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 th
e 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.
The durations (T90) of 315 GRBs detected with Fermi/GBM (8-1000 keV) by 2011 September are calculated using the Bayesian Block method. We compare the T90 distributions between this sample and those derived from previous/current GRB missions. We show
that the T90 distribution of this GRB sample is bimodal, with a statistical significance level being comparable to those derived from the BeppoSAX/GRBM sample and the Swift/BAT sample, but lower than that derived from the CGRO/BATSE sample. The short-to-long GRB number ratio is also much lower than that derived from the BATSE sample, i.e., 1:6.5 vs 1:3. We measure T90 in several bands, i.e., 8-15, 15-25, 25-50, 50-100, 100-350, and 350-1000 keV, to investigate the energy-dependence effect of the bimodal T90 distribution. It is found that the bimodal feature is well observed in the 50-100 and 100-350 keV bands, but is only marginally acceptable in the 25-50 keV and 350-1000 keV bands. The hypothesis of the bimodality is confidently rejected in the 8-15 and 15-25 keV bands. The T90 distributions in these bands are roughly consistent with those observed by missions with similar energy bands. The parameter T90 as a function of energy follows bar T90 propto E^{-0.20pm 0.02} for long GRBs. Considering the erratic X-ray and optical flares, the duration of a burst would be even much longer for most GRBs. Our results, together with the observed extended emission of some short GRBs, indicate that the central engine activity time scale would be much longer than T90} for both long and short GRBs and the observed bimodal T90 distribution may be due to an instrumental selection effect.
Well-sampled optical lightcurves of 146 gamma-ray bursts (GRBs) are complied from the literature. Multiple optical emission components are extracted with power-law function fits to these lightcurves. We present a systematical analysis for statistical
properties and their relations to prompt gamma-ray emission and X-ray afterglow for each component. We show that peak luminosity in the prompt and late flares are correlated and the evolution of the peak luminosity may signal the evolution of the accretion rate. No tight correlation between the shallow decay phase/plateau and prompt gamma-ray emission is found. Assuming that they are due to a long-lasting wind injected by a compact object, we show that the injected behavior favors the scenarios of a long-lasting wind after the main burst episode. The peak luminosity of the afterglow onset is tightly correlated with Eiso, and it is dimmer as peaking later. Assuming that the onset bump is due to the fireball deceleration by the external medium, we examine the Gamma_0-Eiso relation and find that it is confirmed with the current sample. Optical re-brightening is observed in 30 GRBs in our sample. It shares the same relation between the width and the peak time as found in the onset bump, but no clear correlation between the peak luminosity and Eiso as observed in the onset bumps is found. Although its peak luminosity also decays with time, the slope is much shallower than that of the onset peak. We get L t^{-1}_{p}$, being consistent with off-axis observations to an expanding external fireball in a wind-like circum medium. The late re-brightening may signal another jet component. Mixing of different emission components may be the reason for the observed chromatic breaks in different energy bands.
Well-sampled optical lightcurves of 146 gamma-ray bursts (GRBs) are compiled from the literature. By empirical fitting we identify eight possible emission components and summarize the results in a synthetic lightcurve. Both optical flare and early sh
allow-decay components are likely related to long-term central engine activities. We focus on their statistical properties in this paper. Twenty-four optical flares are obtained from 19 GRBs. The isotropic R-band energy is smaller than 1% of $E_{gamma, rm iso}$. The relation between isotropic luminosities of the flares and gamma-rays follows $L^{rm F}_{rm R, iso}propto L_{{gamma}, rm iso}^{1.11pm 0.27}$. Later flares tend to be wider and dimmer, i.e., $w^{rm F}sim t^{rm F}_{rm p}/2$ and $L^{rm F}_{rm R, iso}propto [t^{rm F}_{rm p}/(1+z)]^{-1.15pm0.15}$. The detection probability of the optical flares is much smaller than that of X-ray flares. An optical shallow decay segment is observed in 39 GRBs. The relation between the break time and break luminosity is a power-law, with an index of $-0.78pm 0.08$, similar to that derived from X-ray flares. The X-ray and optical breaks are usually chromatic, but a tentative correlation is found. We suggest that similar to the prompt optical emission that tracks $gamma$-rays, the optical flares are also related to the erratic behavior of the central engine. The shallow decay component is likely related to a long-lasting spinning-down central engine or piling up of flare materials onto the blastwave. Mixing of different emission components may be the reason of the diverse chromatic afterglow behaviors.
