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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. This has the potential for creating a bright transient that could be useful for determining whether a 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 electron/positron 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 ~1e43-1e44 erg/s on a timescale of several hours to days. This is dimmer than predicted by simpler analytic models because the large optical depth of electron/positron 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 timescale 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.