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 of81 disk-dominated galaxies (disk/total >= 0.9) selected from the SDSS. Wemeasure V_2.2 from long-slit H-alpha rotation curves and infer M_* from galaxyi-band luminosities (L_i) and g-r colors. We find logarithmic slopes of2.60+/-0.13 and 3.05+/-0.12 for the L_i-V_2.2 and M_*-V_2.2 relations, somewhatshallower than most previous studies, with intrinsic scatter of 0.13 dex and0.16 dex. Our direct estimates of the total-to-stellar mass ratio within2.2R_d, assuming a Kroupa IMF, yield a median ratio of 2.4 for M_*>10^10 Msunand 4.4 for M_*=10^9-10^10 Msun, with large scatter at a given M_* and R_d. Thetypical ratio of the rotation speed predicted for the stellar disk alone to theobserved rotation speed at 2.2R_d is ~0.65. The distribution of R_d at fixedM_* is broad, but we find no correlation between disk size and the residualfrom the M_*-V_2.2 relation, implying that this relation is an approximatelyedge-on view of the disk galaxy fundamental plane. Independent of the assumedIMF, this result implies that stellar disks do not, on average, dominate themass within 2.2R_d. We discuss our results in the context of infall models ofdisk formation in cold dark matter halos. A model with a disk-to-halo massratio m_d=0.05 provides a reasonable match to the R_d-M_* distribution for spinparameters \lambda ranging from ~0.04-0.08, and it yields a reasonable match tothe mean M_*-V_2.2 relation. A model with m_d=0.1 predicts overly strongcorrelations between disk size and M_*-V_2.2 residual. Explaining the widerange of halo-to-disk mass ratios within 2.2R_d requires significant scatter inm_d values, with systematically lower m_d for galaxies with lower $M_*$.Comment: 18 pages, 2 tables, 7 figures, Accepted to ApJ, Table 1 updated, otherwise minor change