A Pulsar Wind Nebula Model Applied to Short GRB 050724

A subset of short gamma-ray bursts (sGRBs) have been found to be characterized by near-infrared/optical bumps at $\sim 1$ days, some of which exhibit almost concurrent X-ray flares. Although the near-infrared/optical bumps may be a signature of kilonovae, the X-ray flares are not consistent with kilonovae. It is widely believed that sGRBs are produced by the mergers of double compact objects, during which sub-relativistic ejecta are launched. In this paper we propose that the above optical/X-ray features are indicative of the formation of long-lived magnetars following the mergers of double neutron stars. Observations and theoretical works imply that the spin-down power of the magnetars is injected into the ejecta as ultra-relativistic electron-positron pairs, i.e. pulsar wind nebulae (PWNe). Here we suggest such a PWN model and find that the optical bump and X-ray flare observed in GRB 050724 can be well understood in this PWN model. We show that the optical bump and X-ray flare may have different origins. Our results strengthen the evidence for the formation of magnetars in double neutron star mergers and justify the validity of the PWN model.