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Magnetars have been considered as progenitors of magnetar giant flares (MGFs)and fast radio bursts (FRBs). We present detailed studies on afterglowemissions caused by bursts that occur in their wind nebulae and surroundingbaryonic ejecta. In particular, following the bursts-in-bubble model proposedby Murase, Kashiyama \& M\'esz\'aros, we analytically and numerically calculatespectra and light curves of such afterglow emission. We scan parameter spacefor the detectability of radio signals, and find that a burst with$\sim10^{45}~{\rm erg}$ is detectable with the Very Large Array or othernext-generation radio facilities. The detection of multi-wavelength afterglowemission from MGFs and/or FRBs is of great significance for their localizationand revealing their progenitors, and we estimate the number of detectableafterglow events.

Multi-wavelength afterglow emission from bursts associated with magnetar flares and fast radio bursts