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Stream–disk shocks as the origins of peak light in tidal disruption events

Nature volume 625, pages 463–467 (2024)Cite this article

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Abstract

Tidal disruption events (TDEs) occur when stars are ripped apart1,2 by massive black holes and result in highly luminous, multi-wavelength flares3,4,5. Optical–ultraviolet observations5,6,7 of TDEs contradict simple models of TDE emission2,8, but the debate between alternative models (for example, shock power9,10 or reprocessed accretion power11,12,13,14,15,16) remains unsettled, as the dynamic range of the problem has so far prevented ab initio hydrodynamical simulations17. Consequently, past simulations have resorted to unrealistic parameter choices10,12,18,19,20,21, artificial mass injection schemes22,23 or very short run-times24. Here we present a three-dimensional radiation-hydrodynamic simulation of a TDE flare from disruption to peak emission, with typical astrophysical parameters. At early times, shocks near pericentre power the light curve and a previously unknown source of X-ray emission, but circularization and outflows are inefficient. Near peak light, stream–disk shocks efficiently circularize returning debris, power stronger outflows and reproduce observed peak optical–ultraviolet luminosities25,26. Peak emission in this simulation is shock-powered, but upper limits on accretion power become competitive near peak light as circularization runs away. This simulation shows how deterministic predictions of TDE light curves and spectra can be calculated using moving-mesh hydrodynamics algorithms.

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Fig. 1: Density and dissipation.
Fig. 2: Dynamical evolution of the bound debris.
Fig. 3: TDE light curves.
Fig. 4: Observables as a function of time.

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Data availability

The simulation results presented in this study are available from the corresponding author upon request. RICH is publicly available to download from GitLab (https://gitlab.com/eladtan/RICH). Animated versions of the simulation results are available online, including both an overall, top-down view of the disruption and formation of an accretion flow (https://www.youtube.com/watch?v=O3IWCPO_Thk) and also a side view that better illustrates the formation of an outflow (https://www.youtube.com/watch?v=_kpBQjwf3Z4).

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Acknowledgements

We thank A. Horesh, P. Jonker, B. Metzger, T. Piran and E. M. Rossi for their discussions. We also thank C. Bonnerot and R. Saxton for their feedback. N.C.S. received support from the Israel Science Foundation (Individual Research Grant 2565/19) and the BSF portion of an NSF–BSF joint research grant (NSF grant no. AST-2009255 and BSF grant no. 201977).

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  1. Racah Institute of Physics, The Hebrew University, Jerusalem, Israel

    Elad Steinberg & Nicholas C. Stone

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  1. Elad Steinberg
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Contributions

E.S. ran the simulations of the TDE and produced the figures and also modified the publicly available RICH code to include radiation transport and a realistic equation of state. N.C.S. wrote the paper. Both authors contributed equally to the physical interpretation of the numerical results.

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Correspondence to Elad Steinberg.

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Extended data figures and tables

Extended Data Fig. 1 Convergence checks for our simulation.

Panel (a) shows stream scale-heights in 2D simulations designed to study the sensitivity of stream compression to numerical resolution and input physics. The blue solid line reproduces the study of BL2250 from their dynamically cold initial conditions and adiabatic EOS. The red dashed curve uses a more realistic initial temperature of 4000 K, but is otherwise the same. The solid yellow line shows high-resolution 2D results with the initial conditions taken from our 3D simulation (as well as our realistic EOS). The dashed purple line is the same as the yellow line, but with a reduced vertical resolution that corresponds to our 3D resolution. Arrows show the direction of the temporal evolution. In all of the lines, the streams are evolved until they reach the self-intersection radius for the first time. Panel (b) shows the bolometric light curve from our fiducial 3D run (red curves) and a low-resolution 3D test run with 20% the total number of grid cells. Excellent convergence is achieved well before the fallback time (vertical dashed line). Shaded regions correspond to different viewing angles.

Extended Data Fig. 2 Hydrodynamic and geometric features of the bound debris streams.

Panel (a) shows the mass fallback rate \({\dot{M}}_{{\rm{f}}{\rm{b}}}(t)\) at two different epochs: one immediately post-disruption (blue) and another after the most tightly bound debris has passed apocenter for the first time (red). The overlap between the curves illustrates the relatively minor effect of recombination on center-of-mass orbital dynamics, as well as the lack of gravitational fragmentation in the debris streams. In panel (b), we show the stream linear density λ as a function of orbital true anomaly f (in the Newtonian limit, f = 0 is pericenter, and f = π apocenter). As expected, there is little difference between the adiabatic (red) and realistic (blue) equations of state. In panel (c), we plot the cylindrical radii in the transverse direction that enclose 50% (solid) and 90% (dashed) of the stream mass (colors are the same as in panel b). Here we see that heating effects from recombination can puff up bound debris streams at the factor ≈ 3 level in comparison to an adiabatic stream, leading to more violent recompression shocks at pericenter.

Extended Data Fig. 3 Mass profiles.

The instantaneously enclosed mass in the inner radii of the simulation, plotted as a function of time since disruption. For the entire duration of the simulation, the fraction of stellar debris inside the gravitational softening length of h = 60R⊙ never exceeds ≈ 1.5 × 10−3 (blue curve). The mass fractions inside even larger radial cuts are rather small as well, justifying our use of a softened potential on scales ≲ h.

Extended Data Fig. 4 Density profiles.

Projections of gas density ρ onto the xz (left) and yz (right) planes, shown at t = 47 (top), t = 55 (middle), and t = 62 (bottom) days. Logarithmic color schemes are labeled in sidebars. Early on, most dynamically bound debris has not yet returned to pericenter, and remains in geometrically thin debris streams. By peak light (e.g. the t = 62 day panels), an order unity fraction of the bound debris has undergone partial circularization, inflating into a quasi-ellipsoidal accretion flow on scales of ~ 1000R⊙.

Extended Data Fig. 5 Dissipation rates.

Projections of energy dissipation rates \(\dot{u}\) onto the xz (left) and yz (right) planes, shown at t = 47 (top), t = 55 (middle), and t = 62 (bottom) days. Logarithmic color schemes are labeled in sidebars. At early times, dissipation is localized near pericenter in the nozzle shock. Later, as a quasi-ellipsoidal accretion disk forms, the locus of dissipation extends to larger radii at stream-disk shocks.

Extended Data Fig. 6 Time evolution of the spatial geometry of dissipation.

Panel (a): the dissipation radius \({r}_{{\rm{diss}}}=\int \,r\dot{E}dV/\int \dot{E}dV\). At early times, the primary site of dissipation is at small radii near stream pericenter. The dissipation radius grows slowly until ≈ 55 days, when it begins to increase in size at a much faster rate. Panel (b): time evolution of the average azimuthal dissipation angle ϕdiss. The color bar measures the dimensionless angular localization of dissipation, Rdiss ≤ 1. Both are calculated via the formulae \({{\bf{R}}}_{{\rm{diss}}}=\int \widehat{{\bf{r}}}\dot{E}dV/\int \dot{E}dV\) and \(\cos {\phi }_{{\rm{diss}}}={{\bf{R}}}_{{\rm{diss}}}\cdot \widehat{{\bf{x}}}/| {R}_{{\rm{diss}}}| \). At early times, the primary site of dissipation is localized at positive angles near and slightly downstream of stream pericenter (i.e. in material that is free-falling into its compression). The dissipation angle begins to oscillate strongly around and after t ≈ 55 days, and strongly delocalizes in angle.

Extended Data Fig. 7 Time evolution of gas eccentricity.

The mass-weighted eccentricity e (color-coded via the legend on the right) of the bound gas as a function of distance from the SMBH. The vertical dashed line shows the original tidal radius, and the left side of the plot terminates at the softening radius. At all radii, e generally decreases with time, reaching low, quasi-circular values ≲ 0.3 inside a radius of 100 − 200R⊙ by the end of the simulation.

Extended Data Fig. 8 Features of the emission surfaces.

Panel (a): angle-averaged thermalization (Rth; blue, red curves) and photospheric (Rph; black, pink curves) radii plotted as functions of time. The photosphere is always larger than Rth, demonstrating the dominance of scattering opacity. This is shown with an arithmetic mean (blue, black curves) and a geometric mean (red, pink curves). The stronger time evolution in the geometric means highlights the higher initial asymmetry in the actual thermalization surface/photosphere, but the convergence of the two means shows that this asymmetry declines over time. Panel (b): the dimensionless gas radial velocity, ∣Vr∣/Vesc, at the thermalization radius, plotted as a function of time. As in Extended Data Fig. 8, we show both arithmetic (blue, black) and geometric (red, pink) angle averages. We break up the thermalization surface into inflowing (black, pink) and outflowing (blue, red) components. The ratio Vr/Vesc < 1 always, implying that the gas on the thermalization surface is, on average, bound to the SMBH.

Extended Data Fig. 9 Synthetic spectra.

The emitted spectrum νLν plotted against wavelength λ (and equivalently effective temperature T) at 3 different times: t = 45.73 days (panel a), t = 56.12 days (panel b), and t = 62.21 days (panel c). In each of these three panels, the six different curves correspond to six different viewing angles on the simulation’s principal axes. The stellar debris orbits in the xy-plane with a pericenter on the positive x-axis. As time goes on, the emitted spectra become cooler.

Extended Data Fig. 10 Properties of optical/UV black body fits.

The occurrence rates for black body properties of our simulation at t = 65 days, binned over 192 different observing angles. The top, middle, and bottom panels show occurrence rates for fitted luminosity, blackbody temperature, and blackbody radius, respectively. There is a limited spread (roughly half an order of magnitude) in each of these quantities, depending on viewing angle.

Extended Data Fig. 11 Thermal X-ray properties.

The occurrence rates for X-ray luminosities in our simulation at t = 65 days, binned over 192 different observing angles. The top and bottom panels show occurrence rates for Swift XRT-band X-ray luminosity and the optical-to-X-ray ratio, respectively. Typical X-ray luminosities vary by an order of magnitude depending on viewing angle, from 1042−43 erg s−1, with some outlying viewing angles as dim as 1041 erg s−1. By the time of peak optical light shown here, the optical to X-ray ratio is ~ 100, with more than an order of magnitude of scatter.

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Steinberg, E., Stone, N.C. Stream–disk shocks as the origins of peak light in tidal disruption events. Nature 625, 463–467 (2024). https://doi.org/10.1038/s41586-023-06875-y

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