Determining the Efficiency of Converting Magnetar Spindown Energy into Gamma-Ray Burst X-Ray Afterglow Emission and Its Possible Implications

Plateaus are common in X-ray afterglows of gamma-ray bursts. Among the few scenarios regarding their origin, the leading one is that there exists a magnetar inside and it persistently injects its spindown energy into an afterglow. In previous studies, the radiation efficiency of this process is assumed to be a constant at greater than or similar to 0.1, which is quite simple and strong. In this work we obtain the efficiency from a physical point of view and find that this efficiency strongly depends on the injected luminosity. One implication of this result is that those X-ray afterglow light curves that show steeper temporal decay than t(-2) after the plateau phase can be naturally understood now. Also, the braking indexes deduced from afterglow fitting are found to be larger than those in previous studies, which are more reasonable for newborn magnetars.