Measuring the neutron star equation of state with gravitational wave observations (0901.3258v1)

Abstract: We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron star compactness (the ratio of the mass of the neutron star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of ~1 km at 100 Mpc.

• The paper demonstrates that measuring EOS-induced deviations in gravitational wave phasing during the late inspiral allows neutron star radii to be estimated with about 1 km accuracy.
• The study utilizes advanced numerical simulations and piecewise polytropic models to effectively capture tidal effects and waveform discrepancies in binary neutron star mergers.
• The results indicate that gravitational wave observations in the 500–1000 Hz band, using configurations like Advanced LIGO, can constrain neutron star pressure and stiffness.

Insights into the Measurement of Neutron Star Equations of State Using Gravitational Waves

This paper, authored by Jocelyn S. Read et al., explores the utilization of gravitational wave (GW) observations to determine the equation of state (EOS) of neutron stars. The focus is on quantifying the deviations of gravitational waveforms from the point-particle (PP) approximation observed during the late inspiral phase of binary neutron star (BNS) mergers.

The paper employs numerical simulations to examine how variations in the EOS, particularly its stiffness, affect gravitational wave forms. Previous propositions suggested utilizing effective cutoff frequencies to limit the EOS. However, this paper posits that a more accurate approach involves measuring the deviations in gravitational wave phase evolution during finite size effects in the late inspiral stage. The simulations aim to estimate the point at which gravitational waveforms become distinguishable from a point-particle model at effective distances of up to 100 Mpc.

Results indicate that gravitational wave observations between 500-1000 Hz hold significant potential for constraining EOS pressure and radius. The authors estimate that neutron star radii can be measured with an accuracy of approximately 1 km at 100 Mpc, providing realistic equations of state. Observational scenarios assume detectors like Advanced LIGO in broadband and narrowband configurations, with noise considerations aligned with optimal orientations and luminosity distances.

Key Observations

1. Numerical Methodology: The paper uses simulations based on the Shibata and Uryū evolution codes, which cover the final orbits and merger phases of neutron star binaries. This involves modeling neutron star matter with a parameterized EOS, where the core's stiffness is varied while keeping certain parameters constant, such as adiabatic indices.
2. EOS and Parameters: The EOS is parameterized using a piecewise polytropic model, which captures the behavior of realistic EOS. The pressure $p_1$ and compactness $GM/c^2R$ proved decisive in determining tidal effects. Various polytrope models (2H, H, HB, B, and 2B) represent different EOS softness or stiffness, revealing that the stiffness profoundly influences waveform deviations.
3. Frequency Spectrum Analysis: Fourier transforms of the numerical waveforms show that significant EOS-induced departures commence at frequencies between 700-1000 Hz. The calculated spectrum is matched against detector noise spectra, evaluating Advanced LIGO noise configurations and the anticipated noise for the Einstein Telescope.
4. Detectability and Accuracy: The effectiveness of measuring EOS-induced effects depends on detector configurations. With Advanced LIGO's broadband configuration, the EOS effects are detectable at around 100 Mpc. Narrowband configurations centered at frequencies typical for pulsar detection also show promise. The potential to narrowfully estimate neutron star radii and core pressures from GW measurements is emphasized as highly significant for astrophysical research.
5. Parametric Sensitivity: By evaluating waveform gradients within the parameter space, the paper estimates that the pressure parameter $p_1$ at a certain density can be measured with notable accuracy. This is compelling for neutron star astrophysics, signifying improved understandings of the star's internal structure and size determination with gravitational wave observations.

Implications and Future Directions

The paper presents compelling evidence for the use of advanced gravitational wave detectors to experimentally interrogate neutron star EOS characteristics. Potential future developments include expanding the parameter space coverage, reducing numerical noise, and transcending current simulation limits to achieve even more refined waveform predictions.

Significantly, the paper highlights the reliance on numerical simulations to enhance waveform templates, which consequently might improve source parameter inference from future gravitational wave detections. Understanding neutron star EOS via gravitational waves could critically impact theoretical astrophysics by providing empirical data to support or refine existing models of dense matter physics. The potential advancements in this avenue underscore an exciting frontier in GW astronomy with broad implications for the paper of ultra-dense nuclear material.