204 Dark Matter
dynamics may easily be modified by such fields [6]. But this argument works only on
the gas halo, and does not affect the velocity distribution of stars. Also, the existence
of magnetic fields of sufficient strength remains to be demonstrated; in our Galaxy it
is only a few microgauss, which is insufficient.
The accepted solution is then that there exist vast amounts of nonluminous DM
beyond that accounted for by luminous, baryonic matter. One natural place to look for
DM is in the neighborhood of the Solar System. In 1922,Jacobus C. Kapteyndeduced
that the total density in the local neighborhood is about twice as large as the luminous
density in visible stars. Although the result is somewhat dependent on how large one
chooses this ‘neighborhood’ to be, modern dynamical estimates are similar.
Our Galaxy is complicated because of what appears to be a noticeable density dip
at 9 kpc and a smaller dip at 3 kpc. To fit the measured rotation curve one needs at
least three contributing components: a central bulge, the star disk+gas, and a DM
halo. No DM component appears to be needed until radii beyond 15 kpc.
The rotation curve of most galaxies can be fitted by the superposition of contri-
butions from the stellar and gaseous disks, sometimes a bulge, and the dark halo,
modeled by a quasi–isothermal sphere. The inner part is difficult to model because
the density of stars is high, rendering observations of individual star velocities diffi-
cult. Thus the fits are not unique, the relative contributions of disk and dark matter
halo is model-dependent, and it is sometimes not even sure whether galactic disks do
contain dark matter. Typically, dark matter constitutes about half of the total mass.
In Figure 9.1 we show the rotation curves fitted for 11 well-measured galaxies [7]
of increasing halo mass. One notes, that the central dark halo component is indeed
much smaller than the luminous disk component. At large radii, however, the need for
a DM halo is obvious. On galactic scales, the contribution of DM generally dominates
the total mass. Note the contribution of the baryonic component, negligible for light
masses but increasingly important in the larger structures.
It appears that cusped profiles are in clear conflict with data on spiral galaxies.
Central densities are rather flat, scaling approximately as휌 0 ∝푟−luminous^2 ∕^3. The best-fit
disk+NFW halo mass model fits the rotation curves poorly, it implies an implausibly
low stellar mass to light ratio and an unphysically high halo mass. Clearly the actual
profiles are of very uncertain origin.
One notes in Figure 9.1 that the shape of the rotation curve depends on the halo
virial mass so that the distribution of gravitating matter is luminosity dependent. The
old idea that the rotation curve stays constant after attaining a maximum is thus a sim-
plification of the real situation. The rotation velocity can be expressed by aUniversal
Rotation Curve[7]: all spiral galaxies appear to lie on a curve in the four-dimensional
space of luminosity, core radius, halo central density and fraction of DM.
What is required to explain the Universal Rotation Curve and the cored profiles is
some kind of interaction between baryons and dark matter, which has not met with
any success. A more successful idea may be dark matter self-interaction.
Elliptical Galaxies. Elliptical galaxies are quite compact objects which mostly lack
neutral gas and which do not rotate so their mass cannot be derived from rotation
curves. The total dynamical mass is then the virial mass as derived from the velocity