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Thermal effects on tidal deformability in the last orbits of an inspiraling binary neutron star system

The study of binary neutron stars mergers by the detection of the emitted gravitational waves is one of the most promised tools to study the properties of dense nuclear matter at high densities. It is worth claiming that, at the moment, strong evidence that the temperature of the stars is zero during the last orbits before coalescing, does not exist. Nevertheless, theoretical studies suggest that the temperature concerning the inspiral phase, could reach even a few MeV. According to the main theory, tides transfer mechanical energy and angular momentum to the star at the expense of the orbit, where friction within the star converts the mechanical energy into heat. During the inspiral, these effects are potentially detectable. Different treatments have been used to estimate the transfer of the mechanical energy and the size of the tidal friction, leading to different conclusions about the importance of pre-merger tidal effects. The present work is dedicated to the study of the effect of temperature on the tidal deformability of neutron stars during the inspiral of a neutron star system just before the merger. We applied a class of hot equations of state, both isothermal and adiabatic, originated from various nuclear models. We found that even for low values of temperature ($T<1$ MeV), the effects on the basic ingredients of tidal deformability are not negligible. On the other hand, in the case of the adiabatic star, the thermal effects on tidal deformability remain imperceptible, up to the value $S=0.2 \ {\rm k}_{B}$. According to the main finding, the effect of the temperature on the tidal deformability is indistinguishable. The consequences of the above result are discussed and analyzed.