Modeling the Multi-Band Afterglow of GRB 130831A: Evidence for a Spinning-Down Magnetar Dominated by Gravitational Wave Losses?

The X-ray afterglow of GRB 130831A shows an "internal plateau" with a decay slope of $\sim$ 0.8, followed by a steep drop at around $10^5$ s with a slope of $\sim$ 6. After the drop, the X-ray afterglow continues with a much shallower decay. The optical afterglow exhibits two segments of plateaus separated by a luminous optical flare, followed by a normal decay with a slope basically consistent with that of the late-time X-ray afterglow. The decay of the internal X-ray plateau is much steeper than what we expect in the simplest magnetar model. We propose a scenario in which the magnetar undergoes gravitational-wave-driven r-mode instability, and the spin-down is dominated by gravitational wave losses up to the end of the steep plateau, so that such a relatively steep plateau can be interpreted as the internal emission of the magnetar wind and the sharp drop can be produced when the magnetar collapses into a black hole. This scenario also predicts an initial X-ray plateau lasting for hundreds of seconds with an approximately constant flux which is compatible with observation. Assuming that the magnetar wind has a negligible contribution in the optical band, we interpret the optical afterglow as the forward shock emission by invoking the energy injection from a continuously refreshed shock following the prompt emission phase. It is shown that our model can basically describe the temporal evolution of the multi-band afterglow of GRB 130831A.