Dark Matter and Stellar Mass in the Luminous Regions of Disk Galaxies

We investigate the correlations among stellar mass (M*), disk scale length (Rd), and rotation velocity at 2.2 disk scale lengths (V2.2) for a sample of 81 disk-dominated galaxies (disk/total >=0.9) selected from the SDSS. We measure V2.2 from long-slit H(alpha) rotation curves and infer M* from galaxy i-band luminosities (Li) and g - r colors. We find logarithmic slopes of 2.60 +- 0.13 and 3.05 +- 0.12 for the (forward fit) Li-V2.2 and M*-V2.2 relations, somewhat shallower than most previous studies, with intrinsic scatter of 0.13 and 0.16 dex, respectively. Our direct estimates of the total-to-stellar mass ratio within 2.2Rd, assuming a Kroupa IMF, yield a median ratio of 2.4 for M* > 1010 M(circle dot operator) and 4.4 for M* = 109-1010 M(circle dot operator), with large scatter at a given M* and Rd. The typical ratio of the rotation speed predicted for the stellar disk alone to the observed rotation speed at 2.2Rd is ~0.65. The distribution of scale lengths at fixed M* is broad, but we find no correlation between disk size and the residual from the M*-V2.2 relation, implying that the M*-V2.2 relation is an approximately edge-on view of the disk galaxy fundamental plane. Independent of the assumed IMF, this result implies that stellar disks do not, on average, dominate the mass within 2.2Rd. We discuss our results in the context of infall models where disks form in adiabatically contracted cold dark matter halos. A model with a disk-to-halo mass ratio md = 0.05 provides a reasonable match to the Rd-M* distribution for spin parameters (lambda)ranging from ~0.04 to 0.08, and it yields a reasonable match to the mean M*-V2.2 relation. A model with md = 0.1 predicts overly strong correlations between disk size and M*-V2.2 residual. Explaining the wide range of haloto-disk mass ratios within 2.2Rd requires significant scatter in md values, with systematically lower md for galaxies with lower M* or lower stellar surface density (sigma)*.