# Constraining the Braking Index and Energy Partition of Magnetar spindown with {\em Swift}/XRT data

## TL;DR

This study analyzes Swift/XRT data of long GRB afterglows to measure the braking index of magnetars, revealing that gravitational wave radiation often dominates the energy loss, challenging previous assumptions of magnetic dipole dominance.

## Contribution

It provides the first systematic measurement of the braking index in GRB-associated magnetars and assesses the energy partition between magnetic dipole and gravitational wave radiation.

## Key findings

- Braking indices range between 3 and 5, with a mean of 4.02.
- Most energy is released via gravitational waves for typical magnetar parameters.
- Braking index and energy ratio are anticorrelated, depending on initial spin and ellipticity.

## Abstract

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 {\em 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 ($n_{\rm c}=4.02\pm 0.11$). 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 cannot 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.