Exciting Stellar Eccentricity in Gaia BH3 via a Hidden Black Hole Binary

TL;DR

Gaia BH3's highly eccentric outer orbit challenges simple binary explanations. The authors propose that a hidden inner black-hole binary (BHB) excites the outer eccentricity via an apsidal precession resonance as the inner binary decays. For Gaia BH3-like masses, an inner BHB with a_in ~ 1–3 au and e_in ≳ 0.95 can drive e_out to ≈ 0.73, leaving inner parameters around a_in ~ 0.25–0.5 au and e_in ~ 0.75–0.85; stability analysis narrows the viable configurations. The mechanism tolerates moderate misalignment and predicts observable signatures, including short-term RV modulations (~10–50 m s^-1) and slow apsidal precession (≈0.01–0.08 deg yr^-1), testable by Gaia and dedicated RV campaigns. The approach provides a new perspective on Gaia BH3's formation and is readily applicable to other detached eccentric BH binaries such as HD 130298, Gaia BH1, and Gaia BH2.

Abstract

We propose that the high eccentricity of the stellar orbit in Gaia BH3 system could be excited through a secular resonance effect if the inner dark object is, in effect, a tight and eccentric black hole binary (BHB). During the orbital decay of the inner BHB, the apsidal precession rate of the inner binary matches that of the outer stellar orbit, and this resonance advection can drive the outer eccentricity into some extreme values. For a Gaia BH3-like system, we show that a near equal-mass ($q=0.8$) BHB with an initial semi-major axis of 1--3 au and an initial eccentricity $\gtrsim 0.95$ is able to excite the outer orbit to the observed value, leaving a current BHB with semi-major axis 0.25--0.5 au and eccentricity $\sim 0.8$. The eccentric inner BHB imprints two observable signatures on the outer star: (1) short-term RV modulations with an amplitude $\lesssim 100$ m/s and (2) long-term apsidal precession with a rate $\lesssim 0.1^{\circ}$/yr. Although neither of these is detected in the currently available astrometry and RV data, we show that these signals are detectable with the full Gaia astrometry data and dedicated high-precision and/or long-term RV observations. Our work provides a new perspective on the dynamical formation of Gaia BH3, and the methodology is readily applicable to similar systems such as HD 130298, Gaia BH1, and Gaia BH2.

Figures (6)

• Figure 1: Valid initial configurations and the eccentricity of the outer binary at 13 Gyr. The enclosed region by the three conditions---stability (solid curve), resonance (dashed curve), and merger time (dotted and dashed-dotted curves, for two chosen ages)---indicates the initial BHB configurations that could potentially undergo apsidal precession resonance. Colored circles and squares represent the initial configurations used in our numerical integrations, with face colors corresponding to the eccentricity of the outer binary at 13 Gyr. Circles denote systems that have not merged after 13 Gyr, whereas squares represent those that have merged. Initial parameters of inner BHBs consistent with the observations after 13 Gyr of evolution are highlighted with black open circles. The black plus symbol marks the example system whose time evolution is shown in Figure \ref{['fig:time-evolution']}.
• Figure 2: Time evolution of the semi-major axes $a$, eccentricities $e$ and apsidal precession rates $\dot{\varpi}$ of inner and outer binaries. This system is initialized with $a_{\text{in},0}=1.25$ au, $e_{\text{in},0}$=0.97, and $\varpi_\text{in}=\varpi_\text{out}=0\degree$, as highlighted by the black plus symbol in Figure \ref{['fig:1']}. The red (inner) and blue (outer) curves represent the numerical solutions of the double-averaged secular equations as detailed in Liu2015MNRAS.
• Figure 3: The black open circles indicate the present orbital parameters $a_{\text{in}}$ and $e_{\text{in}}$ of inner BHBs that are able to reproduce the observed eccentricity of the stellar orbit in Gaia BH3 and remain stable at the end of the integration. The green-filled circle highlights the final state of the example system, whose time evolution is shown in Figure \ref{['fig:time-evolution']}. The red contours show the semi-amplitude of short-term RV oscillations (Equation \ref{['equ:rv']}) due to the orbital motion of the inner BHB, and the blue contours show the expected apsidal precession rate of the stellar orbit (Equation \ref{['equ:precession']}). The gray-shaded region indicates the unstable region of a coplanar triple with $e_\text{out}=0.73$ according to Equation \ref{['equ:stable']}.
• Figure 4: Time evolution of the outer eccentricity in misaligned triples with various mutual inclination angles ($i_\text{mut}$). The systems are initialized with $a_{\text{in},0}=1.29$ au, $e_{\text{in},0}$=0.97, $\Omega_\text{in}=\Omega_\text{out}=0\degree$, $\omega_\text{in}=0\degree$, and $\omega_\text{out}=180\degree$, similar to that in Figure \ref{['fig:time-evolution']}, except for the mutual inclination, which now varies from $0\degree$ to $60\degree$. The black dashed line marks the observed value of the stellar eccentricity ($e_\text{obs}\approx 0.73$).
• Figure 5: Similar to Figure \ref{['fig:1']} but for three different BH systems (HD 130298, Gaia BH1, and Gaia BH2) based on relevant parameters as detailed in subsection \ref{['subsect:4.2']}.