pith. sign in

arxiv: 2606.02691 · v1 · pith:64E4UW4Enew · submitted 2026-06-01 · 🌌 astro-ph.HE

Systematic Error in Approximate Models of the GRB Early Afterglow

Benjamin Amend , Eric R. Coughlin , Jonathan Zrake This is my paper

Pith reviewed 2026-06-28 12:53 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords gamma-ray burst afterglowreverse shockNewtonian regimeBlandford-McKee solutiontwo-zone modelhydrodynamic simulationssystematic error
0
0 comments X

The pith

Newtonian reverse shocks leave hours where two-zone models mispredict GRB afterglow emission.

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

The paper tests the two-zone model commonly used to approximate GRB afterglow dynamics before the onset of Blandford-McKee self-similarity. Simulations reveal that when the reverse shock remains Newtonian, it finishes crossing the ejecta shell well before self-similarity develops, creating an extended period of mismatched hydrodynamics. During this interval the model can overpredict reverse-shock emission across radio to ultraviolet bands or forward-shock emission in X-rays, depending on the chosen transition rule. A reader would care because early afterglow light curves are used to infer ejecta properties and circumburst conditions.

Core claim

When the reverse shock is Newtonian, it crosses the ejecta shell long before Blandford-McKee self-similarity is established, leaving a prolonged interval that can span hours in observer time in which the true hydrodynamic evolution is not captured by standard semi-analytic prescriptions. This mismatch can substantially overpredict the reverse-shock emission from radio through ultraviolet frequencies, or overpredict the forward-shock emission at X-ray frequencies, depending on how the transition away from the two-zone model is prescribed.

What carries the argument

The two-zone model, which divides the outflow into forward-shocked circumburst medium and reverse-shocked ejecta until the Blandford-McKee self-similar phase begins.

If this is right

  • The Newtonian reverse shock finishes crossing the ejecta long before self-similarity, creating an hours-long gap in model validity.
  • Reverse-shock emission from radio through ultraviolet can be substantially overpredicted during this gap.
  • Forward-shock emission at X-ray frequencies can be substantially overpredicted, depending on the transition prescription used.
  • Standard semi-analytic prescriptions therefore fail to describe the true evolution in the pre-self-similar phase for Newtonian reverse shocks.

Where Pith is reading between the lines

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

  • Observers fitting early afterglow data with two-zone models may need to restrict those fits to later times or switch to full hydrodynamic calculations when the reverse shock is expected to be Newtonian.
  • The duration of the mismatch interval offers a new observable diagnostic for the initial Lorentz factor and shell thickness of the ejecta.
  • The choice of transition prescription from the two-zone model to the self-similar phase becomes a source of systematic uncertainty that should be quantified in population studies.

Load-bearing premise

High-resolution special relativistic hydrodynamics simulations accurately capture the true physical evolution of the outflow before Blandford-McKee self-similarity begins.

What would settle it

A side-by-side comparison of two-zone model light curves against full hydrodynamic simulation outputs or early afterglow observations that shows whether the reported overpredictions occur at the stated frequencies during the identified interval.

Figures

Figures reproduced from arXiv: 2606.02691 by Benjamin Amend, Eric R. Coughlin, Jonathan Zrake.

Figure 1
Figure 1. Figure 1: A schematic diagram of the fluid primitives in the ‘two￾zone’ model. The zones are: (4) unshocked ejecta, (3) shocked ejecta, (2) shocked circumburst medium, and (1) unshocked cir￾cumburst medium. The fluid primitives are spatially uniform within each zone, and the fluid states in zones 1 and 4 are known time-dependent boundary conditions. the comoving density of the unshocked ejecta is ρ4(r) = ρej  r rej… view at source ↗
Figure 2
Figure 2. Figure 2: Time series of the post-forward-shocked circumburst medium (γ2|FS) and the pre-reverse-shocked ejecta (γ4|RS) for a k = 0 blast wave in the RRS regime where fej = 5.928 × 104 and γej = 5.623 × 102 . There is a precipitous drop in γ4|RS as the reverse shock finishes sweeping through the ejecta shell, and a broken power-law knee in γ2|FS as the post-forward-shocked fluid begins to transition from a t−1/2 sca… view at source ↗
Figure 3
Figure 3. Figure 3: Reverse shock crossing and deceleration timescales vs. ejecta Lorentz factors and overdensity parameters for a series of initial conditions that span from the NRS through RRS regimes in ISM (k = 0, left) and wind-like (k = 2, right) circumburst media. Both ∆ej = 0.01rej and Mej = 4πr2 ej∆ejfejρcbγej were held fixed across all instances for each type of ambient medium. Shown are the analytic predictions fro… view at source ↗
Figure 5
Figure 5. Figure 5: Dimensionless thermal energy density in the reverse- (top) and forward- (bottom) shocked regions for a blast in a wind-like (k = 2) environment with a Newtonian reverse shock. Two sets of two-zone model predictions are shown: one where the switch to late-stage prescriptions occurs at t∆ (‘Two-Zone (t∆)’), and one where the switch occurs at tdec (‘Two-Zone (tdec)’), with g = 1/2 in both instances. The simul… view at source ↗
Figure 4
Figure 4. Figure 4: A comparison of fluid primitive radial profiles as pre￾dicted by the two-zone model and as observed in simulations at various times up to and including t∆ for a blast in a wind￾like medium (k = 2) in the NRS regime. The variable η rep￾resents (r − RCD)/(RCD − RRS) for RRS ≤ r ≤ RCD, and (r − RCD)/(RFS − RCD) for RCD ≤ r ≤ RFS. Expectedly, the simulation gradually drifts away from the two-zone model as the … view at source ↗
Figure 6
Figure 6. Figure 6: Spectral flux density of a mock GRB afterglow with a Newtonian reverse shock expanding into a wind-like (k = 2) circumburst medium, with fej = 105 , γej = 31.6, and ∆ej = 0.01 × rej = 1012 cm. Spectra from the SRHD simulation are compared to the two-zone model, the Blandford-McKee solution, and hybrid prescriptions that switch from the two-zone model to Blandford-McKee plus reverse-shocked-ejecta evolution… view at source ↗
Figure 7
Figure 7. Figure 7: Observer-frame light curves for the same mock GRB afterglow shown in [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

Gamma-ray burst (GRB) afterglows are thought to arise when relativistic ejecta launched by a compact central engine drive a blast wave into the surrounding circumburst medium, producing broadband synchrotron emission. We present a rigorous assessment, based on high-resolution special relativistic hydrodynamics simulations, of a widely adopted `two-zone model' for approximating the dynamics of the early afterglow phase. Before the onset of the Blandford-McKee (BMK) self-similar solution, the outflow generally produces two emission components, associated with the forward-shocked circumburst medium and the reverse-shocked ejecta. The subsequent evolution depends on whether the reverse shock significantly decelerates the ejecta as it crosses the shell, separating the so-called relativistic and Newtonian reverse shock regimes. We show that when the reverse shock is Newtonian, it crosses the ejecta shell long before BMK self-similarity is established, leaving a prolonged interval that can span $\sim$ hours in observer time in which the true hydrodynamic evolution is not captured by standard semi-analytic prescriptions. We demonstrate that this mismatch can substantially overpredict the reverse-shock emission from radio through ultraviolet frequencies, or overpredict the forward-shock emission at X-ray frequencies, depending on how the transition away from the two-zone model is prescribed.

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 presents high-resolution special relativistic hydrodynamics (SRHD) simulations to evaluate the standard two-zone model for the early afterglow phase of gamma-ray bursts. It claims that, in the Newtonian reverse-shock regime, the reverse shock crosses the ejecta shell well before the onset of Blandford-McKee self-similarity, leaving an extended hydrodynamic phase (potentially hours in observer time) that is not captured by common semi-analytic prescriptions; this mismatch can lead to substantial overpredictions of reverse-shock emission (radio to UV) or forward-shock emission (X-rays) depending on the transition prescription adopted.

Significance. If the central hydrodynamic result holds, the work identifies a concrete, previously under-appreciated limitation in widely used approximations for GRB afterglow modeling, with direct implications for broadband light-curve and spectral interpretations across radio through X-ray bands. The reliance on high-resolution SRHD simulations rather than analytic fitting provides a falsifiable, simulation-grounded test of the two-zone model's domain of validity.

major comments (2)
  1. [Methods] Methods section: the abstract and strongest claim rest on high-resolution SRHD simulations demonstrating that the Newtonian reverse shock crosses before BMK self-similarity, yet no resolution study, convergence test, or quantitative error analysis is described; without these, the load-bearing assertion that the true evolution lies outside the two-zone model for an extended interval cannot be verified at the reported level of rigor.
  2. [Results] Results/figures: the demonstration that the mismatch 'substantially overpredicts' emission requires explicit quantitative comparison (e.g., factor by which flux is overpredicted at specific frequencies and times); the current description leaves the magnitude of the systematic error as a qualitative statement rather than a measured discrepancy.
minor comments (2)
  1. Provide the specific ejecta Lorentz factor, shell thickness, and circumburst density values used to obtain the ~hours observer-time interval; this would allow readers to assess how generic the prolonged non-self-similar phase is.
  2. Clarify the precise criterion used to identify the 'onset of BMK self-similarity' in the simulations (e.g., radial profile matching, energy conservation, or Lorentz-factor evolution threshold).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work's significance and for the constructive major comments. We address each point below and will make the requested revisions to strengthen the rigor of the presentation.

read point-by-point responses

  1. Referee: [Methods] Methods section: the abstract and strongest claim rest on high-resolution SRHD simulations demonstrating that the Newtonian reverse shock crosses before BMK self-similarity, yet no resolution study, convergence test, or quantitative error analysis is described; without these, the load-bearing assertion that the true evolution lies outside the two-zone model for an extended interval cannot be verified at the reported level of rigor.

    Authors: We agree that a resolution study and convergence tests are necessary to support the central claims at the required level of rigor. In the revised manuscript we will add a new subsection to the Methods section that specifies the grid resolutions employed, reports the numerical scheme and Courant factor, and presents explicit convergence tests. These will include side-by-side comparisons of the reverse-shock crossing time, post-shock Lorentz-factor profiles, and density structure at three successively doubled resolutions, demonstrating that the key hydrodynamic result (crossing well before Blandford-McKee self-similarity) is stable to within a few percent. revision: yes

  2. Referee: [Results] Results/figures: the demonstration that the mismatch 'substantially overpredicts' emission requires explicit quantitative comparison (e.g., factor by which flux is overpredicted at specific frequencies and times); the current description leaves the magnitude of the systematic error as a qualitative statement rather than a measured discrepancy.

    Authors: We accept that the magnitude of the systematic error must be quantified rather than stated qualitatively. In the revised Results section we will add a new figure and accompanying table that post-process the simulation snapshots with a synchrotron emission code and directly compare the resulting light curves to those generated by the standard two-zone prescriptions. The comparison will report numerical factors (e.g., flux overprediction by a factor of X at 1 GHz at observer time t_obs = Y hours, and similarly for optical and X-ray bands) for both the Newtonian-reverse-shock and transition-prescription cases, making the size of the discrepancy explicit and falsifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central claim rests on direct comparison of high-resolution SRHD simulations against existing two-zone semi-analytic prescriptions. The finding that Newtonian reverse shocks cross the ejecta before BMK self-similarity, and the resulting emission mismatch, is obtained from the numerical evolution itself rather than any parameter fit, self-definition, or load-bearing self-citation chain. No derivation step reduces to its inputs by construction, and the work remains self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of SRHD simulations and the standard definition of the two-zone model drawn from prior literature; no free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (2)
  • domain assumption Synchrotron radiation is the dominant emission mechanism from forward and reverse shocks in GRB afterglows.
    Invoked as the basis for emission calculations in the two-zone model.
  • domain assumption The Blandford-McKee self-similar solution describes the late-time outflow dynamics.
    Used as the reference point after which the two-zone model is no longer applied.

pith-pipeline@v0.9.1-grok · 5758 in / 1462 out tokens · 37984 ms · 2026-06-28T12:53:39.200290+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

52 extracted references · 51 canonical work pages · 32 internal anchors

  1. [1]

    Hydrodynamic Time Scales and Temporal Structure of GRBs

    Hydrodynamic Timescales and Temporal Structure of Gamma-Ray Bursts. , keywords =. doi:10.1086/309835 , archivePrefix =. astro-ph/9508081 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/309835

  2. [2]

    Physics of Fluids , keywords =

    Fluid dynamics of relativistic blast waves. Physics of Fluids , keywords =. doi:10.1063/1.861619 , adsurl =

    work page doi:10.1063/1.861619

  3. [3]

    , keywords =

    Relativistic fireballs - Energy conversion and time-scales. , keywords =. doi:10.1093/mnras/258.1.41P , adsurl =

    work page doi:10.1093/mnras/258.1.41p

  4. [4]

    Mechanical Model for Relativistic Blast Waves

    Mechanical Model for Relativistic Blast Waves. , keywords =. doi:10.1086/508807 , archivePrefix =. astro-ph/0607641 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/508807

  5. [5]

    , keywords =

    jetsimpy: A Highly Efficient Hydrodynamic Code for Gamma-Ray Burst Afterglow. , keywords =. doi:10.3847/1538-4365/ad4d9d , archivePrefix =. 2402.19359 , primaryClass =

    work page doi:10.3847/1538-4365/ad4d9d

  6. [6]

    Nature Astronomy , keywords =

    Precise measurements of self-absorbed rising reverse shock emission from gamma-ray burst 221009A. Nature Astronomy , keywords =. doi:10.1038/s41550-023-01997-9 , archivePrefix =. 2303.13583 , primaryClass =

    work page doi:10.1038/s41550-023-01997-9

  7. [7]

    A Reverse Shock and Unusual Radio Properties in GRB 160625B

    A Reverse Shock and Unusual Radio Properties in GRB 160625B. , keywords =. doi:10.3847/1538-4357/aa8a76 , archivePrefix =. 1705.08455 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/aa8a76

  8. [8]

    A Reverse Shock in GRB 160509A

    A Reverse Shock in GRB 160509A. , keywords =. doi:10.3847/1538-4357/833/1/88 , archivePrefix =. 1606.08873 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/833/1/88

  9. [9]

    A Reverse Shock in GRB 130427A

    A Reverse Shock in GRB 130427A. , keywords =. doi:10.1088/0004-637X/776/2/119 , archivePrefix =. 1305.2453 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/776/2/119

  10. [10]

    J., & Tout, C

    Analysis of two scenarios for the early optical emission of the gamma-ray burst afterglows 990123 and 021211. , keywords =. doi:10.1111/j.1365-2966.2004.08083.x , archivePrefix =. astro-ph/0406027 , primaryClass =

    work page doi:10.1111/j.1365-2966.2004.08083.x 2004

  11. [11]

    Light Curves of GRB Optical Flashes

    Light Curves of Gamma-Ray Burst Optical Flashes. , keywords =. doi:10.1086/317869 , archivePrefix =. astro-ph/0009319 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/317869

  12. [12]

    GRB990123, The Optical Flash and The Fireball Model

    GRB 990123: The Optical Flash and the Fireball Model. , keywords =. doi:10.1086/312039 , archivePrefix =. astro-ph/9902009 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/312039

  13. [13]

    , keywords =

    GRB 990123: reverse and internal shock flashes and late afterglow behaviour. , keywords =. doi:10.1046/j.1365-8711.1999.02800.x , archivePrefix =. astro-ph/9902367 , primaryClass =

    work page doi:10.1046/j.1365-8711.1999.02800.x 1999

  14. [14]

    R., Pols, O

    Intrinsic parameters of GRB 990123 from its prompt optical flash and afterglow. , keywords =. doi:10.1046/j.1365-8711.2000.03922.x , archivePrefix =. astro-ph/9906062 , primaryClass =

    work page doi:10.1046/j.1365-8711.2000.03922.x 2000

  15. [15]

    Optical Flash of GRB 990123: constraints on the physical parameter of the reverse shock

    Optical Flash of GRB 990123: Constraints on the Physical Parameters of the Reverse Shock. , keywords =. doi:10.1088/1009-9271/2/5/449 , archivePrefix =. astro-ph/0306024 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1009-9271/2/5/449

  16. [16]

    GRB 021004: Reverse Shock Emission

    GRB 021004: Reverse Shock Emission. , keywords =. doi:10.1086/367691 , archivePrefix =. astro-ph/0210584 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/367691

  17. [17]

    The afterglow of GRB021211: Another case of reverse shock emission

    The afterglow of GRB 021211: Another case of reverse shock emission. , keywords =. doi:10.1051/0004-6361:20030371 , archivePrefix =. astro-ph/0301345 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:20030371

  18. [18]

    , keywords =

    A unified treatment of the gamma-ray burst 021211 and its afterglow. , keywords =. doi:10.1111/j.1365-2966.2003.07138.x , archivePrefix =. astro-ph/0305446 , primaryClass =

    work page doi:10.1111/j.1365-2966.2003.07138.x 2003

  19. [19]

    The Afterglow, Energetics and Host Galaxy of the Short-Hard Gamma-Ray Burst 051221a

    The Afterglow, Energetics, and Host Galaxy of the Short-Hard Gamma-Ray Burst 051221a. , keywords =. doi:10.1086/506429 , archivePrefix =. astro-ph/0601455 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/506429

  20. [20]

    The Afterglow of GRB 130427A from 1 to 10^16 GHz

    The Afterglow of GRB 130427A from 1 to 10 ^ 16 GHz. , keywords =. doi:10.1088/0004-637X/781/1/37 , archivePrefix =. 1307.4401 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/781/1/37

  21. [21]

    The Early Light Curve of the Optical Afterglow of GRB 021211

    The Early Light Curve of the Optical Afterglow of GRB 021211. , keywords =. doi:10.1086/374684 , archivePrefix =. astro-ph/0302136 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/374684

  22. [22]

    , keywords =

    Short GRB 160821B: A Reverse Shock, a Refreshed Shock, and a Well-sampled Kilonova. , keywords =. doi:10.3847/1538-4357/ab38bb , archivePrefix =. 1905.02159 , primaryClass =

    work page doi:10.3847/1538-4357/ab38bb 1905

  23. [23]

    M., Seljak, U., et al

    Early afterglows in wind environments revisited. , keywords =. doi:10.1111/j.1365-2966.2005.09411.x , archivePrefix =. astro-ph/0508602 , primaryClass =

    work page doi:10.1111/j.1365-2966.2005.09411.x 2005

  24. [24]

    Spectra and Light Curves of Gamma-Ray Burst Afterglows

    Spectra and Light Curves of Gamma-Ray Burst Afterglows. , keywords =. doi:10.1086/311269 , archivePrefix =. astro-ph/9712005 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/311269

  25. [25]

    Radio Transients from Gamma-Ray Bursters

    Radio Transients from Gamma-Ray Bursters. , keywords =. doi:10.1086/187102 , archivePrefix =. astro-ph/9307024 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/187102

  26. [26]

    Optical and Long Wavelength Afterglow from Gamma-Ray Bursts

    Optical and Long-Wavelength Afterglow from Gamma-Ray Bursts. , keywords =. doi:10.1086/303625 , archivePrefix =. astro-ph/9606043 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/303625

  27. [27]

    GRB after-glow: Supporting the cosmological fireball model, constraining parameters, and making predictions

    Gamma-Ray--Burst Afterglow: Supporting the Cosmological Fireball Model, Constraining Parameters, and Making Predictions. , keywords =. doi:10.1086/310809 , archivePrefix =. astro-ph/9704116 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/310809

  28. [28]

    Shocked by GRB 970228: the afterglow of a cosmological fireball

    Shocked by GRB 970228: the afterglow of a cosmological fireball. , keywords =. doi:10.1093/mnras/288.4.L51 , archivePrefix =. astro-ph/9704153 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/288.4.l51

  29. [29]

    Discovery of the X-Ray Afterglow of the Gamma-Ray Burst of February 28 1997

    Discovery of an X-ray afterglow associated with the -ray burst of 28 February 1997. , keywords =. doi:10.1038/42885 , archivePrefix =. astro-ph/9706065 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/42885 1997

  30. [30]

    , year = 1997, month = apr, volume =

    Transient optical emission from the error box of the -ray burst of 28 February 1997. , year = 1997, month = apr, volume =. doi:10.1038/386686a0 , adsurl =

    work page doi:10.1038/386686a0 1997

  31. [31]

    , year = 1997, month = sep, volume =

    The radio afterglow from the -ray burst of 8 May 1997. , year = 1997, month = sep, volume =. doi:10.1038/38451 , adsurl =

    work page doi:10.1038/38451 1997

  32. [32]

    Predictions for The Very Early Afterglow and The Optical Flash

    Predictions for the Very Early Afterglow and the Optical Flash. , keywords =. doi:10.1086/307508 , archivePrefix =. astro-ph/9901338 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/307508

  33. [33]

    Observation of contemporaneous optical radiation from a gamma-ray burst

    Observation of contemporaneous optical radiation from a -ray burst. , keywords =. doi:10.1038/18837 , archivePrefix =. astro-ph/9903271 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/18837

  34. [34]

    Discovery of a Radio Flare from GRB 990123

    Discovery of a Radio Flare from GRB 990123. , keywords =. doi:10.1086/312227 , archivePrefix =. astro-ph/9903441 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/312227

  35. [35]

    Off-Axis Gamma-Ray Burst Afterglow Modeling Based On A Two-Dimensional Axisymmetric Hydrodynamics Simulation

    Off-axis Gamma-ray Burst Afterglow Modeling Based on a Two-dimensional Axisymmetric Hydrodynamics Simulation. , keywords =. doi:10.1088/0004-637X/722/1/235 , archivePrefix =. 1006.5125 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/722/1/235

  36. [36]

    Gamma-ray burst afterglow broadband fitting based directly on hydrodynamics simulations

    Gamma-Ray Burst Afterglow Broadband Fitting Based Directly on Hydrodynamics Simulations. , keywords =. doi:10.1088/0004-637X/749/1/44 , archivePrefix =. 1110.5089 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/749/1/44

  37. [37]

    , keywords =

    Gamma-Ray Burst Afterglows in the Multimessenger Era: Numerical Models and Closure Relations. , keywords =. doi:10.3847/1538-4357/ab93cf , archivePrefix =. 1909.11691 , primaryClass =

    work page doi:10.3847/1538-4357/ab93cf 1909

  38. [38]

    J., & Tout, C

    Early afterglow emission from a reverse shock as a diagnostic tool for gamma-ray burst outflows. , keywords =. doi:10.1111/j.1365-2966.2004.08099.x , archivePrefix =. astro-ph/0403461 , primaryClass =

    work page doi:10.1111/j.1365-2966.2004.08099.x 2004

  39. [39]

    Optical Flashes and Radio Flares in GRBs afterglow: Numerical Study

    Optical Flashes and Radio Flares in Gamma-Ray Burst Afterglow: Numerical Study. , keywords =. doi:10.1086/317021 , archivePrefix =. astro-ph/9910241 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/317021

  40. [40]

    Modeling GRB 050904: Autopsy of a Massive Stellar Explosion at z=6.29

    Modeling GRB 050904: Autopsy of a Massive Stellar Explosion at z=6.29. , keywords =. doi:10.1086/520699 , archivePrefix =. astro-ph/0612256 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/520699

  41. [41]

    The Physics of Gamma-Ray Bursts

    The physics of gamma-ray bursts. Reviews of Modern Physics , keywords =. doi:10.1103/RevModPhys.76.1143 , archivePrefix =. astro-ph/0405503 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.76.1143

  42. [42]

    , keywords =

    A semi-analytical solution to the forward-reverse shock hydrodynamics of the gamma-ray burst afterglow. , keywords =. doi:10.1093/mnras/stac1198 , archivePrefix =. 2204.13014 , primaryClass =

    work page doi:10.1093/mnras/stac1198

  43. [43]

    Hydrodynamics of a Relativistic Fireball: the Complete Evolution

    Hydrodynamics of a Relativistic Fireball: The Complete Evolution. , keywords =. doi:10.1086/306868 , archivePrefix =. astro-ph/9803217 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/306868

  44. [44]

    The Dynamics and Afterglow Radiation of Gamma-Ray Bursts. I. Constant Density Medium. , keywords =. doi:10.1088/0004-637X/698/2/1261 , archivePrefix =. 0902.2396 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/698/2/1261

  45. [45]

    Radiative processes in astrophysics

  46. [46]

    , keywords =

    Synchrotron Self-Absorption in Radio Supernovae. , keywords =. doi:10.1086/305676 , adsurl =

    work page doi:10.1086/305676

  47. [47]

    Afterglow emission in Gamma-Ray Bursts: I. Pair-enriched ambient medium and radiative blast waves

    Afterglow emission in gamma-ray bursts - I. Pair-enriched ambient medium and radiative blast waves. , keywords =. doi:10.1093/mnras/stt872 , archivePrefix =. 1211.2806 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stt872

  48. [48]

    , keywords =

    The Radio to GeV Afterglow of GRB 221009A. , keywords =. doi:10.3847/2041-8213/acbfad , archivePrefix =. 2302.04388 , primaryClass =

    work page doi:10.3847/2041-8213/acbfad 2041

  49. [49]

    , keywords =

    From Coasting to Energy-conserving: New Self-similar Solutions to the Interaction Phase of Strong Explosions. , keywords =. doi:10.3847/2041-8213/ad87cc , archivePrefix =. 2409.10600 , primaryClass =

    work page doi:10.3847/2041-8213/ad87cc 2041

  50. [50]

    Deceleration of arbitrarily magnetized GRB ejecta: the complete evolution

    Deceleration of arbitrarily magnetized GRB ejecta: the complete evolution. , keywords =. doi:10.1051/0004-6361:200810756 , archivePrefix =. 0810.2961 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:200810756

  51. [51]

    Living Reviews in Relativity , keywords =

    Numerical Hydrodynamics in Special Relativity. Living Reviews in Relativity , keywords =. doi:10.12942/lrr-2003-7 , adsurl =

    work page doi:10.12942/lrr-2003-7 2003

  52. [52]

    The interaction phase of engine-driven explosions and high-energy winds

    The interaction phase of engine-driven explosions and high-energy winds. arXiv e-prints , keywords =. doi:10.48550/arXiv.2605.16490 , archivePrefix =. 2605.16490 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.16490