Converged simulations of the nozzle shock in tidal disruption events

TL;DR

The paper investigates whether nozzle shocks can provide the rapid energy dissipation needed to deflect debris in tidal disruption events. Using 3D general relativistic SPH with adaptive particle refinement (APR), the authors push pericenter resolution to the equivalent of $4.1\times10^{10}$ particles, ensuring energy conservation and reducing artificial heating. They find the nozzle shock dissipates only $\sim 4\times10^{-5}$ of the orbital energy ($M\sim160$, deflection $\approx0.34^{\circ}$), indicating nozzle shocks cannot drive large deflections; instead, relativistic precession–induced stream–stream collisions are likely responsible for significant energy release and disk formation. These results resolve a long-standing question about nozzle shocks in TDEs and refine predictions for early emission and obscuration, while highlighting the importance of high-resolution, convergence-tested simulations in interpreting TDE dynamics.

Abstract

When debris from a star that experienced a tidal disruption events (TDE) after passing too close to a massive black hole returns to pericenter on the second passage, it is compressed, leading to the formation of nozzle shocks (in the orbital plane) and pancake shocks (perpendicular to the orbital plane). Resolving these shocks is a long-standing problem in the hydrodynamic simulations of parabolic TDEs. Excessive numerical energy dissipation or heating unrealistically expands the stream. In this Letter, we apply adaptive particle refinement to our 3D general relativistic smoothed particle simulations to locally increase the resolution near the pericenter. We achieve resolutions equivalent to $6.55\times10^{11}$ particles, allowing us to converge on the true energy dissipation. We conclude that only $4\times10^{-5}$ of the orbital energy is dissipated in nozzle shocks for a Sun-like star tidally disrupted by a $10^6$ solar-mass black hole, therefore the nozzle shocks are unlikely to be important in the evolution of TDEs.

Figures (5)

• Figure 1: Demonstration of the APR boundaries used (16 levels in the figure). The spherical boundaries are centred on the MBH. The outermost boundary is at $r=2200 r_{\rm g} \approx 3.25\times10^{14} {\rm cm}$ with $\Delta r = 137.5 r_{\rm g} \approx 2.03\times 10^{13} {\rm cm}$ between each boundary, where $r_{\rm g} = GM/c^2$ is the gravitational radius of the MBH. $r=2200r_{\rm g}$ is the same in all simulations whereas $\Delta r = 1100, 550, 275, 183.3$ for 2, 4, 8, 12 level simulations respectively.
• Figure 2: Snapshots of the simulations with 0, 2, 4, 8, 12, 16 levels of splitting at $t=14.4$ days after stellar disruption (first pericenter passage). The eccentricity of the most bound gas ($e_{\rm mb,simulated} \sim 0.96$) is smaller than predicted in Section \ref{['sec:ana']} ($e_{\rm mb,analytic} \sim 0.99$) due to the heating from nozzle and pancake shocks on the first pericenter passage. The amount of energy dissipation at pericenter and thus stream fanning post-pericenter decreases with resolution until it converges at 12 levels of refinement (equivalent to a global 41B particle simulation). The binary simulation dumps plotted are available on Zenodo: 10.5281/zenodo.17225834.
• Figure 3: The mean fraction of energy dissipated near the pericenter. The fraction drops almost linearly in log scales until convergence at 12 levels of splitting. Using linear fits to the four points before convergence and separately to the two points after convergence, we estimate the nozzle shock converge at approximately $2.24\times10^{10}$ particles. The error bars represent the statistical standard errors of our measurements and not the true uncertainties of the energy fractions. Data is available on Zenodo: 10.5281/zenodo.17225834.
• Figure 4: Difference in initial orbital energy and final orbital energy after splitting as a function of distance from the MBH for various splitting methods. The difference in energies is lowest across all radii for the method which splits particles along the geodesic and updates the metric (Method 5) - the method we employ in this work.
• Figure 5: Measuring the specific thermal and kinetic energies as a function of angular coordinate $\theta$ relative to the MBH as the leading edge of the tidal stream passes through pericenter. The pink region represents the estimated pericenter used in Section \ref{['sec:circ eff']}. Left: one snapshot with very few particles for the 0-, 2- and 4-level simulations. Particles are only present in 13, 26, 33 beams, respectively, of the 60 beams plotted. Right: the average of four adjacent snapshots, showing enough particles to meaningfully analyse in the lower resolution simulations, with 25, 56, 59 beams occupied for 0, 2 and 4 level simulations, respectively. Data is available on Zenodo: 10.5281/zenodo.17225834.