Formation of Close Binaries through Massive Black Hole Perturbations and Chaotic Tides

TL;DR

This work extends the Hills mechanism by modeling the long-term evolution of binaries around a MBH, incorporating outer-orbit relaxation, MBH tidal perturbations, and dynamical tides. Using an iterative-map approach for a single $l=m=2 f$-mode and REBOUND for close encounters, it shows that chaotic tides can efficiently harden wide binaries into close systems ($a_b \lesssim 10\,R_*$), with up to about half of wide binaries in the empty loss-cone regime undergoing chaotic tides. The resulting close binaries can produce the fastest hyper-velocity stars and connect to nuclear transients such as repeating partial TDEs and QPEs, while also offering a pathway to EMRIs through subsequent evolution. The findings highlight chaotic tides as a robust channel forming close binaries in galactic nuclei and motivate future work on the full post-CT binary evolution and observational signatures.

Abstract

Hills breakup of binary systems allows massive black holes (MBH) to produce hyper-velocity stars (HVSs) and tightly bound stars. The long timescale of orbital relaxation means that binaries must spend numerous orbits around the MBH before they are tidally broken apart. Repeated MBH tidal perturbations over multiple pericenter passages can perturb the binary inner orbit to high eccentricities, leading to strong tidal interactions between the stars. In this work, we develop a physical model of the MBH-binary system, taking into account outer orbital relaxation, MBH tidal perturbations, and tidal interactions between the binaries in the form of dynamical tides. We show that when the inner orbit reaches high eccentricities such that the pericenter radius is only a few times stellar radii ($R_*$), the stellar oscillation modes can grow chaotically and rapidly harden the binaries to semi-major axes $a_b\lesssim 10\,R_*$. We find that a significant fraction (up to 50\%) of initially wide binaries that are in the empty loss-cone regime ($a_b\sim 1.0\,{\rm AU}$) do not undergo Hills breakup as wide binaries, but instead experience chaotic growth of tides and become close binaries. These tidally hardened binaries provide a new channel for the production of the fastest HVSs, and are connected to other nuclear transients such as repeating partial tidal disruption events and quasi-periodic eruptions.

Figures (16)

• Figure 1: Overview of the physical processes in the MBH-binary three-body system. The binary system is on a highly eccentric orbit around the MBH. On a timescale of $t_{L,\rm relax}$ (eq. \ref{['eq:t-relax-AM']}), the outer pericenter radius $r_p$ gradually changes because of the gravitational encounter with other field stars. In our simulation, the gravitational encounters are not resolved; instead, the outer orbit relaxation is handled using a simplified version of Fokker-Planck formulation (Section \ref{['sec:Methods-outer-relaxation']}). Every time the binary passes through the pericenter around the MBH, its inner eccentricity is perturbed by the MBH's tidal forces (Section \ref{['sec:Methods-MBH-perturbation']}). When the inner eccentricity $e_b$ grows to a sufficiently large value, two binary stars start to interact tidally near the inner pericenter, which causes the energy transfer between the inner orbit and the stellar oscillations. Under certain conditions (eq. \ref{['eq:chaotic-tides-phase-change']}), the stellar mode amplitude will grow chaotically, leading to the rapid hardening of the binary system (Section \ref{['sec:Methods-chaotic-tides']}). Finally, there exists various precessions that can affect the MBH perturbations on $e_b$ (Appendix \ref{['sec:App-precessions']}).
• Figure 2: The binary separation $r_b(t)$ as a function of time. The binary system is on an eccentric orbit around the MBH, with $a=0.5\,\text{pc}$ and $r_p=6.0\,r_t$ (upper panel), $3.0\,r_t$ (lower panel). The inner orbit has initial SMA $a_{b,0}=1.0\,\text{AU}$ and eccentricity $e_{b,0}=0.9$. The outer orbit has $\boldsymbol{L}$ in $+\hat{z}$ direction and pericenter on $-\hat{x}$ axis. The initial orientation of the binary system are specified by the orbital elements $i_{b,0}=0.7\pi$ (inclination angle), $\omega_{b,0}=0.1\pi$ (argument of pericenter), $\Omega_{b,0}=0.95\pi$ (longitude of ascending node), and $M_{b,0}=1.0$ (mean anomaly). The gray vertical line marks the time of the outer pericenter passage, the red horizontal line is the sum of the two binary star's radii, and the inner pericenter radii are highlighted with circular markers. For $r_p=3.0\,r_t$ (bottom panel), the binary separation and inner pericenter radii drop below $2\,R_*$ temporarily near the outer pericenter, which highlights the sharp change in $e_b$ when $r_p$ is small. In our simulation, the binary system on the lower panel is flagged as collision as soon as the binary separation becomes less than $2\,R_*$.
• Figure 3: The change in the stellar oscillation phase (Eq. \ref{['eq:chaotic-tides-phase-change']}) due to the variation in inner orbital period after the energy kick from the inner pericenter passage. The horizontal line, $\Delta\phi=1$, is the crude requirement for triggering the chaotic tides. The intersections between this horizontal line and the curves are $r_{b,\rm ct}$. Depending on the value of $a_b$, $r_{b,\rm ct}$ ranges from 3 to 4 $R_*$.
• Figure 4: The simulation flow of our MBH-binary three-body system. The end states of the binary system are highlighted with yellow color. The simulation is stopped when the system reaches any of the end states, or when the total simulation time exceeds $0.1\,t_{\text{2B,relax}}$.
• Figure 5: Example trajectories of the MBH-binary system. All systems have the same initial conditions $(a,t_{\text{2B,relax}},a_{b,0},e_{b,0})=(0.5\,\text{pc},1\,\text{Gyr},1.0\,\text{AU},0.64)$. Top panel: The evolution of $r_p$ and $r_{p,b}$. The initial state of the systems is marked with the yellow diamond. The states of the systems prior to the final outer pericenter passage are highlighted with triangles. Bottom four panels: $r_p$ and $r_{p,b}$ evolution as the function of outer orbit number for the same trajectories as in the top panel. The random walk in $r_p$ and the eKL-like oscillation can be clearly seen.