0 andrs. Figure 15.17 compares the results for the DM halos with those for
DM-dominated, LSB galaxies and dwarf galaxies. The halos are consistent with
observational data: smaller halos are denser.
15.4.3.3 Correlations between mass, concentration and redshift
Navarroet al(1997) argued that the halo profiles have a universal shape in the
sense that the profile is uniquely defined by the virial mass of the halo. Bullock
et al(2001) analysed concentrations of thousands of halos at different redshifts.
To some degree they confirm the conclusions of Navarroet al(1997): halo
concentration correlates with its mass. However, some significant deviations
were also found. There is no one-to-one relation between concentration and
mass. It appears the the universal profile should only be treated as a trend:
the halo concentration does increase as the halo mass decreases, but there are
large deviations for individual halos from that ‘universal’ shape. Halos have an
intrinsic scatter of concentration: at the 1σlevel halos with the same mass have
(logcvir)= 0 .18 or, equivalently,Vmax/Vmax= 0 .12.