Tidal Love Numbers of Neutron Stars

By T. Hinderer. 2007

1,063 citations recorded by the source corpus.

For a variety of fully relativistic polytropic neutron star models we calculate the star’s tidal Love number k2. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n ≈ 0.5–1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second-order differential equation for the perturbation to the metric coefficient gtt and matching the exterior solution to the asymptotic expansion of the metric in the star’s local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to ~24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.

Subfields: Astronomy and Astrophysics, Geophysics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/3a959f22c5b16d60be6327bb80a5acec02ee8dec

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In Astronomy and Astrophysics

1. Diego Rubiera-García
2. Kent Yagi
3. N. Yunes
4. Aneta Wojnar
5. G. Olmo
6. Dimitrios Psaltis
7. F. Özel
8. Nai-Bo Zhang

In Geophysics

1. Kent Yagi
2. N. Yunes
3. F. Özel
4. Dimitrios Psaltis
5. C. Raithel
6. Bao-An Li
7. Nai-Bo Zhang
8. Jun Xu

In Ocean Engineering

1. N. Yunes
2. Diego Rubiera-García
3. G. Olmo
4. Kent Yagi
5. C. Raithel
6. F. Özel
7. Dimitrios Psaltis
8. Bao-An Li

Citations in the corpus

• Approximate Universal Relations for Neutron Stars and Quark Stars (2016, methodology): “The tidal deformability is related to the dimensionless tidal Love number (also known as the tidal apsidal constant) of the second kind k2 [155] via k2 = 3λ2/(2R (5)) [154].”
• Static response and Love numbers of Schwarzschild black holes (2020, background): “In an orbiting binary system, the Love numbers of the constituents affect the gravitational wave signal at subleading post-Newtonian order [38], which means that gravitational waves can serve as a probe of the Love numbers of both black holes and other astrophysical objects, from neutron stars [39] ”
• Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian (2016, background): “[50] and generalized to higher multipoles in Refs.”
• Unequal mass binary neutron star mergers and multimessenger signals (2016, background): “5) [38] and their compaction ratios C ' 0.”
• The Nuclear Symmetry Energy (2016, background): “The tidal polarizability can be expressed in terms of the dimensionless tidal Love number k2 and the neutron star radius R as λ = 2k2R(5)/(3G), being the Love number solution of a system of first-order differential equations where the EoS is the only input [156].”
• From hadrons to quarks in neutron stars: a review (2017, methodology): “For an introduction to calculations of λ for general relativistic stars see [170], and for the effects of tidal deformations on gravitational merger waveforms see [171–173] and references therein.”