3.1 Maximum Disks ?
It is customary to construct composite disk/halo mass models of spirals assuming a ``maximum disk'' solution, or to adopt a ``best fit''. In such models, the data from surface photometry are used, assuming a constant mass-to-light ratio, to calculate the expected rotation curve for the visible components, bulge and disk. From the observed HI gas density, and a suitable factor to include helium, a rotation curve is calculated also, and quadratically added to the first one. The resulting curve is then compared with the observed rotation curve, and an additional dark halo component is introduced when necessary. For extended HI rotation curves, such an analysis has been done by several authors, e.g. Begeman et al. (1991). The constancy of the mass-to-light with radius is usually justified by the absence of colour gradients, indeed, data of De Jong (1996) shows that colour gradients are small, and if present, in the sense that disks become bluer outwards. In the latter case the use of near infrared data is preferred, since it accounts better for the contribution to the mass of the old stellar disk.
Athanassoula et al. (1987) introduce criteria from spiral structure theory, and in particular those for swing amplification (Toomre 1981), in order to get limits on the dynamical importance of the disk. This leads to a range of values possible for (M / L)disk, in case one is asking for the possibility to have m = 2 structures and for the suppression of m = 1 structures. They find that the requirement to have halos with non hollow cores usually is consistent with the absence of m = 1 structures, and that such models are preferred when considerations of stellar populations and the buildup of Sc disks at a constant rate of star formation over a Hubble time are taken into account.
Bottema (1993), from an analysis of velocity dispersions, claims that the maximum velocity of the disk component is 63% of the maximum observed velocity. The path to this result is strewn with assumptions, the most important of which are that disks are exponential with a velocity ellipsoid close to that in the solar neighbourhood, that Freeman's (1970) law holds, and that (B - V)old disk = 0.7 for all disks. For NGC 3198 his result corresponds closely to the ``no m = 2'' solution proposed by Athanassoula et al. (1987).
Recent work by Navarro (1998), based on fitting rotation curves with a dark halo profile which fits well the cosmological simulations of Navarro et al. (1996), show that in his mass models the dark matter also dominates in the inner parts of spiral galaxies. Indeed, his decompositions for NGC 3198 are so dark matter dominated that m = 2 structures will not be swing amplified at any radius.
However, Debattista & Sellwood (1998) produce a clear argument in favour of maximum disks : the dynamical friction of a bar against a dark halo slows it down, and only in a maximum disk situation does the corotation radius at the end of the simulation extend to roughly 20% further than the end of the bar. If the halo is more concentrated, as in Navarro's models, the bar slow down is so strong that corotation is at several times the bar length, completely inconsistent with current notions about bar pattern speeds. From realistic hydrodynamical simulations of the gas flow in barred spirals, which well mimic the observed dust lanes as regions of strong shocks, Athanassoula (1992) places corotation at about 1.2 ± 0.2 times the bar length. Other determinations of bar pattern speeds, based e.g. on the location of rings, which are presumed to be linked to resonances, concur with this (e.g. Elmegreen 1996 for a review).