6.3 The Dark Matter Fraction in Spirals
As noted above, Salucci and Frenk (1989) predicted the fall in the rotation curves of bright spirals from Persic and Salucci's (1988) claim that faint galaxies have more DM within R25. Similarly, the empirical results of Casertano and van Gorkom (1991) could be the result of an increase in the DM fraction at lower luminosities. However, it is possible to imagine other causes for the correlation between the rotation curve shape and maximum rotation velocity. Such concerns prompted additional studies of the DM fraction in spirals.
Persic and Salucci's (1988) original approach was based on considerations of centrifugal equilibrium of spiral disks. The presence of the disk pushes the observed rotation velocity above that due to the halo alone. This is somewhat surprising if one recalls that the Tully-Fisher law, which relates velocity to luminosity, and thus disk mass, has a very small dispersion. One might expect variations in DM fraction to cause deviations from the Tully-Fisher law, since they would complicate the relation between velocity and luminosity. Persic and Salucci (1988; 1991a) exploited this fact and showed that accounting for the variation in disk-to-halo mass ratio not only further reduced the dispersion in the Tully-Fisher relation, but also reproduced the observed non-linearity (Mould, Han and Bothun 1989).
Persic and Salucci (1990a) applied their method to an enlarged sample of galaxies and found results consistent with their earlier claims. The disk-to-halo mass ratio within R25 was found to be proportional to a power law of galaxy luminosity:
where
0.5, A
1 and LB*
is the knee of the
galaxy luminosity function.
Persic and Salucci
(1990b)
also used the traditional maximum disk method to
investigate this question. They again found an anticorrelation between DM
content within R25 and galaxy luminosity.
Yet another independent technique for extracting the DM fraction has been
introduced by
Salucci, Ashman and
Persic (1991).
The idea is similar to one pioneered by
Tinsley (1981).
The starting point is the well-known observation
that the surface brightness profiles of spiral galaxies follow
Freeman's (1970)
law: I(R) = I0
exp(-R). Here R
is galactocentric distance,
-1 is the disk
scale-length, and the central surface brightness
I0 is roughly constant from one galaxy to another. The
mass-to-light ratio
of the stellar disk, (M / LB)*, is obtained
from observed galaxy colors
and a theoretical relation between color and mass-to-light ratio based on
stellar population synthesis models. By converting from surface brightness to
surface mass density using (M/LB)*,
Salucci et al. (1991)
derived the
rotational velocity produced by a disk of a given luminosity. This predicted
velocity was compared to observed rotation curves, and excess velocities were
attributed to the effects of the dark halo. This technique also indicated an
increase in the DM fraction with decreasing luminosity.
One of the advantages of this general method is that it can be applied to large
samples of galaxies.
Salucci et al. (1992)
have extended the technique to
galaxies with HI linewidths. Their sample of 258 galaxies is 5 times larger
than any employed in previous investigations of this kind. The trend of
higher DM fractions in faint spirals is once again confirmed.
A somewhat different
view has been put forward by
Jablonka and Arimoto
(1992).
They carried out an analysis similar to that of
Salucci et al. (1991),
but using a new population synthesis model. They found
no dependence of DM fraction on galaxy color. This may be primarily
the result of a poorly selected galaxy sample that is likely to wash out
any exisiting trend.
Persic, Salucci and
Ashman (1992)
find that the population synthesis model
of Jablonka and
Arimoto (1992),
along with a suitably selected galaxy sample,
gives results consistent with the usual DM trend.
Other workers have reported results that support higher DM fractions in
low-luminosity galaxies.
Pierce (1990)
found that the total
(disk plus halo) I-band mass-to-light ratio of disk galaxies
increases with decreasing luminosity. Specifically,
(M/LI) rises significantly at a luminosity
log(LI /
L)
9.8
which coincides with the change in the slope of
the Tully-Fisher relation. This non-linearity can be produced by a
gradual increase in the mass-to-light ratio with decreasing luminosity
(cf. Persic and
Salucci 1991a)
Forbes (1992)
has used R-band photometry and HI rotation curves to
estimate the DM fraction in a sample of spirals. He finds clear evidence for
larger amounts of DM in the fainter galaxies.
One novel aproach has been adopted by
Maloney (1992)
who uses low-redshift
Lyman- absorption features to
infer the properties of dark
galactic halos. These features are assumed to be produced by gas within
spiral halos. He concludes that either typical dark halos extend to very
large radii (around 1 Mpc; a possibility that is shown to be unlikely in
Section 8), or that the DM fraction in
low-luminosity galaxies is higher.
Kormendy (1990)
used published mass models of disk galaxies derived from
rotation curves to study trends in the DM content. He too found a tendency
for lower luminosity disk galaxies to have higher DM fractions and central
densities. Two relations of interest are
and
where rc is the core radius of the DM halo.
As Kormendy (1990)
stressed, these relations contain a good deal of
uncertainty, although they do fit in with the general trend that has
emerged over the last few years.
Borgani et al. (1991),
using the mass decomposition method of
Persic and Salucci
(1990a),
found that the mean density within the optical radius is given by
< >
0.003(LB / LB*)-0.9
M
pc-3.
It is worth noting that equation (6.1) is consistent with an
increase in DM fraction with decreasing galaxy luminosity.
If Mhalo >> Mdisk, then
m becomes large, and organized spiral
structure is unable to form. Low-luminosity disk galaxies rarely have
well-defined spiral arms, consistent with the view that their halos dominate
the dynamics even within the optical radius.
Phookun (DMW; also
Phookun et al. 1992)
is using this idea to study one-armed spiral galaxies. From
equation (6.1) it is apparent that disks with no surrounding halo are dominated
by the m = 1 mode and are therefore likely to exhibit a single
spiral arm.
NGC 4027 is one such example under
study. Unfortunately, it seems difficult
to establish whether this object has a negligible halo, since other
processes such as interactions with other galaxies
could also produce a one-armed structure.
Byrd, Freeman and
Howard (1992)
have suggested that the leading spiral arm
in NGC 4462 is most easily understood as a arising from
an interaction with a smaller galaxy.
In this case, their simulations indicate that the halo-to-disk
mass within the optical radius must be around 8. While leading-arm spirals
are rare, these sorts of detailed studies of indivdual galaxies may add
to our knowledge of the DM fraction in spirals.
Some theoretical implications of the trends of DM fraction with
galaxy luminosity are discussed in
Sections 10 and 11.