Imprints of gravitational waves from magnetar spindown in GRB X-ray afterglows

Given that newborn magnetars are considered potential central engines of gamma-ray bursts (GRBs), there is strong motivation to identify gravitational wave (GW) signatures within GRB samples. If the X-ray afterglow of a GRB is powered by a magnetar, and the initial spindown of the magnetar is dominated by the GW radiation induced by $r$-mode instability or magnetic-field-induced deformation, the decay of the X-ray flux would record the information of the GW radiation. We find that GRB 130603B potentially represents a rare and precious case where the spindown of the central magnetar is dominated in-turn by $r$-mode and magnetic distortion-induced GW radiation. By fitting the X-ray light curve of GRB 130603B in this model, we obtain the initial spin period of magnetar $\sim 5.3\times 10^{-4}$ s, the effective dipole magnetic field strength $\sim 5.2\times 10^{14}$ G, the ellipticity of the magnetar $\sim 1.3\times 10^{-4}$, and the amplitude of $r$-mode oscillation $\sim3.3\times 10^{-2}$. It may serve as a reliable approach for investigating neutron star physics by comparing the parameters estimated using the method presented in this manuscript with those obtained from future GW observations.