Bridging Roche Lobe Overflow and micro-TDEs: The Runaway Evolution of Eccentric Mass Transfer in Star-Black Hole Binaries

Technical Summary: Bridging Roche Lobe Overflow and Micro-TDEs

Problem Statement
Binary systems containing stellar-mass black holes (sBHs) and stars on eccentric orbits present a theoretical gap between two established regimes: stable Roche-lobe overflow (RLOF) in circular binaries and violent, single-passage tidal disruption events (TDEs). While semi-analytical models have attempted to describe the secular evolution of eccentric binaries, they rely on orbit-averaged equations and parameterized mass transfer rates that may fail to capture the nonlinear structural response of the star. Conversely, previous hydrodynamical simulations have largely focused on the terminal phase of deep tidal encounters or single pericenter passages, neglecting the long-term evolutionary pathways that determine whether a system settles into stable mass transfer or undergoes runaway disruption. The critical transition region, governed by the competition between adiabatic stellar expansion and orbital widening, remains poorly understood.

Methodology
The authors employ Smoothed Particle Hydrodynamics (SPH) using the code Phantom to simulate the interaction between a $1 M_\odot$ Sun-like main-sequence star and a $10 M_\odot$ stellar-mass black hole. The simulations utilize an adiabatic equation of state ($\gamma = 5/3$) and neglect radiative cooling, a justified assumption given that the interaction timescale (orbital periods) is orders of magnitude shorter than the stellar thermal timescale. This ensures that tidal dissipation and shock heating are trapped within the stellar envelope, driving adiabatic expansion.

The study tracks systems for tens to over 100 orbital periods ($P_0$), initializing them well outside the tidal radius to capture the onset of interaction. The parameter space is explored by varying the initial eccentricity ($e_0 = 0.30, 0.55, 0.70$) and the dimensionless pericenter distance ($b_0 = r_{p,0}/r_{tide,0} = 3.33, 3.45, 3.57$). The authors distinguish between bound and unbound material using a Bernoulli parameter criterion that includes specific enthalpy, and they track orbital evolution using both dynamical (energy/angular momentum) and geometric methods.

Key Results
The simulations reveal two distinct evolutionary pathways dictated by the initial pericenter distance ($b_0$):

1. Runaway Disruption (e.g., Run A, $b_0 = 3.33$):

   • Mechanism: Mass loss at pericenter triggers adiabatic expansion of the stellar envelope. Because the star's adiabatic mass-radius exponent ($\zeta_{ad}$) is more negative than the Roche lobe's response ($\zeta_L$), the stellar radius expands faster than the Roche lobe.
   • Feedback Loop: This creates a positive feedback loop where the increased Roche-lobe filling factor drives higher mass loss rates, which in turn drives further expansion.
   • Outcome: The system undergoes catastrophic disruption within $\sim 40 P_0$. The debris forms a geometrically thick, shock-heated accretion torus.
   • Accretion: The black hole experiences a super-Eddington accretion rate peaking at $\sim 5 \times 10^6 \dot{M}_{Edd}$, followed by a decay scaling as $t^{-9/4}$.

2. Stable Mass Transfer (e.g., Run B, $b_0 = 3.57$):

   • Mechanism: While mass loss initially drives stellar expansion, the associated loss of orbital angular momentum causes the binary orbit to widen significantly.
   • Regulation: The orbital widening enlarges the Roche lobe sufficiently to counteract the stellar expansion. The system reaches a quasi-stable equilibrium where the mass loss rate stabilizes, and the filling factor remains below unity.
   • Outcome: The system persists in a long-lived mass-transfer phase (simulated up to $150 P_0$) without total disruption.
   • Accretion: The accretion rate is sustained but lower, peaking around $10^5 \dot{M}_{Edd}$, exhibiting quasi-periodic modulation.

Threshold Sensitivity
The transition between these outcomes is sensitive to $b_0$. Run C ($b_0 = 3.45$) demonstrates a "delayed runaway," where the system mimics stable transfer for $\sim 70 P_0$ before the positive feedback loop eventually dominates. Variations in eccentricity ($e_0$) at fixed $b_0$ show that lower eccentricities at $b_0=3.33$ lead to earlier disruption, while $b_0=3.57$ remains stable even at lower eccentricities ($e_0=0.30$).

Significance and Claims
The paper claims to provide a unified physical picture connecting eccentric Roche-lobe overflow to the onset of "micro-TDEs" (tidal disruption events involving stellar-mass black holes). The authors argue that the long-term evolution of eccentric binaries is not predetermined but depends on the specific competition between stellar structural response and orbital dynamics.

• Observational Implications: The runaway disruption channel (Run A) is proposed to power fast X-ray/UV or blue/optical transients via super-Eddington accretion onto the sBH, potentially manifesting as apparent Ultra-Luminous X-ray (ULX) sources. The stable mass transfer channel (Run B) is suggested to manifest as repeating, quasi-periodic flares.
• Theoretical Contribution: The work bridges the gap between semi-analytical secular models and violent single-encounter simulations, demonstrating that full hydrodynamical treatment is necessary to capture the breakdown of approximations during the transition from stable to unstable mass transfer.

The authors maintain modesty regarding their conclusions, noting that the transition threshold is shaped by both $b_0$ and $e_0$ rather than a single universal value, and that future work incorporating radiative transfer and magnetic fields is required to fully connect these hydrodynamical outcomes to multi-wavelength observations.