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We numerically investigate orbital evolution of star clusters (SCs) under theinfluence of dynamical friction by field stars of their host disk galaxiesembedded 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 todynamical friction by disk field stars in galaxies with disk masses M_d lessthan 10^9 M_sun. We also find that orbital decay of SCs due to dynamicalfriction is more remarkable in disk galaxies with smaller M_d and highermass-ratios of disks to dark matter halos. The half-number radii R_h, sc andmean masses within R_h,sc of the SC systems (SCSs) in low-mass disk galaxieswith M_d < 10^9 M_sun are found to evolve significantly with time owing todynamical friction of SCs. More massive SCs that can spiral-in to the centralregions of disks can form multiple SC systems with smaller velocity dispersionsso that they can merge with one another to form single stellar nuclei withtheir masses comparable to ~0.4% of their host disk masses. Based on theseresults, we suggest that luminosity functions (LFs) for more massive globularclusters (GCs) with masses larger than 2 * 10^5 M_sun can steepen owing totransformation of the more massive GCs into single stellar nuclei through GCmerging in less luminous galaxies. We also suggest that the half-number radiiof GC systems can evolve owing to dynamical friction only for galaxies withtheir total masses smaller than ~ 10^{10} M_sun.

Dynamical friction of star clusters against disk field stars in  galaxies: Implications on stellar nucleus formation and globular cluster  luminosity functions