Disk-stability constraints on the number of arms in spiral galaxies
  A model based on disk-stability criteria to determine the number of spiral
arms of a general disk galaxy with an exponential disk, a bulge and a dark halo
described by a Hernquist model is presented. The multifold rotational symmetry
of the spiral structure can be evaluated analytically once the structural
properties of a galaxy, such as the circular speed curve, and the disk surface
brightness, are known. By changing the disk mass, these models are aimed at
varying the critical length scale parameter of the disk and lead to a different
spiral morphology in agreement with prior models. Previous studies based on the
swing amplification and disk stability have been applied to constrain the
mass-to-light ratio in disk galaxies. This formalism provides an analytic
expression to estimate the number of arms expected by swing amplification
making its application straight-forward to large surveys. It can be applied to
predict the number of arms in the Milky Way as a function of radius and to
constrain the mass-to-light ratio in disk galaxies for which photometric and
kinematic measurements are available, like in the DiskMass survey. Hence, the
halo contribution to the total mass in the inner parts of disk galaxies can be
inferred in light of the ongoing and forthcoming surveys.
