  Mass models of a sample of 171 low- and high-surface brightness galaxies are
presented in the context of the cold dark matter (CDM) theory using the NFW
dark matter halo density distribution to extract a new concentration-viral mass
relation ($c-M_{vir}$). The rotation curves (RCs) are calculated from the total
baryonic matter based on the 3.6 $\mu m $-band surface photometry, the observed
distribution of neutral hydrogen, and the dark halo, in which the three
adjustable parameters are the stellar mass-to-light ratio, halo concentration
and virial mass. Although accounting for a NFW dark halo profile can explain
rotation curve observations, the implied $c-M_{vir}$ relation from RC analysis
strongly disagrees with that resulting from different cosmological simulations.
Also, the $M/L-$color correlation of the studied galaxies is inconsistent with
that expected from stellar population synthesis models with different stellar
initial mass functions. Moreover, we show that the best-fitting stellar $M/L-$
ratios of 51 galaxies (30\% of our sample) have unphysically negative values in
the framework of the $\Lambda $CDM theory. This can be interpreted as a serious
crisis for this theory. This suggests either that the commonly used NFW halo
profile, which is a natural result of $\Lambda $CDM cosmological structure
formation, is not an appropriate profile for the dark halos of galaxies, or,
new dark matter physics or alternative gravity models are needed to explain the
rotational velocities of disk galaxies.
