Spin Parity of Spiral Galaxies III -- Dipole Analysis of the
  Distribution of SDSS Spirals with 3D Random Walk Simulations
  Observation has not yet determined whether the distribution of spin vectors
of galaxies is truly random. It is unclear whether is there any large-scale
symmetry-breaking in the distribution of the vorticity field in the universe.
Here, we present a formulation to evaluate the dipole component D_{max} of the
observed spin distribution, whose statistical significance sigma_{D} can be
calibrated by the expected amplitude for 3D random walk (random flight)
simulations.
  We apply this formulation to evaluate the dipole component in the
distribution of Sloan Digital Sky Survey (SDSS) spirals. Shamir(2017a)
published a catalog of spiral galaxies from the SDSS DR8, classifying them with
his pattern recognition tool into clockwise and counterclockwise (Z-spiral and
S-spirals, respectively). He found significant photometric asymmetry in their
distribution. We have confirmed that this sample provides dipole asymmetry up
to a level of sigma_{D}=4.00.
  However, we also found that the catalog contains a significant number of
multiple entries of the same galaxies. After removing the duplicated entries,
the number of samples shrunk considerably to 45%. The actual dipole asymmetry
observed for the 'cleaned' catalog is quite modest, sigma_{D}=0.29. We conclude
that SDSS data alone does not support the presence of a large-scale
symmetry-breaking in the spin vector distribution of galaxies in the local
universe. The data are compatible with a random distribution.
