Constraining the Braking Index and Energy Partition of Magnetar spin-down with {\em Swift}/XRT data

Hou-Jun Lü, Lin Lan, En-Wei Liang

Published 2018-12-09Version 1

Observationally, the long-lasting X-ray plateau emission in long GRBs show evidence for ongoing energy injection which may be from magnetar spin-down due to energy released via magnetic dipole (MD) or gravitational wave (GW) radiation. In this paper, by systematically analyzing the {\em Swift}/XRT light curves detected before 2018 July, we find 45 light curves that monotonously decay as smooth broken power-law with redshift measured. By assuming that the central engines of these GRBs are a newly-born magnetar, we measure the braking index $n$ of putative millisecond magnetars via MD and GW radiations. The inferred braking indices are neither closed to 3 nor to 5, but range between them with a normal distribution ($n_{\rm c}=4.02\pm 0.11$). We define one dimensionless parameter $\Re$ which is the ratio between MD and GW components, and find that the energy released of magnetar spin-down in most GRBs of our sample are dominated by GW radiation for given $P_0=3$ ms and $\epsilon=0.005$, 0.01. On the other hand, we find that $\Re$ and braking index $n$ seem to be following an anti-correlation within a large systematic error at $t=0$, but depended on the parameters of $P_0$ and $\epsilon$ values. Those results suggest that the contribution of GW radiation can not be ignored and the larger braking index are leading to GW dominated the energy released of magnetar spin-down if indeed magnetars are operating in some long GRBs.