Deepest X-ray TDE Candidate

• The paper’s main contribution is presenting a unique SMBH binary model that reveals how tidal disruption events manifest with periodic light-curve dips and interrupted fallback dynamics.
• Enhanced TDE rates driven by eccentric Kozai–Lidov oscillations and merger-stage boosts illustrate the impact of close SMBH pairs on stellar disruptions.
• Hydrodynamic simulations and spectral diagnostics offer actionable insights into electromagnetic signatures, constraining aspects of SMBH binary evolution.

A supermassive black hole binary (SMBHB) tidal disruption event (TDE) model describes the dynamical pathways, accretion physics, and electromagnetic signatures when a star is disrupted in the gravitational potential of a close SMBH pair. The SMBHB regime fundamentally modifies the rates, light curves, and interpretation of TDEs relative to the isolated SMBH case. Models employ both analytic celestial mechanics (secular theory, Kozai–Lidov dynamics) and direct N-body/hydrodynamic simulations to address the multi-scale, multi-faceted problem, now recognized as a crucial channel for discovering dormant or hidden SMBHBs, constraining galaxy merger histories, and classifying exotic transients.

1. Dynamical Framework and Hierarchical Structures

In the SMBHB TDE formalism, one typically considers one dominant (primary) SMBH of mass $M_1$ and a secondary SMBH (mass $M_2 = qM_1$, $q \ll 1$ up to $q \sim 1$) with inter-BH separation $a$ ranging from milliparsecs to tenths of a parsec. The system may be imbedded in a stellar nuclear cluster or a post-merger nuclear environment (Liu et al., 2014, Li et al., 2019).

Stars are subject to both classical loss-cone refilling (scattering-dominated) and secular resonant processes. Near the secondary SMBH, the orbit-averaged perturbations of the primary drive high-eccentricity excursions via the eccentric Kozai-Lidov (EKL) mechanism. For the primary, chaotic/chaotic–Kozai stirring and non-axisymmetric torques prevail, particularly in post-merger phases (Fragione et al., 2018, Li et al., 2015).

The critical quantities are:

• Tidal radius: $r_t = R_* (M_{\rm BH}/M_*)^{1/3}$, where $M_*$, $R_*$ are stellar mass/radius,
• Secular timescale (Kozai–Lidov):

$$T_{KL} = \frac{2\pi}{n_1} \frac{M_1+M_*}{M_2} \left(\frac{a}{a_*}\right)^3 (1-e^2)^{3/2},$$

• GR precession quenching: KL cycles suppressed if $T_{GR} < T_{KL}$.

A geometric “Kozai window” ($40^\circ \lesssim i \lesssim 140^\circ$ inclination) enables the most rapid secular TDE flux (Li et al., 2015, Fragione et al., 2018, Liu et al., 2017).

2. TDE Rates, Enhancement Mechanisms, and Mass Dependence

The interaction between two SMBHs generically boosts TDE rates through two channels:

• EKL-induced rate on secondary: For SMBHBs with $M_2 \sim 10^4$--$10^7 M_\odot$ and $M_1 \gtrsim 10^8 M_\odot$, the secondary experiences a substantial hike in TDE rates (up to $\sim10^{-2}$ yr$^{-1}$ for $10^7$--$10^8 M_\odot$ pairs; $\sim 10^{-4}$--$10^{-3}$ yr$^{-1}$ for IMBHs in the Sgr A* environment), which can deplete its cusp population within $\sim 0.5$ Myr (Fragione et al., 2018, Li et al., 2015, Wang et al., 2017).
• Merger-stage rate boost: Direct N-body results partition the evolution into three phases—pre-interaction (nominal single SMBH rates), binary formation (rates amplified by $3$--$10\times$), and hard binary (rates decline but stay above isolated values). In minor mergers, TDEs around the secondary predominantly disrupt stars from the host galaxy of the primary (Li et al., 2019).
• Mass thresholds: For a primary exceeding $M_{1,\rm crit} \simeq 1.15\times10^8 M_\odot$, stellar disruptions become “dark”—no observable flare—since the Schwarzschild radius exceeds $r_t$ (Fragione et al., 2018).

3. Debris Fallback Dynamics and Light-Curve Modulation

In an isolated TDE, the debris fallback rate $\dot M(t)$ follows the standard $\propto t^{-5/3}$ law post $t_{\min}$: $$\dot M_{\rm single}(t) = \frac{M_*}{3 t_{\min}}\left(\frac{t}{t_{\min}}\right)^{-5/3},\quad t_{\min} \simeq 2\pi (2\Delta E)^{-3/2} G M_{\rm BH}.$$

In a binary SMBH, the debris stream interacts with the secondary (or primary, depending on location), producing interruptions, gaps, and recoveries in the fallback curve and associated observed luminosity. The key temporal features:

• Truncation time: $t_{\rm tr} \sim \eta T_{\rm bin}$, with $T_{\rm bin} = 2\pi [a^3/G(M_1+M_2)]^{1/2}$.
• Periodic dips: For $a \sim 0.5$--$2$ mpc, sharp, near-total dips recur at $t_{\rm tr} + nT_{\rm bin}$ (low inclination); plateaus or smooth interruptions for high inclination (Vigneron et al., 2018, Liu et al., 2014, Huang et al., 26 Nov 2025).
• Debris partitions: “Continuous” fallback ($t$-min envelope), plus “delayed” (island) and non-returning components (Ricarte et al., 2015).

Flares attributed to secondary SMBH accretion feature masses and energetics inconsistent with the host galaxy scaling relations—this “mass discrepancy” is a hallmark of the SMBHB TDE channel (Wen et al., 1 May 2024, Mockler et al., 2023).

4. Hydrodynamics, Repeated Partial Disruptions, and Merger Remnant Structure

Binary–star–SMBH hydrodynamical simulations demonstrate outcomes including full or partial binary tidal breakup, collision-induced mergers, and repeated partial TDEs with extended envelopes. Key outcomes:

• Collision-induced mass loss: $\sim 5\%$ for head-on deep ($\beta_b=5$) encounters, $\lesssim 1\%$ for gentle grazing ($\beta_b=0.6$).
• Debris fallback: Plateau in the fallback rate, followed by a $t^{-5/3}$ decay; repeated flares expected on orbital timescales $\sim$ years (Yu et al., 19 Apr 2025).
• Remnant envelopes: Merger remnants with $90\%$ mass within $\sim 5 R_\odot$, extended to $\sim 15 R_\odot$, highly susceptible to further stripping.

This hydrodynamic pathway generates weak, multi-epoch electromagnetic flares potentially mimicking “unusual” TDEs (Yu et al., 19 Apr 2025).

5. Observational Diagnostics, Surveys, and Case Studies

SMBHB-induced TDEs provide unique observable signatures:

• Light-curve interrupted by dips at regular intervals (a direct consequence of binary period); as in SDSS J1201+30 ($T_{\rm bin} \sim 140$ d, $a_b \sim 0.6$ mpc, $q \sim 0.08$) or XID 935 ($T_{\rm bin}=1200$ d, $a \sim 0.003$ pc, $q=0.05$--0.3) (Liu et al., 2014, Huang et al., 26 Nov 2025).
• Discrepancy between flare-inferred BH mass and host scaling mass relation. AT2018fyk (UV/optical/X-ray): $M_{\bullet,s} \sim 2.7 \times 10^5 M_\odot$ (secondary) vs. $M_{\bullet,p} \sim 10^{7.7} M_\odot$ from $M_\bullet$-$\sigma_*$ (Wen et al., 1 May 2024).
• Rebrightening/recurrence timings inconsistent with single-BH fallback dynamics.
• Spectral diagnostics: Hard X-rays from a compact secondary disk corona; super-Eddington UV emission from shocks at the circularization radius.
• Multiwavelength coverage: Light-curve gaps, plateaus, and recoveries; broad emission-line shifts; repeat partial TDE flares.

These features are now directly used to identify dormant SMBHBs in deep time-domain surveys, and future samples will constrain both the occupancy fraction and inspiral rates of milliparsec-scale SMBHBs.

6. Model Limitations, Physical Caveats, and Extensions

Several sources of uncertainty and limitation affect SMBHB TDE modeling:

• Secular approximation breakdown: Chaos and strong interactions dominate for $q \gtrsim 0.1$, small $a$, and when the hierarchical triple fails ($\varepsilon_{oct}>0.1$).
• GR and Newtonian precession: High mass, small $a$, or high $e$ can suppress secular excitation.
• Loss-cone refilling processes: Rate calculations are sensitive to the underlying stellar distribution, relaxation timescales, and triaxiality (Li et al., 2019).
• Hydrodynamic neglect: Ballistic models ignore stream collisions, circularization, and feedback.
• Mass scaling exponents: Rate fits require adjustment for nuclear cusp slope ($\gamma$), stellar mass spectrum, and explicit N-scaling (Li et al., 2019).
• **No formal Bayesian or reduced-$\chi^2$ light-curve fitting yet; “acceptable” matches judged qualitatively (Huang et al., 26 Nov 2025).

This suggests ongoing development and cross-validation are necessary, with direct N-body, hydrodynamic, and semi-analytical frameworks required for robust population synthesis, rate predictions, and EM counterpart modeling.

7. Implications for Galaxy Evolution, Gravitational Waves, and Future Directions

SMBHB TDEs are consequential for multiple domains:

• Galaxy evolution: TDE rates probe nuclear merger phase, cusp clearing, and mass transfer.
• Binary coalescence: Systems overcoming the “final parsec problem” (e.g., $a\sim$ mpc) are prime targets for low-frequency gravitational wave sources (Liu et al., 2014).
• Hypervelocity star production: Ejection rates of a few $10^{-8}$--$10^{-7}$ yr$^{-1}$ in three-body interactions supplement the Galactic HVS population (Fragione et al., 2018, Wang et al., 2017).
• Exotic transients: Weak or repeated partial TDEs, spectral anomalies, and offset accretion.
• Constraints on occupancy fraction: Large transient surveys will facilitate ballot-box statistics for milliparsec SMBHBs in otherwise dormant galaxies.

A plausible implication is that robust identification of SMBHB TDEs will provide direct constraints on nuclear merger timescales, test binary hardening theories, and help calibrate gravitational wave source populations for next-generation detectors.