Abstract
Space-based gravitational-wave detectors, such as the Laser Interferometer Space Antenna, allow for the probing of the interior of white dwarfs in binaries through the imprints of tidal effects on the gravitational wave signal. In this study, we have computed the tidal deformability of white dwarfs in full general relativity, taking into account the crystallization of their core. The elasticity of the core is found to systematically reduce the tidal deformability, especially for low-mass stars. Moreover, it is shown that errors on the tidal deformability due to the use of the Newtonian theory can become important for massive white dwarfs. Finally, the orbital evolution of eccentric binaries is investigated. Measuring the precession rate of these systems could provide estimations of the individual masses. However, it is found that the neglect of crystallization could lead to very large errors.
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