Constraining the braking indices of magnetars

Abstract

Because of the lack of long-term pulsed emission in quiescence and the strong timing noise, it is impossible to directly measure the braking index n of a magnetar. Based on the estimated ages of their potentially associated supernova remnants (SNRs), we estimate the values of the mean braking indices of eight magnetars with SNRs, and find that they cluster in the range of 1-42. Five magnetars have smaller mean braking indices of 1 < n < 3, and we interpret them within a combination of magneto-dipole radiation and wind-aided braking. The larger mean braking indices of n > 3 for the other three magnetars are attributed to the decay of external braking torque, which might be caused by magnetic field decay. We estimate the possible wind luminosities for the magnetars with 1 < n < 3, and the dipolar magnetic field decay rates for the magnetars with n > 3, within the updated magneto-thermal evolution models. Although the constrained range of the magnetars' braking indices is tentative, as a result of the uncertainties in the SNR ages due to distance uncertainties and the unknown conditions of the expanding shells, our method provides an effective way to constrain the magnetars' braking indices if the measurements of the SNR ages are reliable, which can be improved by future observations.