Matter effects on binary neutron star waveforms (1306.4065v1)

Abstract: Using an extended set of equations of state and a multiple-group multiple-code collaborative effort to generate waveforms, we improve numerical-relativity-based data-analysis estimates of the measurability of matter effects in neutron-star binaries. We vary two parameters of a parameterized piecewise-polytropic equation of state (EOS) to analyze the measurability of EOS properties, via a parameter {\Lambda} that characterizes the quadrupole deformability of an isolated neutron star. We find that, to within the accuracy of the simulations, the departure of the waveform from point-particle (or spinless double black-hole binary) inspiral increases monotonically with {\Lambda}, and changes in the EOS that did not change {\Lambda} are not measurable. We estimate with two methods the minimal and expected measurability of {\Lambda} in second- and third- generation gravitational-wave detectors. The first estimate, using numerical waveforms alone, shows two EOS which vary in radius by 1.3km are distinguishable in mergers at 100Mpc. The second estimate relies on the construction of hybrid waveforms by matching to post-Newtonian inspiral, and estimates that the same EOS are distinguishable in mergers at 300Mpc. We calculate systematic errors arising from numerical uncertainties and hybrid construction, and we estimate the frequency at which such effects would interfere with template-based searches.

Matter Effects on Binary Neutron Star Waveforms

This paper addresses the measurable gravitational-wave effects caused by the equation of state (EOS) of binary neutron star systems. Using an expanded set of equations of state and collaborative numerical simulation efforts, the authors focus on the measurability of quadrupole tidal deformability, denoted as $\Lambda$, in second-generation (Advanced LIGO) and third-generation (Einstein Telescope) gravitational-wave detectors.

EOS and Gravitational Wave Signatures

The EOS prescribes the response of cold, dense matter above nuclear densities, directly impacting gravitational-wave signals during neutron-star mergers. Neutron-star binaries undergo tidal interactions that deform the ambient metric, influencing the gravitational-wave emission phase evolution. Crucially, the paper quantifies these deformations using $\Lambda$, which correlates strongly with the fifth power of the stellar radius.

By leveraging numerical-relativity waveforms from two independent codes (Whisky and SACRA), the analysis aims to draw distinctions between EOS configurations based on their impact on waveforms during late inspiral and merger phases. The results delineate clearly measurable departures from point-particle form, especially for EOSs that produce larger neutron-star radii. An accuracy within $\Delta R \approx 1.3 \text{ km}$ is achievable for mergers detectable at an effective distance of $D_{\text{eff}} = 100 \text{ Mpc}$ in Advanced LIGO's high-power detuned mode.

Numerical Simulations and Hybrid Waveforms

The research capitalizes on waveform extraction via different treatments of gravitational radiation, focusing particularly on high-frequency post-merger oscillations. As detectable signals are anticipated to arise from mergers, constructing hybrid waveforms becomes essential. These hybrids merge post-Newtonian models with numerical data through maximum correlation of overlapping time-domains, enhancing detector ability to differentiate EOS effects.

Moreover, employing hybrid waveforms, the authors find improved distinguishability over purely numerical waveforms. While EOSs H and B stand out due to discernible differences in neutron-star radius ($\Delta R$) and tidal deformability ($\Delta \Lambda$), results indicate further reduction in measurement errors using hybrid models as compared to standard post-Newtonian approaches alone.

Implications and Future Directions

This paper forecasts the practical feasibility of EOS parameter estimation in forthcoming observational campaigns using high-sensitivity gravitational-wave detectors. With the detection rates expected during LIGO's operational window yielding multiple potential occurrences per annum, the paper underlines that the EOS-dependent gravitational-wave signatures are consistently measureable within expected signal-to-noise constraints.

Future advancements in numerical relativity enhancing resolution and extending waveform duration across lower frequencies will further fortify parameter constraints on neutron-star matter properties. Additionally, integrating comprehensive simulations involving hydrodynamic and magnetohydrodynamic effects post-merger may expand theoretical insights into EOS details beyond mere tidal influence.

In conclusion, the manuscript delineates a crucial pathway toward understanding neutron-star interiors by discerning EOS impacts via gravitational-wave data, setting a firm foundation for the intersection of numerical relativity and detection physics.