Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral (0911.3535v1)

Abstract: The early part of the gravitational wave signal of binary neutron star inspirals can potentially yield robust information on the nuclear equation of state. The influence of a star's internal structure on the waveform is characterized by a single parameter: the tidal deformability lambda, which measures the star's quadrupole deformation in response to the companion's perturbing tidal field. We calculate lambda for a wide range of equations of state and find that the value of lambda spans an order of magnitude for the range of equation of state models considered. An analysis of the feasibility of discriminating between neutron star equations of state with gravitational wave observations of the early part of the inspiral reveals that the measurement error in lambda increases steeply with the total mass of the binary. Comparing the errors with the expected range of lambda, we find that Advanced LIGO observations of binaries at a distance of 100 Mpc will probe only unusually stiff equations of state, while the proposed Einstein Telescope is likely to see a clean tidal signature.

• The paper calculates tidal deformability across realistic equations of state, highlighting significant variations linked to neutron star radii.
• The paper integrates tidal effects into gravitational waveform models, demonstrating phase shifts in early inspiral that encode EOS properties.
• The paper evaluates gravitational wave detector sensitivity, showing that instruments like Advanced LIGO and the Einstein Telescope can differentiate between stiffer and broader EOS profiles.

Tidal Deformability of Neutron Stars and Gravitational Wave Implications

The paper "Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral" by Hinderer et al. presents a comprehensive examination of how the intrinsic structural properties of neutron stars, specifically their tidal deformability, influence gravitational wave emissions during binary inspiral events. The central parameter of interest, tidal deformability $\lambda$, quantifies the degree to which a neutron star is distorted by its companion's gravitational field, playing a pivotal role in delineating the equation of state (EOS) of dense nuclear matter.

Key Findings

• Tidal Deformability Calculation: The authors calculate the tidal deformability $\lambda$ over a diverse array of realistic EOS. Tidal deformability varies significantly across different EOS, spanning an order of magnitude. This diversity is substantially driven by the disparity in neutron star radii predicted by varying EOS models.
• Gravitational Wave Signal Modulation: By integrating $\lambda$ into gravitational waveform models, the paper demonstrates that tidal effects impart a discernible phase shift to the gravitational wave signal. The modulation is particularly pronounced in the early inspiral, where it can precisely encode the properties of the EOS.
• Detector Sensitivity: The paper evaluates the capacity of gravitational wave detectors, notably Advanced LIGO and the proposed Einstein Telescope, to measure $\lambda$. Advanced LIGO, within a typical detection range of 100 Mpc, is mostly constrained to identify very stiff EOSs. In contrast, the Einstein Telescope’s enhanced sensitivity is likely to discern a more extensive spectrum of tidal signatures.
• EOS Differentiation: The paper reveals a steep increase in measurement error of $\lambda$ correlating with the total mass of the binary system, thus suggesting that EOS effects are more detectable in lower mass neutron star binaries.

Implications and Future Directions

These insights illuminate the significant potential of gravitational wave astronomy as a tool for nuclear physics. Specifically, the potential to constrain the neutron star EOS considerably is highlighted. However, this also underscores the prerequisite of thorough waveform modeling and understanding of point mass dynamics to isolate EOS effects accurately. The need for further analysis, particularly concerning high-frequency waveform content, becomes apparent as an area for prospective research.

Theoretical and Practical Ramifications

From a theoretical perspective, refining the understanding of $\lambda$ contributes to resolving uncertainties surrounding the state of matter at super-nuclear densities. Practically, enhancing detector configurations and multi-detector networks could exponentially augment constraint capabilities, marking meaningful advances in multimessenger astrophysics.

Conclusions

This paper robustly positions tidal deformability as a key parameter in deciphering neutron star structure and composition through gravitational wave observations. As gravitational wave astronomy advances, extending the frequency range of gravitational wave signal analysis, particularly at higher post-Newtonian orders, remains crucial. The integration of increasingly sophisticated numerical simulations and analytic models stands to bridge remaining gaps, providing a clearer picture of the fundamental physics governing compact objects like neutron stars.