Tidal deformability of crystallized white dwarfs in full general relativity

Abstract

Space-based gravitational-wave detectors offer new prospects for probing the interior of white dwarfs in binary systems through the imprints of tidal effects on the gravitational-wave signal. Some of the binaries that will be observed could have evolved for long enough for the white dwarfs to be at least partially crystallized. The apsidal motion constant k 2 (also called the second gravitoelectric Love number) of a cold crystallized white dwarf is computed in full general relativity considering different compositions. The elasticity of the crystallized core is found to systematically reduce the tidal deformability, especially for low-mass stars. Fully relativistic results are compared to those obtained in Newtonian gravity. It is shown that the relativistic correction to the observable tidal deformability k 2 R 5 (where R is the stellar radius) is negligible for low-mass white dwarfs but becomes increasingly important for more massive white dwarfs. When approaching the maximum mass, the application of Newtonian theory instead of general relativity leads to dramatic errors. The case of eccentric binaries, for which the precession of the periastron causes a frequency splitting of the gravitational-wave signal depending on the apsidal motion constants of the two stars, is investigated. Future measurements of the precession rate by the Laser Interferometer Space Antenna, which is planned to be in operation within the next decade, could potentially provide estimates of the individual masses. It is found that the errors incurred by the neglect of the elasticity of the crystallized core could be very large, especially for low-mass white dwarfs. Gravitational-wave observations could thus provide a new way to study the crystallization of white dwarfs.

Imprint of the Crystallization of Binary White Dwarfs on Gravitational Wave Observations with LISA

“…This system is to be solved from the stellar center by using the initial conditions from the Taylor expansions of the different functions up to the surface, where appropriate boundary conditions are imposed (see Ref. [33] for details). The matching of the interior solution with the exterior solution (in vacuum) at the stellar surface allows for the obtainment of the tidal Love number k 2 [27].…”

“…appropriate boundary conditions are imposed (see Ref. [33] for details). The matching of the interior solution with the exterior solution (in vacuum) at the stellar surface allows for the obtainment of the tidal Love number 𝑘 2 [27].…”

“…Detailed results can be found in Ref. [33]. From such measurements, it will potentially be possible to infer the individual masses.…”

Role of Quark Matter and Color Superconductivity in the Structure and Tidal Deformability of Strange Dwarfs

“…Specifying the Eulerian static metric perturbation in the Regge-Wheeler gauge and the static Lagrangian displacement vector, one can compute and simplify Equation ( 11) to obtain a system of six ordinary first-order differential equations to be solved numerically inside the star together with the TOV equations. The full set of equations is given in [38]. Initial conditions at the star center are given by the Taylor expansions of the different functions, and appropriate boundary conditions are imposed at the crust-core interface and at transitions between adjacent hadronic layers marked by density and shear modulus discontinuities (see [38] for details).…”

Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus

“…These are oscillation spectra, in particular interpretation of the observed quasi-periodic oscillations after giant flares of magnetars (e.g., Hansen & Cioffi 1980;Schumaker & Thorne 1983;McDermott et al 1988;Strohmayer et al 1991;Gabler et al 2011Gabler et al , 2012Gabler et al , 2013Gabler et al , 2018Sotani et al 2018;Kozhberov & Yakovlev 2020), the mass distribution asymmetry (mountains) in the crust, which can lead to emission of gravitational waves (see e.g., Ushomirsky et al 2000;Haskell et al 2006;Horowitz 2010;Johnson-McDaniel & Owen 2013;Kerin & Melatos 2022 for the models and Abbott et al 2020; The LIGO Scientific Collaboration et al 2021, 2022 for recent observational constraints). Elastisity can also affect tidal deformability, which leads to quite substantial effects for white dwarf binary evolution (Perot & Chamel 2022), however for neutron star binaries the effect is almost negligi-⋆ E-mail: andr.astro@mail.ioffe.ru ble Penner et al (2011); Biswas et al (2019); Pereira et al (2020); Gittins et al (2020).…”