Triples as Links between Binary Black Hole Mergers, their Electromagnetic Counterparts, and Galactic Black Holes

TL;DR

This paper proposes a physically motivated channel linking GW-detected binary BH mergers, Gaia-detected wide BH–star systems, and accreting X-ray binaries via a passive tertiary in a hierarchical triple. After the inner BH binary merges and experiences a GW recoil kick, the tertiary can either be disrupted to yield a prompt EM counterpart, evolve into a LMXB via tidal interactions, remain as a Gaia-like wide companion, or become unbound. Using hexadecapole secular dynamics plus PN terms and a recoil-kick model, the authors perform a proof-of-concept population study showing that a small but nonzero fraction of mergers can produce observable EM signals on short timescales and that a non-negligible portion can yield Gaia-BH-like post-kick systems, potentially accounting for 1–10% of Milky Way Gaia BHs. They estimate EM and Gaia-BH detection rates, predict characteristic optical–UV transients with delays of about 10 days, and discuss how this channel links three BH observational channels, offering a rare but testable path for EM counterparts to BH mergers and for Gaia BH formation scenarios.

Abstract

We propose a formation pathway linking black holes (BHs) observed in gravitational-wave (GW) mergers, wide BH-stellar systems uncovered by Gaia, and accreting low-mass X-ray binaries (LMXBs). In this scenario, a stellar-mass BH binary undergoes isolated binary evolution and merges while hosting a distant, dynamically unimportant tertiary stellar companion. The tertiary becomes relevant only after the merger, when the remnant BH receives a GW recoil kick. Depending on the kick velocity and system configuration, the outcome can be: (i) a bright electromagnetic (EM) counterpart to the GW merger; (ii) an LMXB; (iii) a wide BH-stellar companion resembling the Gaia BH population; or (iv) an unbound, isolated BH. Modeling the three-body dynamics, we find that $\sim 0.02\%$ of LIGO-Virgo-KAGRA (LVK) mergers may be followed by an EM counterpart within $\sim$10 days, produced by tidal disruption of the star by the BH. The flare is likely brightest in the optical-UV and lasts days to weeks; in some cases, partial disruption causes recurring flares with a period of $\sim$2 months. We further estimate that this channel can produce $\sim 1-10\%$ of Gaia BH systems in the Milky Way. This scenario provides the first physically motivated link between GW sources, Gaia BHs, and some X-ray binaries, and predicts a rare but robust pathway for EM counterparts to binary BH mergers, potentially detectable in LVK's O5 run.

Figures (4)

• Figure 1: An illustration of the system. The three-body system is composed of two stellar mass BHs and a distant main-sequence stellar tertiary. The angle between the first (second) BH's spin, $S_1$ ($S_2$) and the inner binary angular momentum $L_{\rm BHs}$ is $i_{s1}$ ($i_{s2}$), and the angle in the plane of the orbit, measured from the semimajor axis, is $\varphi_{1}$ ($\varphi_{2}$). Finally, the angle between the inner binary angular momentum and the recoil kick vector is $\alpha$. Post-recoil kick, there are two possible outcomes: unbound orbits (87% of all systems) and bound orbits (13% of all systems). We highlight that 8% of all systems are bound with a period shorter than 10 years, which are Gaia-BH-like systems. In $0.2\%$ of all cases, either a bound or an unbound system results in an EM counterpart. These are designated by having the closest approach $R_c\leq r_{\rm circ}$, where $97.6\%$ (2.4%) of all EM-bright sources are on a bound (unbound) orbit when they cross $r_{\rm circ}$. About 50% of these systems have closest approach smaller than $r_{\rm Roche}$, resulting in a prompt disruption event, and yielding an EM counterpart to the GW emission with a time delay of about $10$ days. Finally, $50\%$ of the EM-signatures have $r_{\rm Roche} < R_c\leq r_{\rm circ}$, which may result in a low-mass X-ray binary (LMXB). Note that as stars evolve beyond the main sequence and become red giants, their radius expands, yielding a larger fraction of systems undergoing mass transfer events. We discuss these probabilities in detail in § \ref{['sec:EMrates']}.
• Figure 2: Two examples of the orbital outcome of a recoil kick on an orbit. We consider a system of two low-spin BHs with $S_1=S_2=0.01$, and spin-orbit angles of $2^\circ$, $1^\circ$, $\Omega_{s1}=90^\circ$ and $\Omega_{s2}=270^\circ$. The mutual inclination is set to $0.1^\circ$. Before the kick, the star has a semi-major axis of $20$ au and eccentricity $e_\star=0.9$ ( right column), and $e_\star=0.83$ ( left column). The argument of periapsis of the inner (outer) binary at the time of the merger is $300^\circ$ ($20^\circ$). These angles are relevant for the rotation of the various vectors to the invariant plane. See text for more details. We assume that the kick took place when the star's phase was at $10^\circ$ ( right column), and $5^\circ$ ( left column). Various post-merger quantities are shown as a function of the mass ratio of the two original BHs, $q$. The bottom row shows the closest approach, Equation (\ref{['eq:Rc']}). Overplotted are the tidal radius, $r_{\rm circ}$, and the Roche radius $r_{\rm Roche}$. We expect EM signatures for BHs that approach their stellar companion within these radii. The middle row depicts the post-kick semi major axis $a_{\star,n}$, solid red lines and pericenter $a_{\star,n}(1-e_{\star,n})$, dashed purple lines. Overplotted are the initial (pre-kick) semi-major axis and pericenter of the star, solid and dashed gray lines, respectively. Lastly, Gaia-BH1's semi-major axis and pericenter ($a_{\rm Gaia~BH1}$, and $r_{p,\rm Gaia~BH1}=a_{\rm Gaia~BH1}(1-e_{\rm Gaia~BH1})$) are also overplotted, in pink and light purple lines El-Badry+23GaiaH1. The top row shows the normalized velocity $u_k=v_{\rm kick}/v_r$, and $\sin\gamma$, where $\gamma$ is the angle between the radius vector and the post-kick velocity vector. The grid highlights that when $u_k=1$, $\gamma\to 0^\circ$, thus $R_c\to 0$. Note that here a lower (higher) pre-kick eccentricity, while keeping all of the other parameters constant, yields a wider, more easily unbound (tighter) post-kick binary. The opposite trend is expected for a kick that takes place at apo-center, see Equations (\ref{['eq:singamma2apo']}) and (\ref{['eq:ukperi']}).
• Figure 3: Post-kick orbital configurations of the proof-of-concept population. Top panel presents the post-kick bound population ($13\%$ of all systems), and shows the eccentricity (y-axis) and semi-major axis (x-axis) of the star-BH orbit. Over-plotted are the orbital parameters of Gaia BH1 El-Badry+23GaiaH1 and the approximate part of the parameter space, potentially detectable by Gaia (defined by having a period up to 10 years and pericenter larger than $r_{\rm circ}$). Bottom panel shows the closest approach (which is the pericenter for bound systems) of all of the systems in the simulation as a function of the angle between the recoil kick vector and the star's initial (pre-kick) orbital velocity, i.e., $\theta = {\bf v}_r\cdot {\bf v}_{\rm kick}/(v_r v_{\rm kick})$. Over-plotted is the Roche radius. The color code depicts the star's initial (pre-kick) semi-major axis. The points with red edges are those that have $R_c\leq r_{\rm circ}$ and are therefore likely to produce EM emission.
• Figure 4: Time delay distribution for the EM counterpart, assumed to be the time between the merger of the inner BH binary and when the BH remnant -- star separation shrinks below $r_{\rm circ}$. Both bound ($87\%$ of all systems with $R_c\leq r_{\rm circ}$) and unbound systems, as well as those that crossed the star's Roche limit ($\sim 50\%$ out of all systems with $R_c\leq r_{\rm circ}$), exhibit the same distribution. The average of this distribution is $\sim 10$ days. We note that the fallback time of the bound debris onto the BH is on the order of a day, or less, see Equation (\ref{['eq:TDEFB']}).