Galaxies 205<MI> = –18.5<MI> = –20.5.50V(R)/V(R)aptV(R)/V(Rapt
)V(R)/V(R)aptV(R)/V(Rapt
)0 .5 1 1.5 21.5(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
.5
(^00) .5 1 1.5 2
1
R/Rapt R/Rapt
Figure 9.1The rotation curves fitted for 11 well-measured galaxies of increasing halo mass
[7].
dispersions of stars and the anisotropies of their orbits. However, to disentangle the
total mass profile into its dark and its stellar components is not straightforward,
because the dynamical mass decomposition of dispersions is not unique. The lumi-
nous matter in the form of visible stars is a crucial quantity, indispensable to infer the
dark component. When available one also makes use of strong and weak lensing data,
and of the X-ray properties of the emitting hot gas. The gravity is then balanced by
pressure gradients as given by Jeans’ Equation (see Chapter 11).
Inside the half light radius푅푒the contribution of the dark matter halo to the cen-
tral velocity dispersion is often very small, it is dominated by the stars, so that the
dark matter profile is intrinsically unresolvable. On the average the dark matter com-
ponent contributes less than 5% to the total velocity dispersions. The outer mass pro-
file is compatible with the NFW Equation (9.7) and Burkert Equation (9.9) formuli.
Important information on the mass distribution can be obtained from the Fundamen-
tal Plane, Equation (9.6). which yields the coefficients푎= 1. 8 ,푏= 0 .8. Note that this