This so-called "maximum disk" problem is related
to the core/cusp problem, since in the current
CDM picture the
dark halo
dominates the potential in the central parts also in high surface brightness
spirals. Several ways have been explored to break the mass model
degeneracy using other dynamical considerations
concerning the importance of the disk in the inner parts of spiral galaxies.
Athanassoula et al. (1987,
ABP) use swing amplifier criteria,
which depend on the rotation curve shape
and on a characteristic X parameter dependent on the epicyclic frequency
, the number of arms m,
and the active surface mass density of the disk.
By requiring that the swing amplification of the m = 2 perturbations
is possible, the range of mass-to-light ratios is limited to
a factor of 2 : a lower limit set by requiring that the disk is massive
enough to just allow amplification of the m = 2 perturbations, and an
upper limit set by requiring that amplification of the m = 1 perturbations
is just prohibited. Usually the latter condition holds for a model
with maximum disk and a non-hollow halo.
Peculiar motions due to the spiral arms were clearly seen in the early M81 21-cm line data, and modeled with a spiral density wave response calculation by Visser (1980), who did not include a dark halo in his models. The presence of "wiggles" in position-velocity curves from long slit data are thus associated with the spiral arms. Kranz et al. (2001) use such data for NGC 4254 and try to reproduce the observed velocity perturbations with a stationary gas flow model using the K-band image of this galaxy as input to the evalution of the disk part of the galactic potential. They find that a maximum disk model produces too large velocity perturbations, and put an upper limit on the disk mass fraction (the mass ratio between a given disk model and the maximum disk model) of 0.8. However, this galaxy is lopsided in the HI, the spiral may be evolving, the small bar in the center of the galaxy might have a different pattern speed than the main spiral pattern, the inclination may be higher than the authors take it, and the adopted method may favour lower disk mass fractions (Slyz et al. 2003). Kranz et al. (2003) report on a similar analysis for four more cases, and find a trend that the brightest spirals (those with the highest rotational velocities), seem to have maximum disks, but that towards lower luminosity spirals the relative influence of the dark matter in the inner parts increases. Comparison with data from ABP shows good agreement with this trend (cf. Figure 4b).
Weiner et al. (2001) model the stationary gas flow in the barred spiral NGC 4123, using a potential derived from an optical image, and find that the best fit to the velocity data requires a maximum disk model for the mass distribution. Lindblad, Lindblad & Athanassoula (1996) find likewise a relatively good fit for the bright barred spiral NGC 1365 with a maximum disk model. Figure 4 suggests that faster rotators have rounder disks, which are more self-gravitating.
A view not necessarily in contradiction is voiced by Courteau et al. (2003), who contend that on average, disks with Vmax < 200 km/s are sub-maximal. They argue this on the basis of velocity dispersion data from Bottema (1997) - which I deem having too large error bars -, work on disk stability by Fuchs - yes, but see Fuchs (2002) -, the absence of the expected correlated scatter in the Tully-Fisher relation (Courteau & Rix 1999) - but disk maximality seems to depend on Vmax - , and the result on the lens 2237+0305. Nevertheless, they find that Tully-Fisher relations for barred and un-barred galaxies are similar, in agreement with previous work, so barredness does not affect maximality.
Trott & Webster (2002) combine for 2237+0305 their lens model with HI rotation data further out. There is little need for a dark halo in the central parts, which are dominated by a bulge-bar system. Their statement that the disk is not maximal is partly influenced by their inclusion of the bar into the bulge, even though bars are thought to originate in the disk. For our own Galaxy, data on the microlensing towards the bulge-bar system likewise suggest that dark matter does not dominate in the central parts (Bissantz & Gerhard 2002).