The long-lasting X-ray plateau emission in long gamma-ray bursts ( GRBs ) shows observational evidence for ongoing energy injection , which may be from magnetar spindown due to energy released via either magnetic dipole ( MD ) or gravitational wave ( GW ) radiation .
In this paper , by systematically analyzing the Swift /XRT light curves detected before 2018 July , we find 45 light curves with a measured redshift that monotonically decay as a smooth broken power law .
By assuming that the central engines of these GRBs are newly born magnetars , we measure the braking index n of putative millisecond magnetars , due to MD and GW radiations .
The inferred braking indices are not close to 3 or 5 , but range between them with a normal distribution ( n _ { c } = 4.02 \pm 0.11 ) .
We define a dimensionless parameter \Re , which is the ratio between the MD and GW components , and find that the energy released via magnetar spindown in most GRBs of our sample is dominated by GW radiation for P _ { 0 } = 3 ms and \epsilon = 0.005 and 0.01 .
On the other hand , we find that \Re and the braking index n seem to be anticorrelated within a large systematic error at t = 0 , but depend on the values of the parameters P _ { 0 } and \epsilon .
These results suggest that the contribution of GW radiation can not be ignored , and that a larger braking index leads to GWs dominating the energy released during magnetar spindown if indeed magnetars are operating in some long GRBs .