Maximal Disks and the Tully-Fisher Relation

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Scientific paper

We use Tully-Fisher (TF) residuals for more than 600 luminous, high-surface brightness (HSB) spirals from the catalogs of Courteau (1992) and Mathewson et al. (1992) to show that a maximal disk fit is ruled out by the statistics of the rotation speed, V{_2.2}, at 2.2 exponential scale lengths. For maximal disks, a large fraction of the total rotational support should arise from their stellar mass. Therefore the size, or surface-brightness, of the disk should be a significant additional parameter in the TF relation. At a given absolute luminosity, M_r, (i.e. fixed mass), more compact disks (as measured by Rexp) should have higher rotation speeds, V{_2.2}. Using our well-defined sample of exponential disks, we find that the fractional deviations, Delta log V{_2.2} and Delta log Rexp, from the mean relations, V{_2.2}(M_r) and Rexp(M_r), are not significantly correlated. The case of {partial log {V{_2.2}} / partial log {Rexp}}=-0.5, expected for pure exponential disks, is clearly ruled out. Broad-band colors and spectral synthesis models allow us to show that the color dependence on disk scale length at a fixed luminosity is small, thus reinforcing our dynamical interpretation. We use simple models of adiabatic infall of the luminous matter to explore what values of {partial log {V{_2.2}} / partial log {Rexp}} are expected in the presence of modest bulges and a variety of dark matter halos. We find that the TF relation requires that Vdisk ~ 0.5 Vtot (Vdisk/Vtot=0.66 at 95% confidence), fairly insensitive to the details of the dark matter halo and the presence of a bulge. Traditionally, a disk is considered maximal if Vdisk = (0.85 +/- 0.10) Vtot; our result thus excludes the notion of maximal disks for luminous spirals. Sub-maximal disks are also consistent with constraints from stellar velocity dispersions in HSB spirals (Bottema 1997), and establish a natural continuity between HSB and LSB galaxies which appear to be completely dark matter dominated even in their inner regions.

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