Analytic modelling of tidal effects in the relativistic inspiral of binary neutron stars

TL;DR

The two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses are presented, and a tidal extension of the effective-one-body (EOB) model is compared.

Abstract

To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB)model. The typical numerical phasing errors over the $\simeq 22$ GW cycles are $Δφ\simeq \pm 0.24$ rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians.

Figures (2)

• Figure 1: Comparison of the EOB $Q_\omega$ curves for different choices of the effective tidal amplification factor $\hat{A}_\ell^{\rm tidal}(u) = 1+\bar{\alpha}_1 u +\bar{\alpha}_2 u^2$, with the corresponding NR ones (dashed lines with open circles) for the two binaries considered. The dotted line corresponds to the "tidal-free" ( or "point-mass") EOB, namely when ignoring tidal effects. The figure also includes two Taylor-T4 models: tidal-free, and augmented by LO tidal effects.
• Figure 2: Comparison between NR and EOB phasing for the M2.9C.12 (left panels) and M3.2C.14 (right panels) binaries. The top panels show the real parts of the $h_{22}$ waveforms, while the bottom panels show the corresponding phase differences. Note the excellent agreement almost up to the time of merger (vertical dashed and dot-dashed lines) and the very large errors when tidal effects are neglected (dotted line).