I-Love-Q Relations for Realistic White Dwarfs

The space-borne gravitational wave interferometer, LISA, is expected to detect signals from numerous binary white dwarfs. At small orbital separation, rapid rotation and large tidal bulges may allow for the stellar internal structure to be probed through such observations. Finite-size effects are encoded in quantities like the moment of inertia ($I$), tidal Love number (Love), and quadrupole moment ($Q$). The universal relations among them (I-Love-Q relations) can be used to reduce the number of parameters in the gravitational-wave templates. We here study I-Love-Q relations for more realistic white dwarf models than used in previous studies. In particular, we extend previous works by including (i) differential rotation and (ii) internal temperature profiles taken from detailed stellar evolution calculations. We use the publicly available stellar evolution code MESA to generate cooling models of both low- and high-mass white dwarfs. We show that differential rotation causes the I-Q relation (and similarly the Love-Q relation) to deviate from that of constant rotation. We also find that the introduction of finite temperatures causes the white dwarf to move along the zero-temperature mass sequence of I-Q values, moving towards values that suggest a lower mass. We further find that after only a few Myrs, high-mass white dwarfs are well-described by the zero-temperature model, suggesting that the relations with zero-temperature may be good enough in most practical cases. Low-mass, He-core white dwarfs with thick hydrogen envelopes may undergo long periods of H burning which sustain the stellar temperature and allow deviations from the I-Love-Q relations for longer times.