  We investigate the properties of spiral shocks in a steady, adiabatic,
non-axisymmetric, self-gravitating, mass-outflowing accretion disk around a
compact object. We obtain the accretion-ejection solutions in a gaseous
galactic disk and apply them to the spiral galaxies to investigate the possible
physical connections between some galaxy observational quantities. The
self-gravitating disk potential is considered following Mestel's (1963)
prescription. The spiral shock-induced accretion-ejection solutions are
obtained following the point-wise self-similar approach. We observe that the
self-gravitating disk profoundly affects the dynamics of the spiral structure
of the disk and the properties of the spiral shocks. We find that the
observational dispersion between the pitch angle and shear rate and between the
pitch angle and star formation rate in spiral galaxies contains some important
physical information. There are large differences in star formation rates among
galaxies with similar pitch angles, which may be explained by the different
star formation efficiencies caused by the distinct galactic ambient conditions.
