Dynamical friction of star clusters against disc 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 disc galaxies embedded in dark matter haloes. We find that SCs with masses larger than similar to 2 x 10(5) M-circle dot can show significant orbital decay within less than 1 Gyr due to dynamical friction by disc field stars in galaxies with disc masses (M-d) less than 10(9) M-circle dot. We also find that orbital decay of SCs due to dynamical friction is more remarkable in disc galaxies with smaller M-d and higher mass ratios of discs to dark matter haloes. The half-number radii (R-h,R-sc) and mean masses within R-h,R-sc of the SC systems (SCSs) in low-mass disc galaxies with M-d <= 10(9) M-circle dot 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 discs can form multiple SCSs with smaller velocity dispersions so that they can merge with one another to form single stellar nuclei with their masses comparable to similar to 0.4 per cent of their host disc masses. Based on these results, we suggest that luminosity functions for more massive globular clusters (GCs) with masses larger than 2 x 10(5) M-circle dot 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 similar to 10(10) M-circle dot.