Unexpectedly Weak General Relativistic Effects in Strongly Relativistic Tidal Disruption Events

Abstract

Tidal disruption events (TDEs) occur when stars are destroyed by supermassive black holes and are among the brightest nuclear transients. It has been thought that strong relativistic effects rapidly dissipate orbital energy and produce prompt disk formation when the stellar pericenter is smaller than $\sim 10$ gravitational radii. Using a general relativistic hydrodynamic simulation of a strongly relativistic TDE around a $10^{6}\,M_{\odot}$ black hole, we find instead that the overall evolution is similar to weakly relativistic TDEs: the debris remains highly eccentric, with most of the returned mass residing near the orbital apocenter ($\sim 250\times$ the initial pericenter distance), and shocks, rather than accretion, power the event. The simulation starts from the initial stellar approach and follows the debris evolution up to $35\,\text{days}$ after the peak mass-return time ($\simeq$ $23\,\text{days}$). Although early shocks driven by strong relativistic apsidal precession and pericenter nozzle compression dissipate orbital energy efficiently, they last only about a week ($\sim 0.3$ of the peak mass-return time). Stream self-interactions increase the incoming stream's angular momentum, thereby expanding its pericenter distance, weakening precession and shocks, and reducing dissipation. These results, along with previous work on weakly relativistic TDEs, suggest that circularization may be intrinsically slow regardless of the strength of relativistic effects, and the flow remains highly eccentric and extended during the peak of optical/UV luminosity.

Figures (15)

• Figure 1: The overall debris evolution (top) in our simulation, along with the circularization rate (bottom). The top row shows the density contours in the $x-y$ plane, spanning a distance of $500$$r_g$, at three different times, representing the early phase (left), its transition (middle) to the late phase (right). The red dash-dotted line traces the expected ballistic geodesic of the incoming debris, and the grey star-shaped scatter marks the initial position of the star. The vertical long panel on the right shows a zoomed-out view of the density at $23$ days, with velocity streamlines (grey) appended. We include a dark arrow marking a representative location of self-intersection shocks (see § \ref{['subsec:shock']}). The velocity fields are the three-velocity of the fluid, defined as $V^{i} = \sqrt{g_{ii}}u^{i}/u^{t}$, where $g_{ii}$ is the $(i,i)$ metric component and $u^{\mu}$ is the four-velocity. The circularization rate, defined in Equation \ref{['eqn:eff']}, measures the pace of circularization: $100$ % for complete circularization within $1$$t_{0}\simeq 23$ days (see § \ref{['subsec:circular']}). The dark dashed line represents the moving average of the time series. In the bottom row, the blue shaded region marks the regime where relativistic effects are strong and promote energy dissipation via shocks.
• Figure 2: Temporal evolution of the density contour (in the log$_{10}$ scale) along the equatorial plane in the domain comoving with the center-of-mass of the star. Note that the plotting extent increases with time. In each panel, the upper-left text box lists the position of the center-of-mass of the fluid in units of $r_g$ and $r_p$; the lower-left text box indicates the time since the pericenter passage. In each panel, the red arrow indicates the direction toward the SMBH.
• Figure 3: Orbital energy (left) and fallback rate (right) distributions of the stellar debris at a few different times. In the left-hand panel, we include vertical brown lines that indicate the $\Xi$ factor from Equations \ref{['eqn:tfallback']} and \ref{['eqn:mfallback']}. In the right-hand panel, we indicate the peak fallback time $t_0$ (brown dashed-dotted line), in units of $t_{g}=r_{g}/c$, and the scaling relation $t^{-5/3}$ (purple dashed-dotted line) for reference.
• Figure 4: (Left) Time evolution of the enclosed mass profile at five epochs. The green dashed curve shows the mass whose apocenter $\approx 2a(E) < r$ for the $dM/dE$ shown in the left panel of Figure \ref{['fig:combined_distribution']}. Note that it is hidden under the other curves for $r \gtrsim 1100\,r_g$. (Right) Profiles of the mass inflow/outflow rate, normalized to the canonical peak mass-return time $\dot{M}_0$, at the first four times shown in the left panel. Contributions from outgoing (dashed black) and incoming (solid red) fluid, and their net (blue) are shown separately. For the net rate, we use different line styles to distinguish net inflow (solid) and outflow (dashed) rates. In both panels, the vertical grey lines indicate the initial stellar pericenter distance, while for the right panel only, the horizontal brown line indicates the Eddington mass accretion rate, assuming a radiative efficiency of unity.
• Figure 5: Time evolution of the mass accretion rate (top), the total internal energy within the simulation domain (middle), and the rates of internal energy change (bottom). In the top panel, the mass accretion rate is normalized by the Eddington value (assuming a radiative efficiency of unity) and the gray dot-dashed line shows the (similarly normalized) mass fallback rate, when it reaches a steady state, which is also shown in the right panel of Figure \ref{['fig:combined_distribution']}. In the bottom panel, we compare: the heating rate, i.e., internal energy changes by means of shocks or adiabatic compression/expansion (yellow); the advected internal energy loss rate, i.e., losses due to mass flows across the inner boundary (red); and the net rate of internal energy change within the domain (cyan), i.e., the difference between the first two minus the energy carried out of the domain when gas leaves through the $\theta$ boundary. In the top and bottom panels, a black dashed line represents the time-averaged value of the corresponding time series. In the middle panel, we include a $\propto t$ scaling relation.