Wind-mediated Eddington-limited emission in a $10^{4}M_\odot$ Black Hole Tidal Disruption Event

Technical Summary: Wind-mediated Eddington-limited Emission in a $10^4 M_\odot$ Black Hole Tidal Disruption Event

Problem Statement
Tidal Disruption Events (TDEs) are among the brightest thermal transients, yet the physical origin of their early-time luminosity peak remains uncertain. While classical models predict efficient circularization of stellar debris into a compact accretion disc, observations often reveal lower blackbody temperatures, larger radii, and luminosities that do not strictly follow the fallback rate of bound debris. Furthermore, the existence and demographics of Intermediate-Mass Black Holes (IMBHs, $10^4 - 10^6 M_\odot$) remain debated, partly due to a lack of robust models describing TDEs in this mass regime. Previous simulations have struggled with the extreme dynamic range required to resolve both global orbital evolution and the critical hydrodynamic processes at pericenter, such as nozzle shocks and radiative transfer.

Methodology
The authors present the first end-to-end, three-dimensional radiation-hydrodynamics simulation of a main-sequence star ($M_\star = 0.5 M_\odot$, $R_\star = 0.47 R_\odot$, polytropic index $n=1.5$) disrupted by a non-spinning IMBH ($M_{\rm BH} = 10^4 M_\odot$). The simulation utilizes the RICH code, employing a flux-limited diffusion (FLD) scheme for grey radiative transport and realistic equations of state including hydrogen/helium ionization and recombination.

Key methodological features include:

• Gravity: A Paczyński–Wiita potential approximates relativistic apsidal precession, with artificial smoothing applied within $r < 0.6 r_p$ for computational efficiency.
• Resolution: The study employs an adaptive mesh refinement (AMR) scheme, achieving unprecedented resolution for global 3D TDE simulations. Three resolution levels (Low, Middle, High) were tested to assess convergence. The High-resolution run utilizes up to $4 \times 10^6$ cells, with minimum cell sizes reaching $\approx 0.04 R_\odot$ and minimum cell masses of $\approx 1.5 \times 10^{-15} M_\odot$ in the orbital plane.
• Physics: The simulation tracks the conversion of orbital energy into thermal and radiation energy, explicitly calculating irreversible dissipation rates and the evolution of the photosphere.

Key Results
The simulation reveals a distinct evolutionary path for IMBH TDEs compared to Supermassive Black Hole (SMBH) events:

1. Inefficient Circularization: The stellar debris fails to circularize efficiently. Despite the formation of a nozzle shock at pericenter, the dissipation of orbital energy is insufficient to form a compact accretion disc within the simulated timeframe ($\approx 2.2 t_{\rm fb}$). The bound material retains high eccentricity ($e \approx 0.93$), remaining on highly elliptical orbits.
2. Wind-Mediated Emission: Instead of a disc, a low-density, radiation-driven wind forms near pericenter. This outflow expands quasi-spherically, advecting radiation generated at smaller radii outward. The wind becomes unbound and radiation-dominated ($E_{\rm rad} / E_{\rm th} \sim 10$) by the end of the simulation.
3. Eddington-Limited Luminosity: The bolometric light curve peaks at approximately $2 L_{\rm Edd}$ ($\sim 8 \times 10^{41}$ erg/s) around $t \approx 1.5 t_{\rm fb}$ before settling near the Eddington limit ($L_{\rm Edd} \approx 3 \times 10^{41}$ erg/s).
   • Crucially, the total dissipation rate exceeds the emergent luminosity by over an order of magnitude. The photosphere, located at radii of $\approx 10^{13}$ cm (expanding to $\approx 10^{14}$ cm), acts as a bottleneck, preventing the prompt radiation of the dissipated energy.
   • The peak luminosity is orders of magnitude lower than naive estimates based on the fallback rate ($L \sim 0.1 \dot{M}_{\rm fb} c^2 \sim 10^{46}$ erg/s), confirming that shock dissipation is highly inefficient in this regime.
4. Convergence: While the nozzle shock at pericenter is likely under-resolved, global metrics (photospheric radius, light curve shape, total dissipation rate) are qualitatively converged and largely quantitatively robust across the three resolution levels. The primary difference between resolutions is a temporal delay in the onset of saturation and mass loss in higher-resolution runs.

Significance and Observational Implications
The paper claims that this work provides a self-consistent explanation for the early-time emission of IMBH TDEs, attributing it to shock-powered, wind-mediated emission rather than accretion disc formation. The results suggest that:

• IMBH Detectability: The simulated light curve and temperature ($T \sim \text{few} \times 10^4$ K) are consistent with optical/UV observations. The authors estimate that upcoming surveys like the Vera Rubin Observatory's LSST (g and r bands) could detect such events up to $z \approx 0.1$, while ULTRASAT (near UV) could detect them up to $z \approx 0.06$.
• Model Constraints: The findings challenge models that assume efficient circularization for IMBH TDEs and suggest that the lack of circularization is a robust feature of these events, potentially making them more amenable to mass-injection simulation schemes than SMBH TDEs.
• LFBOT Connection: The derived bolometric luminosity is significantly lower than the peaks of Luminous Fast Blue Optical Transients (LFBOTs), arguing against early-time IMBH TDEs as the dominant explanation for LFBOTs, though late-time disc models remain a possibility.

The authors conclude that while their model relies on simplified gravity and grey radiative transfer, the qualitative conclusion—that IMBH TDEs produce Eddington-limited emission via an expanding, radiation-driven wind with inefficient circularization—is robust. Future work will address higher resolution at the nozzle, multi-group radiative transfer, and magnetohydrodynamics.