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Beyond the Impulsive Approximation: The Dynamics and Radio Emission of Tidal Disruption Jets

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Fabio De Colle, Enrico Ramirez-Ruiz

High Energy Astrophysical Phenomena · Submitted 3 Jul 2026 · 54 references

Pith's verdict: Clean hydro result: continuous fallback powering keeps TDE jets slower and less beamed than equal-energy BM blasts, with a usable tb/td,BM ≲ 0.1 validity cut that most relativistic TDEs miss.

T0 · AI review

How this review was made: An AI referee (grok-4.5) read the paper on July 12, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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arXiv ID2607.03548 (version 1)
Pith IDDAMDFURZ, Pith's permanent record of this paper and its review
CitationEnrico Ramirez-Ruiz, Fabio De Colle. "Beyond the Impulsive Approximation: The Dynamics and Radio Emission of Tidal Disruption Jets." arXiv:2607.03548 (2026). https://pith.science/paper/DAMDFURZ
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The paper

The paper claims

Fallback-powered TDE jets stay slower and less beamed than impulsive blast waves of the same energy, so the Blandford–McKee approximation usually fails and off-axis radio is strongly suppressed.

The reading

Radio afterglows of relativistic tidal disruption events are routinely modeled as impulsive explosions that quickly settle into the Blandford–McKee self-similar solution. This paper shows that the approximation is usually invalid: the jets are fed by stellar fallback over weeks to months, so energy keeps arriving while the blast wave is already decelerating. One- and two-dimensional relativistic hydrodynamics plus synchrotron calculations demonstrate that, for fixed total energy, continuously powered jets drive systematically slower forward shocks, produce delayed and fainter radio peaks, and remain more tightly collimated. The impulsive limit is recovered only when the injection duration is less than about ten percent of the equivalent Blandford–McKee deceleration time—a condition TDEs generally fail. Because off-axis emission is thereby strongly suppressed, non-detections of radio emission place weaker limits on jet production rates; many more TDEs may launch relativistic jets than current catalogs imply.

What carries the argument

The ratio tb/td,BM of engine duration to the deceleration time of an equivalent impulsive blast wave. When this ratio exceeds ~0.1 the blast wave retains memory of continuous energy injection, lowering shock Lorentz factor and beaming throughout the radio-bright phase.

Extended reading notes

Core claim

For fixed total energy, fallback-powered TDE jets produce slower forward shocks, delayed and fainter radio light curves, and substantially weaker off-axis emission than equivalent impulsive Blandford–McKee blast waves; the impulsive approximation holds only when the engine duration is ≲ 0.1 times the Blandford–McKee deceleration time, a regime TDEs rarely occupy.

Load-bearing premise

The claim that the main trends—later peaks, lower luminosities, and strong off-axis suppression—remain intact once synchrotron self-absorption is included, even though the present radiation calculations omit it entirely.

Original abstract

Radio emission from relativistic tidal disruption events (TDEs) is commonly interpreted using the Blandford--McKee solution for an impulsive relativistic blast wave. Unlike gamma-ray bursts, however, TDE jets are powered by fallback accretion, injecting energy over weeks to months. We investigate how this sustained energy injection modifies the dynamics and radio emission of relativistic TDE jets using one- and two-dimensional relativistic hydrodynamic simulations coupled with synchrotron radiation calculations. For a fixed total energy, fallback-powered jets drive slower forward shocks, producing delayed and systematically fainter radio emission. We show that the impulsive approximation is valid only when the duration of energy injection is less than approximately ten percent of the deceleration time of an equivalent Blandford--McKee blast wave, a condition that is generally not satisfied for relativistic TDEs. As a result, continuously powered outflows are significantly less beamed than impulsive explosions, leading to a strong suppression of off-axis radio emission. These results demonstrate that the radio evolution of relativistic TDEs retains memory of the central engine and cannot, in general, be described by an impulsive solution. By substantially reducing the expected off-axis radio emission, sustained fallback-powered jets imply that relativistic jet production in tidal disruption events may be considerably more common than current radio observations suggest.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,384 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.47 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Radio emission from relativistic tidal disruption events (TDEs) is commonly interpreted using the Blandford--McKee solution for an impulsive relativistic blast wave. Unlike gamma-ray bursts, however, TDE jets are powered by fallback accretion, injecting energy over weeks to months. We investigate how this sustained energy injection modifies the dynamics and radio emission of relativistic TDE jets using one- and two-dimensional relativistic hydrodynamic simulations coupled with synchrotron radiation calculations. For a fixed total energy, fallback-powered jets drive slower forward shocks, producing delayed and systematically fainter radio emission. We show that the impulsive approximation is valid only when the duration of energy injection is less than approximately ten percent of the deceleration time of an equivalent Blandford--McKee blast wave, a condition that is generally not satisfied for relativistic TDEs. As a result, continuously powered outflows are significantly less beamed than impulsive explosions, leading to a strong suppression of off-axis radio emission. These results demonstrate that the radio evolution of relativistic TDEs retains memory of the central engine and cannot, in general, be described by an impulsive solution. By substantially reducing the expected off-axis radio emission, sustained fallback-powered jets imply that relativistic jet production in tidal disruption events may be considerably more common than current radio observations suggest.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Radio emission from relativistic tidal disruption events (TDEs) is commonly interpreted using the Blandford--McKee solution for an impulsive relativistic blast wave. background 1.00 0.03 0.02 asserted 0.98
s1 Unlike gamma-ray bursts, however, TDE jets are powered by fallback accretion, injecting energy over weeks to months. background 0.95 0.06 0.02 asserted 1.00
s2 We investigate how this sustained energy injection modifies the dynamics and radio emission of relativistic TDE jets using one- and two-dimensional relativistic hydrodynamic simulations coupled with synchrotron radiation calculations. method 0.62 0.91 0.04 asserted 0.68
s3 For a fixed total energy, fallback-powered jets drive slower forward shocks, producing delayed and systematically fainter radio emission. result 1.00 0.92 0.18 asserted 1.00
s4 We show that the impulsive approximation is valid only when the duration of energy injection is less than approximately ten percent of the deceleration time of an equivalent Blandford--McKee blast wave, a condition that is generally not satisfied for relativistic TDEs. result 0.94 0.89 0.32 asserted 1.00
s5 As a result, continuously powered outflows are significantly less beamed than impulsive explosions, leading to a strong suppression of off-axis radio emission. result 0.94 0.90 0.17 asserted 1.00
s6 These results demonstrate that the radio evolution of relativistic TDEs retains memory of the central engine and cannot, in general, be described by an impulsive solution. interpretation 0.77 0.89 0.72 asserted 1.00
s7 By substantially reducing the expected off-axis radio emission, sustained fallback-powered jets imply that relativistic jet production in tidal disruption events may be considerably more common than current radio observations suggest. interpretation 1.00 0.71 0.29 hedged possibility 0.99

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Top: Density stratification adopted for the cir￾cumnuclear medium surrounding supermassive black holes with masses MBH = 106 and 107 M⊙, based on the models of F. De Colle et al. (2012b). The complex radial struc￾ture motivates the use of numerical simulations to follow the blast-wave evolution. Bottom: Jet kinetic luminosity his￾tories adopted in this work. The solid curves correspond to luminosities inferred from simulations of the disruption of a 1 M⊙ star by black holes with masses 106 and 107 M⊙, while the dashed curves represent idealized models with con￾stant luminosity for t…
Figure 2. Evolution of the radial density profiles for one-dimensional continuously powered (gray) and impulsive (black) blast waves with the same isotropic-equivalent en￾ergy, Eiso = 4 × 1053 erg. Profiles are shown at t = 6, 22.7, 103, 691, 4618, and 30,902 days. The powered model (FB) is driven by the fallback-powered luminosity history corresponding to a 107 M⊙ black hole (
Figure 5. Energy injection time, tb, normalized to the de￾celeration time of an equivalent impulsive Blandford–McKee blast wave, td,BM, as a function of the radio peak time, tr, normalized to the peak time of the corresponding impulsive solution, tr,BM for the one-dimensional simulations shown in Figures 3 and 4. Although the energy injection terminates before the Blandford–McKee deceleration time for all mod￾els (tb < td,BM), the radio emission peaks substantially later than in the impulsive case. significant deceleration occurs (tb < td,BM), the blast wave would rapidly converge toward the…
Figure 6. Radio light curves at ν = 4.86 GHz for one-di￾mensional simulations using the fallback-powered jet lumi￾nosities and circumnuclear density profiles shown in
Figure 7. Density maps from a two-dimensional simulation of a relativistic jet propagating through the circumnuclear medium surrounding a 107 M⊙ black hole at t = 7, 47, and 380 days (left to right). The jet is injected at the inner boundary with Lorentz factor Γjet = 10, isotropic-equivalent energy Eiso = 4 × 1053 erg, and a luminosity history corresponding to the fallback-powered model shown in
Figure 8. Evolution of the jet opening angle in the two-di￾mensional simulation shown in
Figure 11. Comparison between the radio light curves pre￾dicted by the fallback-powered jet model and the observed radio luminosities of the early sample of radio-detected tidal disruption events. The models adopt the fallback luminosity history shown in

Showing 7 of the paper's 11 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2607.03548 by the authors.

References
How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 28 sentences without a confident label

Uses the method or tool of 1 paper
Cites as background 6 papers
  • The interpretation of these radio observations has relied almost exclusively on the framework developed for gamma-ray burst (GRBs) afterglows, in which the explosion is approximated as an impulsive release of energy that rapidly approaches the self-similar Blandford–McKee solution before decelerating through interaction with the surrounding medium [ref] .

    Spectra and Light Curves of Gamma-Ray Burst Afterglows · Introduction · 0.83

  • The interpretation of these radio observations has relied almost exclusively on the framework developed for gamma-ray burst (GRBs) afterglows, in which the explosion is approximated as an impulsive release of energy that rapidly approaches the self-similar Blandford–McKee solution before decelerating through interaction with the surrounding medium [ref] .

    The Shape of Spectral Breaks in GRB Afterglows · Introduction · 0.83

  • In addition to their thermal optical, ultraviolet, and X-ray emission [ref] , many TDEs produce outflows that interact with the circumnuclear medium, giving rise to synchrotron radio emission spanning a wide range of luminosities [ref] .

    Tidal Disruption Events · Introduction · 0.91

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