Super-Eddington Chimneys: On the Cooling Evolution of Tidal Disruption Event Envelopes

Abstract

The formation of a compact accretion disk following a tidal disruption event (TDE) requires that the shocked stellar debris cool efficiently as it settles toward the black hole. While recent simulations suggest that stream dissipation occurs rapidly, how the weakly bound debris subsequently loses its thermal energy to assemble a compact disk near the circularization radius remains uncertain. We investigate this cooling process using axisymmetric radiation-hydrodynamic simulations of quasi-hydrostatic 'TDE envelopes', initialized with the total mass, angular momentum, and binding energy expected from a complete stellar disruption. The envelopes, supported by radiation pressure on large scales and rotation near the circularization radius, evolve through a combination of radiative diffusion, turbulent mixing, and polar outflows. In our fiducial model, a quasi-steady state is achieved in which a polar outflow radiates and expels matter at several times the Eddington luminosity. This enables the envelope to cool and contract, forming a dense, rotationally supported ring near the circularization radius, but on a timescale roughly ten times shorter than the naive photon-diffusion timescale. Comparative models without radiation transport confirm that cooling, not purely adiabatic evolution, is essential to driving this rapid inflow. Nevertheless, across a range of envelope masses, the effective envelope cooling time scales only weakly with its optical depth, implying that advective and wind-driven energy transport dominate over diffusion. Our results demonstrate the cooling-induced contraction, even absent viscosity and associated black hole accretion, can produce luminosities and large photosphere radii consistent with early UV/optical TDE emission. However, more quantitative light-curve predictions must incorporate self-consistent formation and feeding of the envelope by fall-back accretion.

Figures (2)

• Figure 1: Schematic diagram describing the three stages of a tidal disruption event: after the debris streams pass through pericenter ($\sim \rm month$, left panel), their kinetic energy is dissipated into heat through a combination of compression-induced shock heating inside the tidal radius and self-crossing shocks at larger radii. On the other hand, at very late times after the disruption ($\sim \rm year - decade$), X-ray and far-UV observations reveal a geometrically thin disk of size $\sim R_c \sim 10^{12}\,\rm cm$, containing significant mass $\gtrsim 0.1\,M_\star$ (e.g., vanVelzen+19Jonker+20MummeryVanVelzen24). The intermediate phase, $t_{\rm fb} \lesssim t \lesssim 10\,t_{\rm fb}$, which corresponds to the epoch of peak UV/optical light, is subject to larger uncertainties compared to the early and late phases. The qualitative evolution in this phase depends on how the timescales for shock dissipation ($t_{\rm diss}$), cooling of the debris ($t_{\rm cool}$), and viscous accretion ($t_{\rm visc}$), compare to the fallback timescale of the debris ($t_{\rm fb}$) (Sec. \ref{['sec:analytical_estimates']}; Fig. \ref{['fig:TDEtree']}). The present paper explores a scenario in which shock dissipation is fast, but cooling is slow, i.e., $t_{\rm cool} \gtrsim t_{\rm fb} \sim t_{\rm diss}$. In this case, the stellar debris forms of a large quasi-hydrostatic envelope of size $\sim a_{0}$ (middle panel) as defined by the weak initial binding energy of the debris (Eq. \ref{['eq:epsilon_t']}), as seen in several recent simulations (e.g., SteinbergStone24Price+24). Even in the likely event that some mass during this process is placed into a Keplerian disk extending interior to the tidal radius $\lesssim R_t \lesssim 10^{13}\,\rm cm$, its mass is limited to that supplied by the large scale, highly sub-Keplerian envelope on a timescale $t_{\rm cool}$ set by its cooling rate (rather than viscous transport rate of angular momentum). An envelope cooling through a combination of radiation and outflow could power the optical/near-UV emission near peak by releasing the $\epsilon_{\rm c} \sim 10^{52}\,\rm erg\,M_\odot^{-1}$ of energy necessary to form a disk at $r \sim R_c$ (Eq. \ref{['eq:epsilon_c']}) through quasi-spherical accretion over $\sim \rm months$, which goes on to power UV and X-ray emission for $\sim \text{decades}$ (right-panel).
• Figure 2: Schematic decision tree classifying models for early-time TDE emission according to the relative ordering of three timescales: (1) $t_{\rm fb}$, fall-back time over which debris returns to the black hole; (2) $t_{\rm diss}$, dissipation time over which streams kinetic energy is converted to debris thermal energy via shocks; (3) $t_{\rm cool}$, cooling time over which debris energy is lost to radiation and outflows. The dependence of $t_{\rm diss}$ and $t_{\rm cool}$ on TDE parameters is highly uncertain, and focus of extensive research. If dissipation is slow ($t_{\rm diss} \gg t_{\rm fb}$), shocks can power optical emission which tracks the fall-back rate, but accretion onto the SMBH is delayed. However, even if dissipation is fast, this does not necessarily lead to rapid circularization and SMBH accretion. If the cooling time of the debris is slow, the debris forms a large quasi-spherical envelope, as studied in this paper, whose slow contraction powers UV/optical emission and can also lead to the delayed feeding of the SMBH.