SMBH Binary TDE Model Overview

• The model illustrates how chaotic orbital perturbations and the eccentric Kozai-Lidov mechanism significantly enhance TDE rates in SMBHB systems.
• It demonstrates that apparent discrepancies between TDE flare properties and host galaxy scaling relations reveal the influence of a secondary SMBH.
• Hydrodynamic simulations show that binary-induced debris deflection produces characteristic light curve dips, plateaus, and rebrightenings.

A supermassive black hole binary (SMBHB) tidal disruption event (TDE) model provides a dynamical framework for interpreting stellar disruptions in galactic nuclei hosting two closely bound SMBHs. In this regime, strong secular and chaotic orbital perturbations, primarily by the secondary black hole and through mechanisms such as the eccentric Kozai-Lidov (EKL) effect, drive significant enhancements in the rate and observable properties of TDEs compared to isolated SMBHs. Recent models focus on both the dynamical pathways for TDE formation, the interplay with galaxy scaling relations, and the utility of TDE light curves for diagnosing the existence, mass, and orbital parameters of unresolved SMBHBs (Mockler et al., 2023, Fragione et al., 2018, Li et al., 2015, Ricarte et al., 2015, Liu et al., 2014).

1. Physical Framework and Model Ingredients

A typical SMBHB TDE system consists of a primary SMBH (mass $M_1 \sim 10^6$–$10^8\,M_\odot$), a secondary SMBH or IMBH (mass $M_2 \sim 10^3$–$10^7\,M_\odot$), and a population of surrounding stars. The system is dynamically hierarchical, with the secondary orbiting at sub-parsec separations ($a_{\rm out} \sim 0.001$–$0.1$ pc), and susceptible stars orbiting the secondary at $a_{\rm in}$ well inside its Hill sphere at pericenter,

$$R_{\rm H} = a_{\rm out}\,(1 - e_{\rm out})\,\left(\frac{M_2}{M_1}\right)^{1/3}$$

where $e_{\rm out}$ is the binary eccentricity. Stars subject to high mutual inclinations ($40^\circ \lesssim i \lesssim 140^\circ$) relative to the SMBHB orbital plane undergo secular oscillations in eccentricity and inclination. Above a critical SMBH mass $M_{\rm crit} \approx 1.15\times10^8\,M_\odot$ (for solar-type stars), the Schwarzschild radius exceeds the tidal disruption radius and stellar disruptions by the primary become "dark," so only a lower-mass secondary is associated with observable flares (Fragione et al., 2018).

2. Dynamical Mechanisms: Chaotic Perturbations and EKL

In the SMBHB regime, two distinct mechanisms fuel tidal disruption:

Chaotic orbital perturbations: For stars bound to the more massive SMBH, the dominant channel is chaotic angular-momentum scattering, which rapidly refills the loss cone, enhancing the TDE rate via non-secular relaxation and three-body interactions. This effect is robust when the SMBHB is sufficiently close that the combined potential no longer supports regular orbits and the loss cone empties only on short timescales (Mockler et al., 2023, Li et al., 2019).

Eccentric Kozai-Lidov (EKL) mechanism: For stars orbiting the less massive SMBH/secondary, the EKL resonance dominates. Here, secular exchanges between inclination and eccentricity drive $e_{\rm in} \rightarrow 1$. The classic quadrupole-oscillation timescale is

$$T_{\rm KL} \approx \frac{M_1 + M_2}{M_2}\frac{P_{\rm out}^2}{P_{\rm in}}(1 - e_{\rm out}^2)^{3/2}$$

where $P_{\rm in}$ and $P_{\rm out}$ are the inner/outer periods. Maximum eccentricity scales as $e_{\rm in,max} = \sqrt{1 - (5/3)\cos^2{i_0}}$. Octupole effects (higher $e_{\rm out}$, unequal mass ratio) further enhance $e_{\rm in}$ and can produce orbital flips. EKL-driven TDE rates can reach $\sim10^{-2}\,\text{yr}^{-1}$ in $10^7$–$10^8\,M_\odot$ SMBHBs for durations of $\sim0.5$ Myr, depleting the secondary's cusp (Li et al., 2015).

General relativistic (GR) and Newtonian cusp precession quench EKL cycles if their associated timescales ($T_{\rm GR}$, $T_{\rm NT}$) become shorter than $T_{\rm KL}$, thus controlling the window for enhanced TDE production (Li et al., 2015, Fragione et al., 2018).

3. TDE Rate Predictions and Host–Accretor Mass Discrepancy

N-body simulations and semi-analytic calculations indicate that SMBHB systems can drive TDE rates up to $\sim10^{-2}\,\text{yr}^{-1}$, two orders of magnitude above the canonical rate for single SMBHs ($\sim10^{-4}\, \text{yr}^{-1}$). The loss cone—normally depleted by two-body relaxation—is further refilled during the binary's bound phase (Phase II) by non-axisymmetric potentials and torques, particularly in minor mergers. Fitted power-law scalings show the secondary TDE rate evolving as $\dot M_2 \propto q^{0.56}$–$q^{0.63}$ throughout the SMBHB evolution, with $q=M_2/M_1$ (Li et al., 2019).

A defining feature of the SMBHB TDE channel is the disconnect between the SMBH mass inferred from TDE flare light curves and the host galaxy scaling relation (e.g., $M_\bullet$–$\sigma_*$ or bulge mass), which is generally dominated by the primary SMBH. When the secondary triggers the TDE (via EKL or direct perturbation), the observed flare spectra and evolution reflect this smaller mass—leading to an "apparent inconsistency" and identifying otherwise inactive binaries (Mockler et al., 2023, Wen et al., 1 May 2024).

4. Light Curve Signatures: Dips, Rebrightenings, Periodic Modulation

The characteristic SMBHB-modulated TDE light curve includes sharp interruptions, periodic dips, and potential rebrightenings not present in isolated SMBH models. Analytical and numerical studies show two main classes:

• Low inclination ($\theta \lesssim 70^\circ$): Returning debris streams are periodically perturbed by the companion SMBH, yielding sharp interruptions at intervals of the binary period ($T_{\rm bin}$). Each dip reduces the fallback rate nearly to zero, recurrence intervals are $\sim T_{\rm bin}$ (Vigneron et al., 2018, Liu et al., 2014, Huang et al., 26 Nov 2025).
• High inclination ($\theta \gtrsim 70^\circ$): Debris is globally deflected, producing a single, smooth suppression or plateau. Recovery to the $t^{-5/3}$ decline can occur depending on the extent of the deflection (Vigneron et al., 2018).

Specific cases, such as SDSS J1201+30 and XID 935, empirically demonstrate rapid X-ray dips and recoveries—well fit by SMBHB models with primary masses $M_1 \sim 10^7\,M_\odot$ and secondary-to-primary mass ratios $q \sim 0.05$–$0.3$; binary separations inferred from the intervals between dips or cutoffs are typically $\sim0.002$–$0.01$ pc (Liu et al., 2014, Huang et al., 26 Nov 2025, Wen et al., 1 May 2024). Multiple dips and quasi-periodic interruptions are direct signatures of unresolved SMBHBs.

Event	Binary mass ratio $q$	Separation $a$ (pc)	Light curve signature
SDSS J1201+30	0.04–0.18	0.26–0.6 mpc	Sharp dips, recurrence, deep X-ray drop
XID 935 (CDF-S)	0.05–0.30	$\sim$0.003	Steep decline, final interruption
AT2018fyk	$2.7 \times 10^5/10^{7.7}$	$6.7 \pm 1.2 \times 10^{-3}$	UV/X-ray cutoff, rebrightening

5. Hydrodynamic Effects and Fallback Modulation

Recent hydrodynamical SPH simulations show that the fallback rate onto the black holes in SMBHB systems can be decomposed into "continuous" and "delayed" components (Ricarte et al., 2015). Initial debris may miss the accretion radius due to binary-induced stream deflection, creating gaps in the accretion history, while surviving material may self-intersect at shifted loci—modifying circularization and dissipative heating.

The energy distribution of post-collision or EKL-driven debris is typically broader and bimodal relative to single SMBH TDEs, yielding light curves with plateaus followed by canonical $t^{-5/3}$ decay at late times (Yu et al., 19 Apr 2025). In deep encounters, peak fallback rates are $\sim 0.1\, M_\odot\,\text{yr}^{-1}$ with plateaus lasting $\sim50$ days; electromagnetic luminosities are sub-Eddington for $M_{\rm BH} \sim 10^6\, M_\odot$ (Yu et al., 19 Apr 2025). Repeated partial disruptions at orbital intervals (e.g., several years) are expected for extended merger remnants.

6. Observational Implications and Binary Diagnostics

SMBHB TDE models offer effective diagnostics for otherwise undetectable SMBHBs—especially in galaxies where the primary SMBH mass precludes luminous TDEs by sun-like stars. The observation of TDEs in galaxies with bulge masses $M_{\rm bulge} \gtrsim 4.15\times10^{10}\,M_\odot$ strongly indicates either a lower-mass secondary or IMBH acting as the disruptor (Fragione et al., 2018). The pronounced host–flare mass discrepancy, the timing, depth, and recurrence of light-curve dips, and the spectral properties (e.g., soft X-ray excess, plateau + power-law decay) together constrain binary separation, mass ratio, and geometry.

Additional implications include hypervelocity star (HVS) production: SMBHB-induced secular ejections yield HVSs with velocities up to thousands of km/s, contributing to the observed population at a rate $\sim10^{-8}$–$10^{-7}$ yr$^{-1}$ (Fragione et al., 2018, Wang et al., 2017).

7. Model Limitations and Open Directions

Current SMBHB TDE models are built upon ballistic integration, secular dynamics, and hydrodynamic simulations, omitting higher-order GR terms, dissipative tidal effects, gas accretion feedback, and multi-wavelength emission modeling. Rate predictions are sensitive to the details of the stellar cusp profile, background potential, and binary hardening mechanisms. The observed short-timescale variability in certain TDE light curves (e.g., XID 935) is not fully captured by existing models, indicating the need for improved debris self-interaction and radiative transfer schemes (Huang et al., 26 Nov 2025).

A plausible implication is that future high-cadence, multiwavelength transient surveys will enable systematic constraints on the SMBHB population via TDE diagnostics—probing the milliparsec regime and complementing gravitational wave detection (e.g., for systems that have overcome the "final parsec problem") (Liu et al., 2014). SMBHB TDE modeling represents an essential tool in mapping the demographics and dynamical evolution of supermassive black hole binaries in galactic nuclei.