  Low surface brightness (LSB) galaxies form a major class of galaxies, and are
characterized by low disc surface density and low star formation rate. These
are known to be dominated by dark matter halo from the innermost regions. Here
we study the role of dark matter halo on the grand-design, $m=2$, spiral modes
in a galactic disc by carrying out a global mode analysis in the WKB
approximation. The Bohr-Sommerfeld quantization rule is used to determine how
many discrete global spiral modes are permitted. First a typical superthin LSB
galaxy, UGC 7321 is studied by taking only the galactic disc, modelled as
fluid; and then the disc embedded in a dark matter halo. We find that both
cases permit the existence of global spiral modes. This is in contrast to
earlier results where the inclusion of dark matter halo was shown to nearly
fully suppress local, swing-amplified spiral features. Although technically
global modes are permitted in the fluid model as shown here, we argue that due
to lack of tidal interactions, these are not triggered in LSB galaxies. For
comparison, we carried out a similar analysis for the Galaxy, for which the
dark matter halo does not dominate in the inner regions. We show that here too
the dark matter halo has little effect, hence the disc embedded in a halo is
also able to support global modes. The derived pattern speed of the global mode
agrees fairly well with the observed value for the Galaxy.
