Next Contents Previous

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:

Equation 6.3 (6.3)

where gamma approx 0.5, A approx 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(-alphaR). Here R is galactocentric distance, alpha-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 / Lsun) approx 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-alpha 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

Equation 6.4 (6.4)

and

Equation 6.5 (6.5)

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 < rho > approx 0.003(LB / LB*)-0.9 Msun 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.

Next Contents Previous