  We show that a significant correlation (up to 5sigma) emerges between the
bulge index, defined to be larger for larger bulge/disk ratio, in spiral
galaxies with similar luminosities in the Galaxy Zoo 2 of SDSS and the number
of tidal-dwarf galaxies in the catalogue by Kaviraj et al. (2012).
  In the standard cold or warm dark-matter cosmological models the number of
satellite galaxies correlates with the circular velocity of the dark matter
host halo. In generalized-gravity models without cold or warm dark matter such
a correlation does not exist, because host galaxies cannot capture in-falling
dwarf galaxies due to the absence of dark-matter-induced dynamical friction.
However, in such models a correlation is expected to exist between the bulge
mass and the number of satellite galaxies, because bulges and tidal-dwarf
satellite galaxies form in encounters between host galaxies. This is not
predicted by dark matter models in which bulge mass and the number of
satellites are a priori uncorrelated because higher bulge/disk ratios do not
imply higher dark/luminous ratios. Hence, our correlation reproduces the
prediction of scenarios without dark matter, whereas an explanation is not
found readily from the a priori predictions of the standard scenario with dark
matter. Further research is needed to explore whether some application of the
standard theory may explain this correlation.
