Effective One Body description of tidal effects in inspiralling compact binaries

TL;DR

This work extends the effective-one-body (EOB) approach to include tidal interactions in inspiralling neutron star binaries, aiming to model gravitational-wave phasing up to contact and to constrain the nuclear EOS through tidal parameters. The authors formulate a tidal extension of the EOB dynamics by modifying the radial potential with a tidal term $A^{\rm tidal}(r)$ and assess leading and higher-order post-Newtonian tidal corrections via the dimensionless coefficients $\kappa_\ell^{\rm T}$ and related Love numbers $k_\ell$. They compare tidally extended EOB predictions to nonconformally flat NR sequences, showing that 1PN and higher tidal corrections significantly affect late-inspiral dynamics and phasing, and that NR data currently contain systematic 3PN-like errors that must be accounted for. The study also develops radiative tidal corrections to the waveform and demonstrates that accurate NR-EOB calibration is essential to reliably extract EOS information from future GW observations.

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

Figures (5)

• Figure 1: Comparison between various $\delta$-corrected $h_0$'s (defined in Eq. \ref{['eq:h0']}) and the EOB (resummed, solid line) and 3PN (nonresummed, dashed line) point-mass representations of the binding energy.
• Figure 2: Sections of the function $\chi^2(\bar{\alpha}_1,\delta)$ for three values of $\delta$. The figure displays the corresponding ranges of allowed values of $\bar{\alpha}_1$. Note that, for all models, the minima are rather shallow.
• Figure 3: 2B EOS: Explicit comparison between various analytical representations of the binary binding energy and (corrected) numerical relativity data. The correction parameter is chosen to be $\delta=0.8$. The upper panel refers to EOB (resummed) models. The lower panel to PN (nonresummed) models. For ${\rm EOB^{NLO}}$ effects, we use their Padé representation, Eq. \ref{['eq:pade']} with $\bar{\alpha}_1=3.5$. For the 3PN$^{\rm NLO}$ model, we use $\bar{\alpha}_1'=30$.
• Figure 4: Global comparison between EOB$^{\rm NLO}$ and NR binding energies. We use the values $(\bar{\alpha}_1,\delta)=(1.25,1.2)$. The 3PN point-mass curve is added to guide the eye.
• Figure 5: Accumulated GW phase difference (versus GW frequency $\omega_{22}$) between tidal-EOB (quadrupolar) waveforms and a Taylor-T4-based PN waveform with (leading order) tidal corrections, Eq. \ref{['eq:T4bis']}. Waveforms have been suitably aligned (subtracting a relative time and phase shift) at low frequencies. The circles on the plot indicate, for each curve, the dephasing accumulated up to the "contact" frequencies.