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Magnetohydrodynamic waves excited by a coupling between gravitational waves and a strongly magnetized plasma in binaries of neutron stars

Coalescence of binary neutron stars (BNSs) is one of the sources of gravitational waves (GWs) able to be detected by ground-based interferometric detectors. The event GW170817 was the first observed in the gravitational and electromagnetic spectra, showing through this joint analysis a certain compatibility with the models of short gamma-ray bursts (sGRBs) to explain the signature of this system. Due to the intense magnetic fields of the neutron stars, the plasma magnetosphere stays strongly magnetized and the propagation of the GW through plasma can excite magnetohydrodynamic (MHD) modes such as Alfvén and magnetosonic waves. The MHD modes carry energy and momentum through the plasma, suggesting a mechanism to accelerate the matter during the coalescence of the binaries, explaining some characteristics of the fireball model of the sGRBs. We present a semianalytical formalism to determine the energy transferred by the GW-MHD interaction during the inspiral phase of the stars. Using the inferred physical parameters for GW170817, we show that the energy in the plasma can reach maximum value $\sim 10^{35}\,{\rm J}$ ($\sim 10^{32}\,{\rm J}$) for the Alfvén mode (magnetosonic mode) if the angle formed between the background magnetic field and the GW propagation direction is $θ= π/ 4$. Particularly, for $θ= π/ 2$ only the magnetosonic mode is in coherence with the GWs. In this case, the excited energy in the plasma reaches maximum value $\sim 10^{36} {\rm J}$. If the magnetic field on the surface of the progenitors of the event GW170817 was $\sim 2\times 10^{9}\,{\rm T}$ then energies comparable to those inferred for the GRB 170817A could be obtained. In particular, our semianalytical formalism show consistence with the results obtained by other authors through full general relativistic magnetohydrodynamics (GRMHD) simulations. [ABRIDGED]