A Comprehensive Study of Gamma-Ray Burst Optical Emission: I. Flares and Early Shallow Decay Component

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 shallow-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 $L^{\rm F}_{\rm R, iso}\propto L_{{\gamma}, \rm iso}^{1.11\pm 0.27}$. Later flares tend to be wider and dimmer, i.e., $w^{\rm F}\sim t^{\rm F}_{\rm p}/2$ and $L^{\rm F}_{\rm R, iso}\propto [t^{\rm F}_{\rm p}/(1+z)]^{-1.15\pm0.15}$. 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 $-0.78\pm 0.08$, 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.