Hierarchal formation and growth of galaxies through dynamical friction

We study the infall of a subhalo in its parent halo due to dynamical friction. Using expected mass and spatial distributions of subhaloes, in unison with the derived infall time-scale, we calculate the expected merger stellar mass growth rate (SMGR) of the central galaxy in two different models (instantaneous and continuous merging). We find that our continuous merging SMGR (which corresponds to smooth accretion from satellites) agrees with the results of the Millennium-II simulation, predicting low growth rates for low stellar masses ($10^{8}$ M$_{\odot}-10^{10}$ M$_{\odot}$) and accelerating growth for high masses ($10^{10}$ M$_{\odot}-10^{12}$ M$_{\odot}$). Using the derived formulas we study the relative contributions of minor and major mergers to the total merger SMGR at various redshifts. Minor mergers contribute $80\%-90\%$ in the low mass range for $z 1$. This suggests that most merger mass growth is due to minor mergers. We derive an SMGR formula for the very early universe ($z>4$) and use this to show that hierarchial merging of protogalaxies can lead to the modern population of galaxies. Our overall analysis suggests that dynamical friction is the primary cause of galaxy mergers.