Optical and X-ray emission from stable millisecond magnetars formed from the merger of binary neutron stars

The coalescence of binary neutron stars (NSs) may in some cases produce a stable massive NS remnant rather than a black hole. Due to the substantial angular momentum from the binary, such a remnant is born rapidly rotating and likely acquires a strong magnetic field (a 'millisecond magnetar'). Magnetic spin-down deposits a large fraction of the rotational energy from the magnetar behind the small quantity of mass ejected during the merger. If the magnetar outflow is indeed trapped behind the ejecta (instead of placing most of its energy into a collimated jet), this has the potential for creating a bright transient that could be useful for determining whether an NS or black hole was formed in the merger. We investigate the expected signature of such an event, including for the first time the important impact of e(+/-) pairs injected by the millisecond magnetar into the surrounding nebula. These pairs cool via synchrotron and inverse Compton emission, producing a pair cascade and hard X-ray spectrum. A fraction of these X-rays are absorbed by the ejecta walls and re-emitted as thermal radiation, leading to an optical/UV transient peaking at a luminosity of similar to 10(43)-10(44) erg s(-1) on a time-scale of several hours to days. This is dimmer than predicted by simpler analytic models because the large optical depth of e(+/-) pairs across the nebula suppresses the efficiency with which the magnetar spin-down luminosity is thermalized. Nevertheless, the optical/UV emission is more than two orders of magnitude brighter than a radioactively powered 'kilonova'. In some cases, nebular X-rays are sufficiently luminous to re-ionize the ejecta, in which case non-thermal X-rays escape the ejecta unattenuated with a similar peak luminosity and time-scale as the optical radiation. We discuss the implications of our results for the temporally extended X-ray emission that is observed to follow some short gamma-ray bursts (GRBs), including the kilonova candidates GRB 080503 and GRB 130603B.