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Gravitational waves from massive magnetars formed in binary neutron star mergers

Binary neutron star (NS) mergers are among the most promising sources of gravitational waves (GWs), as well as candidate progenitors for short Gamma-Ray Bursts (SGRBs). Depending on the total initial mass of the system, and the NS equation of state (EOS), the post-merger phase can see a prompt collapse to a black hole, or the formation of a supramassive NS, or even a stable NS. In the case of post-merger NS (PMNS) formation, magnetic field amplification during the merger will produce a magnetar with a large induced mass quadrupole moment, and millisecond spin. If the timescale for orthogonalization of the magnetic symmetry axis with the spin axis is sufficiently short the NS will radiate its spin down energy primarily via GWs. Here we study this scenario for various outcomes of NS formation: we generalise the set of equilibrium states for a twisted torus magnetic configuration to include solutions that, at a fixed exterior dipole field, carry a larger magnetic energy reservoir; we hence compute their magnetic ellipticity and the strength of the expected GW signal as a function of the magnitude of the dipole and toroidal field. The relative number of GW detections from PMNSs and from binary NSs is a strong function of the NS equation of state (EOS), being higher (~ 1%) for the stiffest EOSs and negligibly small for the softest ones. For intermediate-stiffness EOSs, such as the n=4/7 polytrope recently used by Giacomazzo \& Perna or the GM1 used by Lasky et al., the relative fraction is ~0.3%; correspondingly we estimate a GW detection rate from stable PMNSs of ~ (0.1-1) yr$^{-1}$ with Advanced detectors, and of ~ (100-1000) yr$^{-1}$ with third generation detectors such as the Einstein Telescope. Measurement of such GW signal would provide strong constraints on the NS EOS and on the nature of the binary progenitors giving rise to SGRBs.