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arxiv: 2603.10208 · v2 · submitted 2026-03-10 · 🌌 astro-ph.HE · gr-qc

Unexpectedly Weak General Relativistic Effects in Strongly Relativistic Tidal Disruption Events

Ho-Sang Chan , Taeho Ryu , Julian Krolik , Tsvi Piran This is my paper

Pith reviewed 2026-05-15 12:40 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords tidal disruption eventsgeneral relativityblack holeshydrodynamic simulationsstellar debrisapsidal precessioncircularizationsupermassive black holes
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The pith

Strongly relativistic tidal disruption events leave debris highly eccentric for weeks after disruption.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper uses a general relativistic hydrodynamic simulation to demonstrate that close-in TDEs do not rapidly circularize into disks despite strong apsidal precession. Early shocks from precession and nozzle compression dissipate energy efficiently but last only about a week before stream self-interactions increase angular momentum and expand the pericenter distance. The debris flow therefore remains highly eccentric with most returned mass near the distant apocenter, and shocks rather than accretion power the luminosity up to 35 days after peak mass return. This implies circularization proceeds slowly regardless of relativistic strength, altering expectations for the structure of the flow during peak optical and UV emission.

Core claim

A GR hydrodynamic simulation starting from the initial approach of a Sun-like star to a non-spinning 10^6 solar-mass black hole and running to 35 days after peak mass return shows that strong relativistic apsidal precession and pericenter nozzle compression drive efficient early shocks, yet these last only ~0.3 of the peak mass-return time. Stream self-interactions subsequently raise the angular momentum of the incoming stream, expanding its pericenter, weakening precession, and reducing further dissipation, so that the debris stays highly eccentric with most mass near the orbital apocenter at ~250 times the initial pericenter distance.

What carries the argument

General relativistic hydrodynamic simulation of debris evolution that tracks apsidal precession, pericenter nozzle compression, and angular-momentum transfer through stream self-interactions.

If this is right

  • Most of the returned stellar mass resides near the orbital apocenter rather than accreting promptly onto the black hole.
  • Shocks driven by stream interactions, not direct accretion, power the observed optical and UV luminosity.
  • The peak brightness occurs while the flow is still highly eccentric and spatially extended.
  • Circularization in TDEs occurs on timescales much longer than the mass-return time even when relativistic effects are strong.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • TDE emission models may need to treat extended eccentric streams rather than assuming prompt disk formation.
  • The short-lived nature of relativistic shocks could explain why some observed TDE light curves lack signatures of rapid circularization.
  • Similar stream-interaction dynamics might operate in TDEs around spinning black holes if initial conditions allow comparable angular-momentum transfer.

Load-bearing premise

The single simulation with a Sun-like star and non-spinning 10^6 solar-mass black hole, at the chosen numerical resolution, accurately captures the long-term dynamics without significant grid artifacts or missing physics.

What would settle it

An observation or higher-resolution simulation showing that the debris stream circularizes into a disk within a few days, or that strong shocks persist well beyond the first week in a strongly relativistic TDE.

Figures

Figures reproduced from arXiv: 2603.10208 by Ho-Sang Chan, Julian Krolik, Taeho Ryu, Tsvi Piran.

Figure 1
Figure 1. 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 rg, 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… view at source ↗
Figure 2
Figure 2. Figure 2: Temporal evolution of the density contour (in the log10 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 rg and rp; the lower-left text box indicates the time since the pericenter passage in t0. In each panel… view at source ↗
Figure 3
Figure 3. 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 Ξ factor from Equations 4 and 6. In the right-hand panel, we indicate the peak fallback time t0 (brown dashed-dotted line) and the scaling relation t −5/3 (purple dashed-dotted line) for reference. 10 1 10 2 10 3 10 4 r (rg) … view at source ↗
Figure 4
Figure 4. Figure 4: (Left) Time evolution of the enclosed mass profile at five epochs. The green dashed curve shows the mass whose apocenter ≈ 2a(E) < r for the dM/dE shown in the left panel of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Time evolution of the mass accretion rate (top), the total internal energy within the simulation domain (mid￾dle), 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 normal￾ized) mass fallback rate, when it reaches a steady state, which i… view at source ↗
Figure 6
Figure 6. Figure 6: Simulation snapshots of the fluid density along the x − y plane at selected epochs (indicated in the upper-left text box), illustrating early-time violent self-intersection shocks that are strong enough to significantly disrupt the incoming streams (see also Z. L. Andalman et al. (2022)). In the left panel, the yellow arrow marks the rough location of the self-intersections, while in the middle and right p… view at source ↗
Figure 7
Figure 7. Figure 7: Fractional specific angular momentum relative to the star’s initial value, shown along the x − y plane at t ≃ 0.26 t0 (which corresponds to the middle panel of Fig￾ure 6). We approximately mark the boundaries of the incom￾ing stream and indicate the positions of the nozzle shock, as well as strong and weak self-intersection (SI) shocks. laterally, creating large contrasts in aspect ratio and density betwee… view at source ↗
Figure 8
Figure 8. Figure 8: Contours of the local vertical scale height (see Equaton 11) and the Newtonian orbital pericenter (right) in the x−y plane at 1 t0. Each panel includes a zoomed-in view of the region near the SMBH. As discussed in the main text, the pericenter distance of the incoming debris increases due to angular-momentum transfer from the outgoing debris. This feature persists even in the late phase. In the Newtonian p… view at source ↗
Figure 9
Figure 9. Figure 9: Snapshots of the fluid density in the x − z plane at 1 t0, overlaid with the velocity streamlines (grey). The snapshot is taken at y = −1000 rg, corresponding to the location indicated by the dark arrow of the zoomed-out view in [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Specific angular momentum relative to the ini￾tial stellar angular momentum profiles. All quantities are further mass-weighted. We also indicate the ratio of the ISCO angular momentum (jISCO, cyan) and the angular mo￾mentum required for direct capture under a parabolic orbit (jpara, green) for reference. 10 1 10 2 10 3 10 2 10 1 10 0 e orb / e circ rp 0.15t0 0.25t0 0.5t0 1.0t0 1.4t0 [PITH_FULL_IMAGE:figu… view at source ↗
Figure 11
Figure 11. Figure 11: Specific orbital energy as a function of distance from the SMBH, normalized by the energy required for cir￾cularization of debris into a circular disk with size of 2 rp, which is GMBH/[4rp]. All quantities are mass-weighted. to 0.7 − 0.9 at t ≃ 1.4 t0. The sharp jump in eccentric￾ity at r ≃ 10 − 20 rg for t ≳ 0.25 t0 in all the profiles presented above marks the approximate position of the orbital pericen… view at source ↗
Figure 13
Figure 13. Figure 13: Temporal evolution of the luminosity (top), the luminosity-weighted average photospheric temperature (middle, ⟨Tph⟩), and the average photospheric radius (bot￾tom, ⟨Rph⟩). Short-dashed lines are moving averages of the raw data shown in gray. In the top panel, a horizontal brown long-dashed line marks the Eddington luminosity, and the red line represents a moving average of the gross heating rate shown in … view at source ↗
Figure 14
Figure 14. Figure 14: Temperature map at 0.3 t0 (when the luminosity peaks and subsequently saturates) in the x − y plane. The photosphere and thermalization surface are shown with red solid and blue-dashed curves, respectively. To estimate the electromagnetic observables, for each snapshot, we first identify the photospheric radius, Rph, defined as τ (Rph) = Z Rout Rph ρ(κsc + κabs)dr = 1, (A1) where Rout denotes the outer ra… view at source ↗
Figure 15
Figure 15. Figure 15: Orbital energy (top), relative specific angular momentum with respect to the star’s initial angular momen￾tum (middle), and the pseudo-entropy (bottom) at different epochs. In the bottom row, the vertical gray line marks logK = 1.15. where hρ is the density-weighted scale height along ra￾dial paths hρ = Z Rph r ρsds/ Z Rph r ρds. (A3) [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Total gas mass with logK > logKcut = 1.15 as a function of time (red) The fallback curve (blue dashed) is identical. The flux at the photosphere along a radial path is esti￾mated as dL dA = Z Rph Rdiff aT4 tcool s 2 R2 ph ds, (A4) where Rdiff is the radius at which the cooling time equals the system evolution time. Setting the lower limit of the integral as Rdiff ensures that the radiation that can es￾cap… view at source ↗
Figure 17
Figure 17. Figure 17: (Left) Map of logKcut − 1.15 in the x − y plane at 1 t0. (Right) Same as the left panel, but measuring the radial variations of logK along different azimuthal angle ϕ. The grey shaded region represent logKcut < 1.15. r ≳ 50 rg. In [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
read the original 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 involving a Sun-like star and a $10^{6}\,M_{\odot}$ non-spinning 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 $35$\,days after the peak mass-return time ($\simeq$ $23$\,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 suggest that circularization in TDEs may proceed slowly regardless of the strength of apsidal precession, with the flow remaining highly eccentric and extended during the peak optical/UV luminosity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper reports a general relativistic hydrodynamic simulation of a tidal disruption event in which a Sun-like star is disrupted by a non-spinning 10^6 solar-mass black hole at a strongly relativistic pericenter. Contrary to the expectation of rapid circularization driven by strong apsidal precession, the simulation shows that the debris stream remains highly eccentric, with the bulk of the returned mass residing near apocenter at ~250 times the initial pericenter distance. Early shocks from relativistic precession and nozzle compression dissipate energy efficiently for only the first ~week (~0.3 of the peak mass-return time), after which stream self-interactions raise the specific angular momentum, expand the pericenter, weaken precession, and reduce further dissipation. The authors conclude that circularization proceeds slowly regardless of apsidal-precession strength, so that the flow stays eccentric and extended during the epoch of peak optical/UV luminosity. The run begins at stellar approach and extends to 35 days after peak mass return.

Significance. If the central result is robust, the work would be significant for TDE theory and interpretation. It directly challenges the long-standing assumption that strong general-relativistic apsidal precession in deeply plunging encounters produces prompt disk formation and efficient accretion. Instead, the simulation indicates that shock-powered emission from an extended, eccentric flow can dominate at peak luminosity, offering a possible explanation for observed TDE light-curve timescales without requiring rapid circularization. The direct integration from realistic initial conditions to late times is a methodological strength that supplies a concrete, falsifiable prediction for the eccentricity distribution at peak brightness.

major comments (2)
  1. [§3] §3 (Numerical Methods): The manuscript presents results from a single GRHD run with fixed initial conditions (Sun-like star, non-spinning 10^6 M_⊙ BH) and does not report a resolution study or convergence tests with respect to grid scale at the nozzle or artificial viscosity. Because the key transition—pericenter expansion and suppression of dissipation after the first week—depends on the angular-momentum gain during stream self-intersections, it is essential to demonstrate that this outcome is insensitive to numerical dissipation. Without such tests the robustness of the late-time eccentricity evolution cannot be assessed.
  2. [§4 and §5] §4 (Results) and §5 (Discussion): The claim that circularization proceeds slowly 'regardless of the strength of apsidal precession' is extrapolated from one simulation. The hydro-only treatment omits radiative cooling (which can thin the stream and change collision geometry) and magnetic fields (which can redistribute angular momentum on orbital timescales). If either process alters the eccentricity evolution by more than ~10–20 % at late times, the generalization does not hold. A quantitative estimate of the possible impact of these missing physics on the reported pericenter expansion would strengthen the central conclusion.
minor comments (2)
  1. [Abstract] Abstract: The statement that the pericenter is 'smaller than ~10 gravitational radii' should be accompanied by the precise value used in the simulation so that readers can judge how deeply relativistic the encounter is relative to prior work.
  2. [Figures] Figure captions and text: Several figures show the spatial distribution of debris at selected times; adding quantitative diagnostics (e.g., time evolution of the mass-weighted eccentricity or specific angular momentum) would make the transition from strong to weak dissipation easier to follow.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their detailed and constructive report. We address each major comment below and indicate the revisions we plan to make.

read point-by-point responses

  1. Referee: §3 (Numerical Methods): The manuscript presents results from a single GRHD run with fixed initial conditions (Sun-like star, non-spinning 10^6 M_⊙ BH) and does not report a resolution study or convergence tests with respect to grid scale at the nozzle or artificial viscosity. Because the key transition—pericenter expansion and suppression of dissipation after the first week—depends on the angular-momentum gain during stream self-intersections, it is essential to demonstrate that this outcome is insensitive to numerical dissipation. Without such tests the robustness of the late-time eccentricity evolution cannot be assessed.

    Authors: We agree that convergence tests are important for validating the numerical results, particularly regarding the angular momentum transfer in stream self-intersections. Performing a full resolution study is computationally intensive for GRHD simulations spanning the required timescales. In the revised manuscript, we will include additional information on the grid resolution used and discuss why the key physical processes are expected to be robust against moderate changes in numerical dissipation. We will also note that the pericenter expansion is driven by the geometry of the intersections rather than small-scale dissipation. revision: partial

  2. Referee: §4 (Results) and §5 (Discussion): The claim that circularization proceeds slowly 'regardless of the strength of apsidal precession' is extrapolated from one simulation. The hydro-only treatment omits radiative cooling (which can thin the stream and change collision geometry) and magnetic fields (which can redistribute angular momentum on orbital timescales). If either process alters the eccentricity evolution by more than ~10–20 % at late times, the generalization does not hold. A quantitative estimate of the possible impact of these missing physics on the reported pericenter expansion would strengthen the central conclusion.

    Authors: We recognize that our results are from a single simulation without radiative cooling or magnetic fields, and that these omissions limit the generality of our conclusions. The hydrodynamical mechanism of angular momentum increase via self-interactions is the core finding, and we expect it to persist even with additional physics, though the exact timescales may vary. We will revise the discussion section to temper the claim, emphasizing that it applies to the hydrodynamic case, and provide a qualitative discussion of how cooling and magnetic fields might influence the outcome without quantitative estimates, as those would require separate studies. revision: partial

standing simulated objections not resolved
  • A quantitative estimate of the impact of radiative cooling and magnetic fields on the pericenter expansion requires additional simulations that are outside the current scope of this work.

Circularity Check

0 steps flagged

No significant circularity; results from direct GRHD simulation

full rationale

The paper's central claims derive from a single general relativistic hydrodynamic simulation initialized with a Sun-like star on a parabolic orbit around a non-spinning 10^6 solar-mass black hole. The evolution to 35 days post-peak mass return is obtained by direct numerical integration of the GRHD equations; the reported pericenter expansion, weakening of apsidal precession, and persistence of high eccentricity are outputs of that integration rather than any fitted parameter, self-referential definition, or load-bearing self-citation. No step reduces the target result to its own inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of general relativistic hydrodynamics applied to the chosen initial conditions; no new physical entities are introduced.

free parameters (2)
  • black hole mass = 10^6 solar masses
    Set to 10^6 solar masses as representative for a TDE involving a Sun-like star.
  • stellar pericenter distance
    Chosen to be strongly relativistic (smaller than ~10 gravitational radii).
axioms (2)
  • standard math General relativistic hydrodynamics equations govern the stellar debris flow
    Standard framework for GR astrophysical simulations invoked throughout.
  • domain assumption Black hole is non-spinning
    Explicitly stated in the simulation setup.

pith-pipeline@v0.9.0 · 5577 in / 1463 out tokens · 51199 ms · 2026-05-15T12:40:08.925377+00:00 · methodology

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