  We investigate structural properties of dark matter halos of disk galaxies in
LCDM cosmology, using a well-defined sample of 81 disk-dominated galaxies from
the SDSS redshift survey. We model the mass-velocity and fundamental plane
relations of these galaxies, which are constructed from the galaxy stellar
mass, disk scale length, and optical Halpha rotation velocity at 2.2 scale
lengths. We calculate a sequence of model galaxy populations, defined by the
distribution of the stellar disk-to-total mass fraction, m_d. We include the
effect of adiabatic contraction of dark matter halos in response to
condensation of baryons. We find that models with constant m_d underpredict the
intrinsic scatter of the TF and FP relations and predict an (unobserved) strong
correlation between TF residuals. Introducing a scatter of disk mass fractions
and allowing the mean value m_d to scale with the stellar surface density
significantly improves observational match of both the slope and intercept of
the TF relation and reduces the predicted residual correlation enough to be
consistent with the data. Our best-fit models with a Kroupa stellar IMF
over-produce the galaxy stellar mass function and predict the virial r-band
mass-to-light ratios, M_vir/L_r, systematically lower than those inferred from
galaxy-galaxy weak lensing and satellite dynamics. We investigate three
possible solutions to these problems: (1) ignoring the effects of adiabatic
contraction, (2) adopting a ``light'' stellar IMF, or (3) considering the lower
halo concentrations predicted for a low cosmological power spectrum
normalization. Any of these solutions yields acceptable residual correlations
and relieves most of the observational tension between the TF relation and the
galaxy stellar mass function (abridged).

Astrophysics