Galaxies with Declining Rotation Curves
  A sample of 22 spiral galaxies compiled from published data is studied. The
galaxy rotation curves pass through a maximum distance of more than $\sim 1$
kpc from the center with a subsequent decrease in the rotation velocity. The
galaxy position in the Tully-Fisher (TF) and baryonic Tully-Fisher (BTF)
diagrams show that the values of maximum rotation velocities are located on the
same sequence with other galaxies, while the velocities at the disk periphery
for some galaxies are significantly lower than the expected values for a given
mass or luminosity. Thus, the decrease in the rotation curve can be associated
with a reduced contribution of the dark halo to the rotation velocity. For
seven galaxies with the longest rotation curves, the disk mass was estimated to
be with the dark halo (Newtonian model) and without the halo (modified
Newtonian dynamics (MOND) model). In four of the galaxies, the MOND model
encounters difficulties in interpreting the rotation curve: in order to be
consistent with the observations, the MOND parameter $a_0$ should differ
significantly from the expected value $a_0 \sim 10^{-8}$ cm/s$^2$, while the
disk mass exceeds the value based on IR photometry and maximum disk model. The
conflict with MOND is the most significant for NGC 157.
