Oscillations and tidal deformations of crystallized white dwarfs

Long predicted more than fifty years ago, strong evidence for the existence of crystalline cores inside white dwarfs has recently been obtained by the Gaia space telescope. It is thus important to investigate how a crystalline core may affect the properties and dynamics of white dwarfs. In this paper, we first study the dependence of the frequencies of the fundamental (f), interfacial (i), and shear (s) oscillation modes on the size of the crystalline core. We find that the frequencies of the i- and s-modes depend sensitively on the size of the core, while the frequency of the f-mode is affected only slightly by at most a few percent for our chosen white dwarf models. We next consider the tidal deformability of crystallized white dwarfs and find that the effect of crystallization becomes significant only when the radius of the core is larger than about 70% of the stellar radius. The tidal deformability can change by a few to about 10 percent when a white dwarf becomes fully crystallized. We also show that there exist approximate equation-of-state insensitive relations connecting the mass, moment of inertia, tidal deformability, and f-mode frequency for pure fluid white dwarfs. Depending on the stellar mass and composition, however, these relations can be affected by a few percent when the white dwarf is crystallized. These changes could leave an imprint on the gravitational waves emitted from the late inspiral or merger of white dwarf binaries, which may be detectable by future space-borne gravitational wave detectors.