Accurate numerical simulations of inspiralling binary neutron stars and their comparison with effective-one-body analytical models

TL;DR

Binary neutron star inspirals offer a principal channel to probe the nuclear-density equation of state through gravitational waves. The authors perform long, high-precision NR simulations of equal-mass BNS with two compactnesses and compare the NR waveforms to tidally extended EOB and Taylor-T4 models, revealing the need for large NNLO tidal corrections to match the NR phasing. A single effective NNLO tidal parameter, $\bar{\alpha}_2$, in the EOB framework suffices to reproduce NR phasing and amplitude up to merger, while LO EOB or unmodified Taylor-T4 substantially deviate. Subtracting tidal effects using the $Q_\omega(\omega)$ diagnostic shows NR data aligns with a point-mass EOB description in the early inspiral, emphasizing the significance of higher-order tidal dynamics. Overall, the study demonstrates that an enhanced EOB approach can accurately model tidal BNS waveforms and lays groundwork for extracting neutron-star EOS information from GW observations.

Abstract

Binary neutron-star systems represent one of the most promising sources of gravitational waves. In order to be able to extract important information, notably about the equation of state of matter at nuclear density, it is necessary to have in hands an accurate analytical model of the expected waveforms. Following our recent work, we here analyze more in detail two general-relativistic simulations spanning about 20 gravitational-wave cycles of the inspiral of equal-mass binary neutron stars with different compactnesses, and compare them with a tidal extension of the effective-one-body (EOB) analytical model. The latter tidally extended EOB model is analytically complete up to the 1.5 post-Newtonian level, and contains an analytically undetermined parameter representing a higher-order amplification of tidal effects. We find that, by calibrating this single parameter, the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, analytical models (either EOB, or Taylor-T4) that do not incorporate such a higher-order amplification of tidal effects, build a dephasing with respect to the numerical waveforms of several radians.

Figures (17)

• Figure 1: Curvature gravitational waveforms $r\psi_4^{22}$ (upper panels) and their instantaneous frequency $M\omega_{22}$ (lower panels) for the M2.9C.12 (left) and M3.2C.14 (right) models. In both cases, the observer's (coordinate) extraction radius is $r_{\rm obs}=500\,M_{\odot}$; this corresponds to $r_{\rm obs }/M= 184.3$ for M2.9C.12 and $r_{\rm obs}/M=165.1$ for M3.2C.14.
• Figure 2: Metric gravitational waveforms $rh_{22}$ and frequencies (upper panels) and the corresponding istantaneous frequency $M\omega_{22}$ (lower panels) obtained from the (double) time-integration of the curvature waveforms of Fig. \ref{['fig:fig_Psi4_waves']} [see Eq. \ref{['eq:int_h_infty']}]. The left panels refer to model M2.9C.12, the right panels to model M3.2C.14. The fact that the waveform modulus grows monotonically without evident spurious oscillations is the indication of the reliability of the determination of the integration constants. See text for details.
• Figure 3: Exploring the properties of $Q_\omega$ curves computed within the EOB model for three binary systems. Tidal interactions are approximated at LO. The inset shows a magnification, in order to highlight the differences among the curves.
• Figure 4: Obtaining the $Q_\omega$ diagnostic from a suitable fitting procedure of the GW phase (for both curvature and metric waveforms). The two vertical lines on the left panels indicate the time interval $\Delta t/M=[1000,2290]$ where we fit the NR phase with Eq. \ref{['eq:phi']}. For completeness we also display the real part of the metric waveform. On the right panels, the (light) dashed lines refer to the $Q_\omega$ obtained by direct numerical differentiation of the raw data; the solid lines are instead obtained from the fitted phase. Although the curves displayed here refer to model M3.2C.14, similar results are obtained also for the binary M2.9C.12.
• Figure 5: Comparing waveforms from isentropic (dashed) and non-isentropic (solid) evolution for BNS model M3.2C.14. Waveforms are computed with the highest resolution and extracted at $r_{\rm obs}=500\,M_{\odot}$. The corresponding phase difference $\phi^{\rm poly_{HR}500}-\phi^{\rm IF_{HR}500}$ is displayed in Fig. \ref{['fig:error_time']}.