2022A&A...666A.138L

The magnetic field may distort neutron stars (NSs), but its effect has not yet been robustly tested through gravitational-wave observations due to the absence of a fast-rotating Galactic magnetar. The investigation of parts of gamma-ray bursts (GRBs) can potentially shed light on the magnetically induced distortion since their central objects may be millisecond magnetars. In this paper we propose a method for estimating the distortions of these possible magnetars under the GRB magnetar scenario. According to the case study of GRB 070521, we find a relation between the effective magnetically induced ellipticity, ϵ_B, eff_, and the effective dipole magnetic field strength on NS surfaces, B_eff, namely ϵ_B, eff_ ∼ 10^–3(B_eff/10¹⁵ G)². Furthermore, we constrain the internal magnetic field structure of the magnetar to be B_eff ∼ 0.02⟨B_t⟩ and B_eff ∼ 0.1 B_t, where ⟨B_t⟩ is the volume-averaged internal toroidal field. This constraint can be used as the initial condition in modeling the structure of NS magnetospheres. Finally, the possibility of testing the method shown in this paper through gravitational-wave observations is discussed.