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

A Pulsar Wind Nebula Model Applied to Short GRB 050724