Tidal Love numbers of neutron stars (0711.2420v4)

Abstract: 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 g_tt, 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.

• The paper corrects typographical errors in key equations and Table 1 to ensure accurate tidal Love number computations.
• It employs fully relativistic models and numerical integration of stellar structure equations to model neutron star responses.
• The refined results highlight a significant up to 24% deviation from Newtonian predictions, improving gravitational wave signal analysis.

Erratum: Tidal Love Numbers of Neutron Stars

The document in question primarily addresses errata related to the original paper on "Tidal Love numbers of neutron stars" by Tanja Hinderer. This corrigendum corrects a couple of typographical errors in the equations (20) and (23) and amends incorrect entries in Table 1 of the original publication.

Overview of the Original Research

The original research by Tanja Hinderer explores the calculation of the tidal Love number $k_2$ for neutron stars using fully relativistic models. The paper approximates various realistic equations of state (EoS) for neutron stars using a polytropic model, typically with an effective polytropic index $n$ ranging from 0.5 to 1.0. The methodology involves deriving the equilibrium stellar model by a numerical integration approach of the Tolman-Oppenheimer-Volkhov equations, followed by calculating linear static perturbations ($l=2$) to the Schwarzschild spacetime via the method articulated by Thorne and Campolattaro.

One of the key results is that relativistic Love numbers differ from their Newtonian counterparts by up to approximately 24%, which holds significance for gravitational wave astronomy. The paper posits that the measurable gravitational wave signals from merging binary neutron stars contain information about these Love numbers, which could offer insights into the neutron star's internal structures.

Erratum Specifics

In this erratum, equations (20) and (23) are corrected to reflect the intended calculations. The corrected equations are essential for the accurate computation of the love numbers $k_2$ and the underlying physics of neutron stars. Equation (23), in particular, provides a refined expression for $k_2$ as a function of the star's compactness parameter and perturbation variables, which is necessary for obtaining consistent astrophysical predictions.

Table 1 has been updated with corrected Love numbers values, reinforcing the initial findings about their dependence on the compactness ratio $M/R$ and polytropic index $n$.

Implications and Future Directions

Hinderer's work, even with the corrections applied, remains significant by aligning well with Newtonian predictions in weak-field limits and highlighting how relativistic effects considerably alter tidal responses in neutron stars. This provides a framework for using gravitational wave observations to constrain neutron star EoS more precisely.

For future research, this corrected formalism paves the way for further improvements in gravitational wave data interpretation and modeling, potentially enabling astronomers to extract cleaner signatures of neutron star internal structure. As gravitational wave observatories advance, particularly with ground and future space-based detectors, further constraints on the EoS will become possible, thereby reducing uncertainties in models of nuclear matter at extreme pressures and densities. Additionally, cross-verifying this data with other astrophysical observations (e.g., X-ray spectroscopy) could provide more comprehensive insights into these dense stellar objects.