Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals (1203.4352v1)

Abstract: The gravitational wave signal from a binary neutron star inspiral contains information on the nuclear equation of state. This information is contained in a combination of the tidal polarizability parameters of the two neutron stars and is clearest in the late inspiral, just before merger. We use the recently defined tidal extension of the effective one-body formalism to construct a controlled analytical description of the frequency-domain phasing of neutron star inspirals up to merger. Exploiting this analytical description we find that the tidal polarizability parameters of neutron stars can be measured by the advanced LIGO-Virgo detector network from gravitational wave signals having a reasonable signal-to-noise ratio of $\rho=16$. This measurability result seems to hold for all the nuclear equations of state leading to a maximum mass larger than $1.97M_\odot$. We also propose a promising new way of extracting information on the nuclear equation of state from a coherent analysis of an ensemble of gravitational wave observations of separate binary merger events.

• The paper enhances the EOB formalism by incorporating tidal effects to accurately capture neutron star inspiral dynamics up to merger.
• It introduces an analytical phasing model at 2.5 PN order that extracts EOS-dependent tidal parameters from gravitational waveform data.
• Advanced detectors like LIGO-Virgo can measure these effects at an SNR of about 16, offering reliable constraints on neutron star EOS.

Measurability of the Tidal Polarizability of Neutron Stars in Late-Inspiral Gravitational-Wave Signals

The paper "Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals" by Damour et al. offers an in-depth analysis of the prospects for measuring the tidal polarizability of neutron stars using gravitational waveform data from binary neutron star (BNS) inspirals. The authors deploy an extended version of the effective one-body (EOB) formalism, which integrates tidal effects to accurately describe the phasing of neutron star inspirals up to the point of merger. This work is pivotal for extracting information about the equation of state (EOS) of nuclear matter present in neutron stars, a fundamental problem in theoretical astrophysics and nuclear physics.

Key Approaches and Findings

1. EOB Formalism and Tidal Effects: The authors enhance the traditional EOB approach by incorporating tidal interactions, allowing a refined analytical description of BNS inspiral dynamics. They validate this approach by confirming its agreement with numerical relativity simulations up to the merger phase. The tidal contribution to the phasing in the frequency domain is shown to be measurable using current and future detectors like the LIGO-Virgo network, assuming a signal-to-noise ratio (SNR) of around 16.
2. Analytical Modeling: By extending the EOB formalism, Damour et al. derive a phasing model that includes tidal contributions up to 2.5 post-Newtonian (PN) order. This model is critical for ensuring accurate data analysis by capturing the phasing of gravitational waves effectively till the late inspiral phase. The derived model proposes a controlled way of using the waveform data to extract tidal polarizability metrics that reflect the neutron star EOS.
3. EOS Dependence and Measurement Accuracy: The paper highlights the sensitivity of neutron star tidal parameters to the EOS, showing that these parameters can be measured with a 95% confidence level with advanced gravitational wave detectors. For instance, the authors propose a new methodology to coherently analyze multiple BNS events to enhance the measurement accuracy of the EOS-dependent quantities.
4. Numerical Analysis and Results Interpretation: The authors exhibit the impact of measurement noise and parameter correlations in these analyses, using a Fisher matrix formalism. They detail the performance of their models across a wide range of realistic EOS scenarios, demonstrating promising results especially for softer EOS, contrary to earlier conservative estimates in the literature.

Implications and Future Directions

• Observational Potential: The work demonstrates the ability of current and next-generation gravitational wave observatories to provide constraints on neutron star EOS through tidal effects, even in the presence of complex noise and correlation environments.
• Model Improvements: By depicting potential increases in analytical accuracy and suggesting avenues for including higher-order multipolar contributions, the authors lay the groundwork for further refining waveform models to include even more subtle relativistic effects.
• Application to Black Hole-Neutron Star (BH-NS) Binaries: While the focus is on BNS systems, the formalism is applicable to mixed binaries, enabling a fuller exploration of astrophysical scenarios involving tidal interactions.

Conclusion

The analytical and numerical framework presented establishes a solid step forward in gleaning detailed properties about the microscopic state of neutron star matter from gravitational wave observations. This paper not only addresses the methodological necessities for accurately modeling the effects of tidal forces in neutron stars but also paves the way for exploiting future observational data, making significant advancements in our understanding of the dense matter EOS and the astrophysical role of neutron stars.