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**Session 77 - Structures of Galaxies.**

*Display session, Friday, January 09*

*Exhibit Hall, *

## [77.02] Maximal Disks and the Tully-Fisher Relation

*S. Courteau (HIA), H. -W. Rix (Steward)*

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 R_exp) 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 R_exp, from
the mean relations, V_2.2(M_r) and R_exp(M_r), are not significantly
correlated. The case of \partial\logV_2.2 \thinspace / \thinspace\partial\logR_exp=-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\logV_2.2 \thinspace / \thinspace\partial\logR_exp
are expected in the presence of modest bulges and a variety
of dark matter halos. We find that the TF relation requires that
V_disk\sim 0.5 V_tot (V_disk/V_tot=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 V_disk = (0.85 \pm 0.10) V_tot; 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.

**Program
listing for Friday**