We continue our systematic statistical study of various components in gamma-ray burst (GRB) optical lightcurves. We decompose the early onset bump and the late re-brightening bump with empirical fits and analyze their statistical properties. Among the 146 GRBs that have well-sampled optical lightcurves, the onset and re-brightening bumps are observed in 38 and 26 GRBs, respectively. It is found that the typical rising and decaying slopes for both the onset and re-brightening bumps are ~1.5 and -1.15, respectively. No early onset bumps in the X-ray band are detected to be associated with the optical onset bumps, while an X-ray re-brightening bump is detected for half of the re-brightening optical bumps. The peak luminosity is anti-correlated with the peak time, L_ppropto t_{p}^{-1.81+/-0.32} and L_ppropto t_{p}^{-0.83+/-0.17} for the onset and re-brightening bumps, respectively. Both L_p and the isotropic energy release of the onset bumps are correlated with E_{gamma, iso}, whereas no similar correlation is found for the re-brightening bumps. Taking the onset bumps as probes for the properties of the fireballs and their ambient medium, we find that the typical power-law index of the relativistic electrons is 2.5 and the medium density profile behaves as npropto r^{-1} within the framework of the synchrotron external shock models. With the medium density profile obtained from our analysis, we also confirm the correlation between initial Lorentz factor (Gamma_0) and E_{gamma, iso} in our previous work. The jet component that produces the re-brightening bump seems to be on-axis and independent of the prompt emission jet component. Its typical kinetic energy budget would be about one order of magnitude larger than the prompt emission component, but with a lower Gamma_0, typically several tens.
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