The termination shock of a magnetar wind: a possible origin of gamma-ray burst X-ray afterglow emission

Context: Swift observations suggest that the X-ray afterglow emission of some gamma-ray bursts (GRB) may have internal origins, and the conventional external shock (ES) cannot be the exclusive source of the afterglow emission. Aims: If the central compact objects of some GRBs are millisecond magentars, the magnetar winds could play an important role in the (internal) X-ray afterglow emission, which is our focus here. Methods: The dynamics and the synchrotron radiation of the termination shock (TS) of the magmnetar winds, as well as the simultaneous GRB ES, are investigated by considering the magnetization of the winds. Results: As a result of the competition between the emission of the wind TS and the GRB ES, two basic types of X-ray afterglows are predicted, i.e., the TS-dominated and the ES-dominated types. Moreover, our results also show that both of the two types of afterglows have a shallow-decay phase and a normal-decay one, as observed by the \textit{Swift} satellite. This indicates that some observed X-ray afterglows could be (internally) produced by the magnetar winds, but not necessarily GRB ESs.