Maximal Disks and the Tully‐Fisher Relation

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Abstract
We show that for luminous, nonbarred, high surface brightness (HSB) spirals the Tully-Fisher relation (TFR) residuals can be used to estimate the relative mass contributions of the stellar disk and the dark halo at the peak of the disk rotation, near 2.2 exponential scale lengths. For "maximal disks," a large fraction (0.85±0.1) of the total rotational support, V2.2, at such radii should arise from their stellar mass. Therefore, the disk size or surface-brightness should be a significant additional parameter in the TFR. At a given absolute luminosity, Mr, more compact disks (as measured by the disk scale length Rexp) should have higher rotation speeds, V2.2. Using a well-defined sample of late-type spirals, deviations, Δlog V2.2, and Δlog Rexp, from the mean relations, V2.2(Mr) and Rexp(Mr), are not significantly correlated. The case of ∂log V2.2/∂log Rexp=-0.5 expected for a maximal disk is ruled out for the majority of these HSB galaxies. We model adiabatic infall of varying amounts of luminous matter into dark matter halos to explore the range of possible values for ∂log V2.2/∂log Rexp. From this, we find that the TFR residuals require a mean value of Vdisk~0.6Vtotal, fairly insensitive to the details of the initial dark matter halo and to the presence of a bulge. This translates to Mhalo~0.6Mtotal within 2.2Rexp or roughly twice more dark matter in the inner parts of late-type spirals than previously accounted for by maximum disk fits. We show that any stellar population differences between disks of different scale lengths lead to lower values of Vdisk/Vtotal. Our result is independent of the shape of the luminosity profile and relies only on the assumption of adiabatic contraction and that the dark matter halo rotation rises in the central parts of the galaxy. Submaximal disks establish a natural continuity between HSB and low surface brightness galaxies, which appear to be completely dark matter dominated even in their inner regions.

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