Effective One Body description of tidal effects in inspiralling compact binaries (0911.5041v1)

Abstract: The late part of the gravitational wave signal of binary neutron star inspirals can in principle yield crucial information on the nuclear equation of state via its dependence on relativistic tidal parameters. In the hope of analytically describing the gravitational wave phasing during the late inspiral (essentially up to contact) we propose an extension of the effective one body (EOB) formalism which includes tidal effects. We compare the prediction of this tidal-EOB formalism to recently computed nonconformally flat quasi-equilibrium circular sequences of binary neutron star systems. Our analysis suggests the importance of higher-order (post-Newtonian) corrections to tidal effects, even beyond the first post-Newtonian order, and their tendency to {\it significantly} increase the effective tidal polarizability'' of neutron stars. We compare the EOB predictions to some recently advocated, nonresummed, post-Newtonian based (Taylor-T4'') description of the phasing of inspiralling systems. This comparison shows the strong sensitivity of the late-inspiral phasing to the choice of the analytical model, but raises the hope that a sufficiently accurate numerical--relativity--``calibrated'' EOB model might give us a reliable handle on the nuclear equation of state

• The paper extends the Effective One Body framework to include tidal effects, improving the modeling of late inspiral gravitational waves.
• It shows that higher-order post-Newtonian corrections significantly influence neutron stars’ tidal polarizability and alter effective two-body interactions.
• The findings imply that calibrating with numerical relativity data can enhance extraction of nuclear equation of state parameters from gravitational observations.

Overview of the Effective One Body Description of Tidal Effects in Inspiralling Compact Binaries

The paper "Effective One Body description of tidal effects in inspiralling compact binaries" by Thibault Damour and Alessandro Nagar presents an extension to the Effective One Body (EOB) formalism aimed at better modeling tidal effects in binary neutron star inspirals. The paper seeks to address the deficiencies in conventional post-Newtonian (PN) methods, which are limited to low-frequency gravitational wave signals. The extension incorporates tidal parameters to refine the predictive capability up to the point of contact between the binary constituents.

Key Findings and Formulations

1. Tidal Effects and Nuclear Equation of State: The late-stage gravitational wave signals from binary neutron star inspirals are potential key sources for insights into the nuclear equation of state, with tidal forces playing a pivotal role here. This paper proposes modifying the EOB formalism to include tidal effects for a more precise analytical description of these inspirals.
2. Feature Comparison with Nonconformally Flat Models: The tidal-EOB formalism is compared to recent numerical quasi-equilibrium models. The findings highlight the necessity of higher-order PN corrections for tidal effects beyond the leading-order term, with these corrections showing a significant impact on the "effective tidal polarizability" of neutron stars.
3. Theoretical Constructs: The paper introduces an effective action description of tidal effects characterized by multipole tidal coefficients. This leads to modifications in two-body interactions and waveform models, leveraging the unique EOB Hamiltonian structure.
4. Impact on Gravitational Wave Phasing: Critical comparisons with existing Taylor-T4 models demonstrate the sensitivity of late-inspiral phases to the choice of analytical models. It posits that using calibrated numerical relativity data alongside an EOB framework could improve both the reliability and precision of extracting nuclear equation of state information from gravitational wave observations.

Implications and Future Directions

The research asserts the potential for the EOB framework to extend beyond its prior capabilities by effectively modeling tidal effects up to the 'contact' phase of the binary inspiral. Incorporating higher-order PN corrections to tidal effects could double their dynamical impact, presenting opportunities for significant refinement of gravitational waveform predictions. This could bolster the ability of Advanced LIGO and similar observatories to extract nuclear physical parameters from observed inspiral events.

Furthermore, the paper emphasizes the need for continued numerical relativity simulations of inspiralling binary neutron stars to calibrate and optimize the EOB framework's description of higher-order PN tidal effects. The accurate calibration against numeric simulations of inspiral dynamics could be crucial for extracting precise nuclear physics data.

In summary, the paper extends the analytical capabilities of the EOB formalism in capturing tidal interactions within neutron star binaries, crucially reinforcing its application for real-world gravitational wave astronomy and enhancing theoretical descriptions of compact binary systems. This advancement not only aids in refining waveform predictions but also expands the viability of gravitational wave observations as a tool for probing deeper astrophysical and nuclear phenomena.