If double neutron star mergers leave behind a massive magnetar rather than a
black hole, a bright early afterglow can follow the gravitational wave burst
(GWB) even if there is no short gamma-ray burst (SGRB) - GWB association or
there is an association but the SGRB does not beam towards earth. Besides
directly dissipating the proto-magnetar wind as suggested by Zhang, we here
suggest that the magnetar wind could push the ejecta launched during the merger
process, and under certain conditions, would reach a relativistic speed. Such a
magnetar-powered ejecta, when interacting with the ambient medium, would
develop a bright broad-band afterglow due to synchrotron radiation. We study
this physical scenario in detail, and present the predicted X-ray, optical and
radio light curves for a range of magnetar and ejecta parameters. We show that
the X-ray and optical lightcurves usually peak around the magnetar spindown
time scale (10^3-10^5s), reaching brightness readily detectable by wide-field
X-ray and optical telescopes, and remain detectable for an extended period. The
radio afterglow peaks later, but is much brighter than the case without a
magnetar energy injection. Therefore, such bright broad-band afterglows, if
detected and combined with GWBs in the future, would be a probe of massive
millisecond magnetars and stiff equation-of-state for nuclear matter.Comment: ApJ, in pres
