Constraining neutron star tidal Love numbers with gravitational wave detectors (0709.1915v2)

Abstract: Ground-based gravitational wave detectors may be able to constrain the nuclear equation of state using the early, low frequency portion of the signal of detected neutron star - neutron star inspirals. In this early adiabatic regime, the influence of a neutron star's internal structure on the phase of the waveform depends only on a single parameter lambda of the star related to its tidal Love number, namely the ratio of the induced quadrupole moment to the perturbing tidal gravitational field. We analyze the information obtainable from gravitational wave frequencies smaller than a cutoff frequency of 400 Hz, where corrections to the internal-structure signal are less than 10 percent. For an inspiral of two non-spinning 1.4 solar mass neutron stars at a distance of 50 Mpc, LIGO II detectors will be able to constrain lambda to lambda < 2.0 10^{37} g cm^2 s^2 with 90% confidence. Fully relativistic stellar models show that the corresponding constraint on radius R for 1.4 solar mass neutron stars would be R < 13.6 km (15.3 km) for a n=0.5 (n=1.0) polytrope.

• The paper presents a novel method that extracts tidal Love numbers from low-frequency gravitational waves during the inspiral phase to constrain neutron star equations of state.
• It uses relativistic neutron star models and post-Newtonian corrections to derive a phase shift dependent on the tidal parameter, achieving a constraint of λ ≤ 2.0×10^37 g cm^2 s^2 for LIGO II.
• Systematic error analysis confirms corrections below 10%, ensuring the robustness of the method and paving the way for future improvements in gravitational wave astronomy.

Constraining Neutron Star Tidal Love Numbers with Gravitational Wave Detectors

The paper by Flanagan and Hinderer presents a detailed examination of the potential to extract information on the nuclear equation of state (EoS) from the gravitational wave (GW) signals emitted during neutron star binaries' inspirals. Their paper concentrates on the early, low-frequency part of the GW signal where finite-size effects due to the neutron stars' tidal interactions manifest as a phase shift. This effect can be succinctly characterized by the tidal Love number, a parameter that encapsulates the star's susceptibility to tidal deformation.

The primary motivation for this research arises from the limited constraints on the nuclear EoS at the high-density interior regimes of neutron stars, specifically densities in the range of $$\rho \sim 2 - 8 \times 10^{14}\,{\rm g}\,{\rm cm}^{-3}$$. Traditional methods of constraining the EoS involve analyzing late inspiral and merger phases at high GW frequencies ($f \gtrsim 500$ Hz), which present significant computational challenges and uncertainties due to the complexity of solving the general relativistic hydrodynamics equations and unknown parameters such as the stars' spin. Flanagan and Hinderer circumvent these issues by focusing instead on the earlier inspiral phase, which allows a cleaner assessment of one specific EoS-related parameter: the tidal Love number.

In their analysis, Flanagan and Hinderer derive an expression for the phase shift in the GW signal due to tidal interactions that depend predominantly on the Love number. Their approach leverages fully relativistic models of neutron stars to calculate Love numbers. For LIGO II detectors, they estimate that for an inspiral event involving two non-spinning $1.4 M_{\odot}$ neutron stars at 50 Mpc, the cutoff frequency at 400 Hz can constrain the tidal parameter $\lambda$ to $$\lambda \leqslant 2.0 \times 10^{37}\,{\rm g}\,{\rm cm}^2{\rm s}^2$$ with 90% confidence. This constraint translates to an upper limit on the neutron star radius of $R \leqslant 13.6 \,{\rm km}$ for specific polytropic models.

The authors meticulously consider different sources of potential systematic errors and confirm that such corrections are below 10%, ensuring robustness in their estimations. Their analysis establishes a framework for extracting the Love numbers from measured GW signals while incorporating known post-Newtonian corrections and tidal interactions.

This paper's implications are significant for theoretical and observational astrophysics. By developing a method to probe the nuclear EoS through Love numbers at lower GW frequencies, researchers can potentially gain access to unique insights about the internal structure of neutron stars and the behavior of matter at nuclear densities, which remains one of the outstanding challenges in modern astrophysics. Moreover, this work highlights the utility of GW astronomy in constraining exotic hypotheses related to neutron star compositions and further paves the way for future improvements in detector sensitivity and data analysis techniques aimed at refining EoS models.

Future work can expand on this by exploring systems involving spinning neutron stars or asymmetric masses, and incorporating higher-order tidal interactions that could provide even finer constraints on neutron star properties. As the field of GW astronomy matures, the insights derived from studies like this could significantly enhance our understanding of the dense matter beyond the reach of terrestrial experiments.