To investigate the magnetic-field-induced distortion of NSs through GRB X-ray plateaus.

Magnetic field may distort neutron stars (NSs), but the effect has not been robustly tested through gravitational-wave observation yet due to the absence of a fast rotating Galactic magnetar. The central objects of Gamma-ray bursts (GRBs) could be millisecond magnetars. Under the magnetar scenario on the X-ray plateaus of GRB afterglows,the spindown evolution modulated by the gravitational-wave radiation may be inferred from some special samples, so that the magnetically-induced distorting can be further estimated. According to two samples, GRB 060807 and GRB 070521, we found that the correlation between the effective ellipticity, $\varepsilon_{\rm B,eff}$, and effective dipole magnetic field strength on a neutron star (NS) surface, $B_{\rm eff}$, is $\varepsilon_{\rm B,eff}\sim 10^{-4} (\frac{B_{\rm eff}}{10^{14}\;\rm G})^{2}$. This result demands that $B_{\rm eff}\sim 0.01 B_{\rm t}$ with $B_{\rm t}$ being the internal toroidal magnetic field strength of NSs. We suggested that the torque generated during few unsymmetrical massive-star collapses may induce differential rotations in proto-NSs to amplify the internal toroidal fields.