Impact of a third body on binary neutron star tidal interactions

TL;DR

The paper investigates how a distant third body alters tidal interactions in a binary neutron-star system by treating the three-body problem perturbatively with $\bar{\epsilon} \ll 1$. It extends an effective-field-theory framework to include the third body's contribution to the total tidal field, deriving modified equations of motion for the inner binary and driven quadrupole dynamics, and computing the resulting GW energy flux and phase dephasing via an energy-balance approach. A dynamic Love-number analysis reveals frequency-dependent shifts $\lambda^d_{1n}$ relative to the static values $\lambda_{1n}$, with closed-form static-limit dephasing and a general integral expression for the phase correction $\delta\psi$; the results indicate that third-body tides can be significant for b-IMRIs (potentially observable by future detectors) but are more modest for b-EMRIs. Overall, the work demonstrates that the total tidal environment in a triple system can imprint measurable signatures on GW signals, motivating further studies of triple dynamics, angular-momentum evolution, and non-circular configurations. The findings have implications for interpreting GWs in astrophysical environments where hierarchical triples are possible, especially for multi-band or third-generation detector era.

Abstract

For waveform modelling of compact binary coalescence, it is conventionally assumed that the binary is in isolation. In this work, we break that assumption and introduce a third body at a distance. The primary goal is to understand how the distant third body would affect the binary dynamics. However, in the present work, we treat the three-body problem perturbatively and study tidal interaction in the binary due to the third body's presence. We introduce appropriate modifications to the equations governing the orbital motions and the evolution equations of the binary component's quadrupole moment. Further, we obtain the radiated energy and accumulated dephasing for the binary. We show that for b-EMRI, the effect is weak in the tidal sector, while for systems such as b-IMRIs, it would be most relevant to study these effects.

Figures (4)

• Figure 1: A schematic figure of the system under consideration from a top down view. The inner binary with component masses and radii $m_i$ and $\boldsymbol{x}_i$ has its center of mass (COM) at $O'$. The center of the third body (larger sphere) is at $O$, hence it is the origin of the chosen coordinate system; $\boldsymbol{r}$ is the relative separation of the components of the inner binary; $\boldsymbol{X}$ is the separation of the outer binary comprising the third body and the COM of the inner binary.
• Figure 2: In the above figure we show the possible values of $\bar{\epsilon}$ for different binary configurations. In the x-axis, we show the mass ratio of the outer binary consisting of the third body and the inner binary $q=M/m_3$, varying from $2\times10^{-6}$ to $0.12$. In the y-axis, we express the distance between the center of the third body and the COM of the inner binary, $\bar{X}$, in terms of the third body mass $m_3$.
• Figure 3: In the above figure, we show how the presence of a third body can affect the orbital motions. In the left column, we plot $r(t)$ and in the right column, we plot $\varphi(t)$. In the first row, we consider $r_0=6M$ and in the second row, it is $10M$. The third body introduces an oscillation around $r_0$. It shows that the more compact a binary is, the less the absolute radial deviation from $r_0$. In the right column, the corresponding phase evolution is shown. Radiation reaction has not been taken into account while generating these plots.
• Figure 4: In the above figure, we show the accumulated dephasing due to the modification in the static tidal interaction due to the third body. The accumulation is computed using Eq. \ref{['eq: dephasing 3 body static tide']} and integrating from 10 Hz to ISCO. Total mass of the equal mass inner binary $M=2.8 M_{\odot}$. Different colour represents different tidal deformability. In the horizontal-axis strength of the third body's field, $\bar{\epsilon}$, is shown. Even for $\bar{\epsilon}\sim \mathcal{O}(10^{-5})$ the accumulated dephasing is $\mathcal{O}(1)$. However, in realistic binaries, that can survive tidal disruption, with smaller $\bar{\epsilon}$ the accumulation is significantly low. Systems with larger $\bar{\epsilon}$ are more likely to show larger observable imprint of the modified tidal interaction.