Constrain magnetar parameters by taking into account the evolutionary effects of radius and moment of inertia with \emph{Swift}/XRT data (2507.11110v1)

Abstract: A newly born millisecond magnetar has been proposed as one possible central engine of some gamma-ray bursts (GRBs) with X-ray plateau emission. In this work, we systematically analyzed the \emph{Swift}/XRT data of long GRBs with plateau emission that were detected before 2023 December, and estimated the magnetar parameters by considering the $R/I$ evolutionary effects, and investigated possible relationships among these parameters and their relation to the GRB jet and magnetar wind radiation. We found that neglecting the evolutionary effects of $R/I$ can lead to systematic overestimation or underestimation of magnetar parameters such as magnetic field strength ($B_p$), spin period ($P_0$), and ellipticity ($\epsilon$) from 20% to 50%. We also found that some tight correlations among different magnetar parameters, as well as between the GRB jet emission and the magnetar wind emission for our selected Equation of states (EoSs). The universal correlations suggest that a nascent magnetar with the faster $P_0$, lower $B_p$, and lower $\epsilon$ are more inclined to power more energetic GRB jet, and the ellipticity deformation and initial spin period of newborn magnetar are likely to originate from the magnetically-induced distortion and correspond to the equilibrium spin period as a result of interaction between the magnetar and its accretion disk, respectively. Finally, we found that the GW signals from the remnants of those GW-dominated GRBs with redshift measurements cannot reach aLIGO sensitivity threshold, and only two cases (GRBs 150323A and 170607A) can reach ET sensitivity threshold. Future GW observations could not only offer the first smoking gun that a protomagnetar can serve as the central engine of GRBs, but could also play a crucial role in precisely constraining the neutron EoS.