2.2. Rotation Curve Decomposition. II. Our Assumptions

Many authors emphasize that mass modeling is uncertain (van Albada et al. 1985; Skillman et al. 1987; Lake & Feinswog 1989). Lake and Feinswog point out that if measurement errors are interpreted strictly, few observations of rotation curves reach large enough radii to determine halo parameters uniquely. Therefore the present results depend on the following assumptions:

1 - Rotation curves that flatten out to V constant are assumed to stay flat outside the radius range measured.

2 - We use maximum disk decompositions. This requires discussion. The unknown mass-to-light ratio of the disk is a problem - the ratio of visible to dark mass can be varied greatly while preserving a good fit to V(r). As the amount of visible mass is reduced, the central DM density must be increased and its core radius must be decreased. The extreme models (van Albada et al. 1985, Fig. 4 and 8) are usually the maximum disk mass that does not require the halo to have a hollow core and a solution with M / L = 0. In giant galaxies, these solutions are very different. If we had no additional constraints, we could say little about halo properties. Fortunately, we have other constraints. We cannot let M / L get arbitrarily small. We observe structures such as bars and spiral density waves that require disks to be self-gravitating. ABP turned this qualitative remark into a practical constraint on M / L by applying Toomre's (1981) swing amplifier instability criterion and requiring that the disk have the proper density to give the observed spiral structure (i.e., two arms but not one). The results converged on essentially the maximum disk solutions for 18 of 21 Sc-Im galaxies studied. The resulting mass-to-light ratios imply plausible young stellar populations. In general, some evidence favors maximum disks (e.g., aga & Iye 1994; Sackett 1997; Debattista & Sellwood 1998; Bosma 1999; Sellwood & Moore 1999; Weiner, Sellwood, & Williams 2001; Gerhard 2004; Athanassoula 2004; Weiner 2004), and other evidence suggests that some disks are submaximal (e.g., Bottema 1993, 1997; Courteau & Rix 1999). Our choice of maximum disk solutions affects only giant galaxies; dwarfs are so DM dominated that M / L uncertainties have little effect. If we used "Bottema disks" instead of maximum disks, parameter correlations with galaxy luminosity would be shallower.

3 - Halo are assumed to have non-singular isothermal mass distributions. IAU Symposium 220 focuses in part on the well known collision (Moore 1994) between the prediction that cold DM (CDM) has cuspy central density profiles (r) (e.g., Navarro, Frenk, & White 1996, 1997 [NFW], who find that r^-1) and observational evidence that at least dwarf galaxies have flat cores. For the purposes of this paper, the difference between isothermals and NFW profiles is nontrivial but relatively benign. An analogous problem arose with elliptical galaxies: Early studies of cores, including the discovery of fundamental plane correlations (Kormendy 1984; Lauer 1985; Kormendy 1987b,c), were published before Hubble Space Telescope (HST) showed that high-luminosity ellipticals have cuspy cores with projected densities (r) r^-m, m 0 to 0.25 at small radii (e.g., Lauer et al. 1995). But pre-HST observations of core radii and central densities probe the same physics as (and, in fact, are roughly proportional to) HST measurements of profile break radii and densities (Kormendy et al. 1994). Most results deduced from ground-based photometry remain valid. We expect that the present DM parameters will prove to measure the relevant physics when the form of the halo density profile is better known. That is, we consider r_c as an approximate profile break radius and ₀ as a measure of the density at r_b or averaged inside r_b; this should be valid whether halos are isothermal or not.