Electromagnetic Emission from newly-born Magnetar Spin-Down by Gravitational-Wave and Magnetic Dipole Radiations

A newly-born magnetar is thought to be central engine of some long gamma-ray bursts (GRBs). We investigate the evolution of the electromagnetic (EM) emission from the magnetic dipole (MD) radiation wind injected by spin-down of a newly-born magnetar via both quadrupole gravitational-wave (GW) and MD radiations. We show that the EM luminosity evolves as $L_{\rm em}\propto (1+t/\tau_c)^{\alpha}$, and $\alpha$ is $-1$ and $-2$ in the GW and MD radiation dominated scenarios, respectively. Transition from the GW to MD radiation dominated epoch may show up as a smooth break with slope changing from $-1$ to $-2$. If the magnetar collapses to a black hole before $\tau_c$, the MD radiation should be shut down, then the EM light curve should be a plateau followed by a sharp drop. The expected generic light curve in this paradigm is consistent with the canonical X-ray light curve of {\em Swift} long GRBs. The X-ray emission of several long GRBs are identified and interpreted as magnetar spin-down via GW or MD, as well as constrain the physical parameters of magnetar. The combination of MD emission and GRB afterglows may make the diversity of the observed X-ray light curves. This may interpret the observed chromatic behaviors of the X-ray and optical afterglow light curves and the extremely low detection rate of a jet-like break in the X-ray afterglow light curves of long GRBs.