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

We investigate the correlations among stellar mass (M*), disk scale length (R_d), and rotation velocity at 2.2 disk scale lengths (V_2.2) for a sample of 81 disk-dominated galaxies (disk/total ≥ 0.9) selected from the SDSS. We measure V_2.2 from long-slit Hα rotation curves and infer M* from galaxy i-band luminosities (L_i) and g - r colors. We find logarithmic slopes of 2.60 ± 0.13 and 3.05 ± 0.12 for the (forward fit) L_i-V_2.2 and M*-V_2.2 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 2.2R_d, assuming a Kroupa IMF, yield a median ratio of 2.4 for M* > 10^10 Msun and 4.4 for M* = 10^9-10^10 Msun, with large scatter at a given M* and R_d. The typical ratio of the rotation speed predicted for the stellar disk alone to the observed rotation speed at 2.2R_d 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*-V_2.2 relation, implying that the M*-V_2.2 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 2.2R_d. 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 m_d = 0.05 provides a reasonable match to the R_d-M* distribution for spin parameters λ ranging from ~0.04 to 0.08, and it yields a reasonable match to the mean M*-V_2.2 relation. A model with m_d = 0.1 predicts overly strong correlations between disk size and M*-V_2.2 residual. Explaining the wide range of halo-to-disk mass ratios within 2.2R_d requires significant scatter in m_d values, with systematically lower m_d for galaxies with lower M* or lower stellar surface density Σ*