Dynamical friction of star clusters against disk field stars in
  galaxies: Implications on stellar nucleus formation and globular cluster
  luminosity functions
  We numerically investigate orbital evolution of star clusters (SCs) under the
influence of dynamical friction by field stars of their host disk galaxies
embedded in dark matter halos. We find that SCs with masses larger than 2 *
10^5 M_sun can show significant orbital decay within less than 1 Gyr due to
dynamical friction by disk field stars in galaxies with disk masses M_d less
than 10^9 M_sun. We also find that orbital decay of SCs due to dynamical
friction is more remarkable in disk galaxies with smaller M_d and higher
mass-ratios of disks to dark matter halos. The half-number radii R_h, sc and
mean masses within R_h,sc of the SC systems (SCSs) in low-mass disk galaxies
with M_d < 10^9 M_sun are found to evolve significantly with time owing to
dynamical friction of SCs. More massive SCs that can spiral-in to the central
regions of disks can form multiple SC systems with smaller velocity dispersions
so that they can merge with one another to form single stellar nuclei with
their masses comparable to ~0.4% of their host disk masses. Based on these
results, we suggest that luminosity functions (LFs) for more massive globular
clusters (GCs) with masses larger than 2 * 10^5 M_sun can steepen owing to
transformation of the more massive GCs into single stellar nuclei through GC
merging in less luminous galaxies. We also suggest that the half-number radii
of GC systems can evolve owing to dynamical friction only for galaxies with
their total masses smaller than ~ 10^{10} M_sun.
