Predicting Multiwavelength Emission Associated with X-Ray Flares and Extended Emission of Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are one of the most extreme transients in the universe, but their explosion and emission mechanism remains unclear. To investigate the nature of GRB jets, here we focus on X-ray flares (XFs) and extended emissions (EEs), which are X-ray emissions that occur 100 to 1000 seconds after the main burst. They can be observed by recently developed multi-wavelength facilities. In this paper, we calculate emissions across multi-wavelengths associated with XFs and EEs under the hypothesis that XFs and EEs are optically-thin synchrotron emissions from nonthermal electrons in relativistic jets. Considering ranges of the dissipation radius $r_{\rm diss}$ and the Lorentz factor $\Gamma$ of the jet, we determine the parameter space in which a detectable emission can be produced at each wavelength. We found that simultaneous ultraviolet and very-high-energy gamma-ray emission associated with XFs or EEs can be detected by Swift/UVOT, SVOM/VT, and CTAO approximately every three years. The detection and non-detection rates for each detector are key to determining the uncertain yet essential values necessary for understanding the physics of GRB jets.