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Signature of r-mode Gravitational-wave Emission in the X-Ray Afterglow of Short GRB 090510

The X-ray plateaus observed in the afterglows of some short gamma-ray bursts (GRBs) are usually interpreted as the contribution from newborn magnetars with magnetic dipole radiation. However, Fan et al. re-examined that interpretation and found that a rapidly rotating magnetar might lose most of the angular momentum to gravitational waves because the total energy released within the X-ray plateau phases in some short GRBs was much smaller than that expected in the magnetar model, which indicates that the signal of gravitational-wave radiation (GWR) might have already existed in current electromagnetic data of short GRBs. In addition, theoretical analysis also showed that the rotational energy of newborn magnetars was carried away via GWR, which was more efficient than magnetic dipole radiation and the shape of the light curve of GRB can be adjusted from the magnetar model merely by considering magnetic dipole radiation. With this motivation, we investigate the X-ray light curve of GRB 090510 in detail and find that the X-ray light curve can be well fit with a magnetar model supposing that the spin evolution of the magnetar is governed by both gravitational radiation generated by unstable r-mode oscillations at early-time and magnetic dipole radiation dominating late-time spin-down evolution. This result suggests that the r-mode instability is likely to play an important role in the evolution of the post-merger remnant. We also discuss the detectability of the r-mode GWR emitted by the long-lived remnant of GRB 090510.