Towards gravitational wave parameter inference for binaries with an eccentric companion

TL;DR

This work addresses the detectability of environmental effects on gravitational-wave signals from binary black holes in three-body systems by introducing a complete Rømer-delay dephasing model that includes arbitrary outer-orbit eccentricity and projection effects. It demonstrates that curvature- and projection-dependent phase features encode information beyond local expansions, enabling constraints on the tertiary mass $m_3$ and outer orbital geometry with Einstein Telescope sensitivity. Through parameter-space surveys and mock injections, it shows that high outer eccentricity ($e_{ m out} \gtrsim 0.7$) and mergers near pericentre ($-\tfrac{\pi}{2} < \nu_m < \tfrac{\pi}{2}$) can yield $\Delta\delta \mathrm{SNR} \gtrsim 8$, breaking degeneracies and allowing discrimination between dynamical and AGN channels; ET could detect a few to tens of such events per year. Reanalysis of GW190814 and O4a events finds no evidence for LOSA, clarifying previous claims and underscoring the need for full-band analyses. The approach lays the groundwork for applying environmental dephasing to LVK data and motivates future population modeling and inclusion of inner-binary eccentricity.

Abstract

We introduce a complete model for dephasing due to line-of-sight acceleration (LOSA) in gravitational wave (GW) signals from stellar-mass binary black holes (BBHs) in three-body systems. Our prescription provides curvature- and projection-dependent phase features that are not recovered by local-expansion-based treatments. We perform parameter-space surveys and mock parameter inferences assuming the nominal sensitivity of the Einstein Telescope (ET) to identify the regime where the time-varying LOSA allows for separate constraints on the outer orbital parameters, in particular the tertiary mass and distance. We estimate that ET may detect a few to tens of such systems per year, provided that all binaries merge dynamically, and demonstrate that these constraints can be used to directly discriminate between a dynamical and AGN origin for BBHs. Finally, we reanalyse the GW190814 event and four O4a events finding no evidence for LOSA, with the previously claimed LOSA in GW190814 disappearing when a sufficiently long data segment is used.

Figures (9)

• Figure 1: Schematic depiction of the premise of this work, in which we study the detectability of the GW phase shift in signals from BBHs whose COM is on an orbit around a third BH. By modelling the outer eccentricity and projection effects, one can in principle constrain the properties of the three-body system.
• Figure 2: $\Delta \delta$SNR contours as a function of outer orbit eccentricity $e_{\rm out}$ and merger true anomaly $\nu_m$, for $m_1 = m_2 = m_3 = 8$ M$_{\odot}$. The panels show the results for three different choices of $\omega_0$, i.e. three different viewing angles. Typically, the largest residuals occur for mergers just before of just after pericentre, where both acceleration and eccentricity signatures are maximal. The black solid contour represents configurations with $\Delta\delta\mathrm{SNR}=8$, which is approximately where it becomes distinguishable from circular dephasing. Additionally, we overplot a contour of constant LOSJ (dashed), according to Eq. \ref{['eq:losj']}.
• Figure 3: Tertiary pericentre distance required to achieve $\Delta \delta{\rm SNR} = 8$ for a merger occurring at pericentre ($\nu_m=0$). Shown are choices for representative masses (colors) and projection angle (dashed lines).
• Figure 4: Shown are the probability $\mathcal{P}_{\nu}$ of finding a binary with a true anomaly within $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ as a function of eccentricty, as well as the probability $\mathcal{P}_e$ of finding a binary with $e> e_{\rm out}$, assuming a thermal distribution. These can be used to give an estimate of the fraction of binaries with the properties discussed in Sec. \ref{['sec:exploration']}.
• Figure 5: Corner plots for 5 outer orbital parameters $m_3, r_\mathrm{p, out}, e_\mathrm{out}, \nu_m,$ and $\omega_0$ for a three-body system observed by ET. The binary merges beyond pericentre, i.e. $\nu_m=-\pi/4$. We set $e_\mathrm{out}=0.65$ and $\omega_0 \sim -\pi/4$. We use $m_1 = 8M_\odot$, $m_2 = 8M_\odot$, $m_3 = 10M_\odot$, $z=0.2$, and $a_\mathrm{out}=0.03$AU. Above the panels, we show the recovered median ($50^{th}$ percentile) and bounds of the 68% credible interval. The same bounds are visualised in the 1-d posteriors in shaded red, as well as the injected true values in bright red.