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arxiv: 2605.16490 · v1 · pith:MYLR3E3Cnew · submitted 2026-05-15 · 🌌 astro-ph.HE

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

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

Pith reviewed 2026-05-20 15:54 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords adiabatic windsshock interactionssimilarity solutionspower-law density profilesenergy-conserving bubblestidal disruption eventsluminous fast blue optical transients
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The pith

Adiabatic winds from engines quickly relax into an interaction-dominated similarity state for overdense ejecta before entering an energy-conserving regime.

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

This paper examines how wide-angle winds inflate bubbles into surrounding media with power-law densities. For sufficiently overdense ejecta, the flow settles rapidly into a similarity solution dominated by the interaction between the wind and the ambient material. These solutions hold for only a few dynamical times until the reverse-shocked shell thickens relative to the forward one, at which point the overdensity reaches order unity. The study uses analytic scalings and hydrodynamic simulations to show that for density profiles shallower than r to the minus 2, the bubble then follows energy-conserving expansion scaling.

Core claim

For sufficiently overdense ejecta, the flow quickly relaxes into an interaction-dominated similarity state at early times and later enters an energy-conserving regime. The interaction solutions are attained within only a few dynamical times and remain valid until the reverse-shocked shell is no longer thin relative to the forward-shocked shell, corresponding to an instantaneous overdensity of order unity. For n less than 2, the flow subsequently converges to the generalized energy-conserving scaling R_s proportional to t to the 3 over 5 minus n, while n equals 2 exhibits a single persistent similarity state.

What carries the argument

The interaction-dominated similarity state attained by adiabatic winds expanding into power-law density profiles rho proportional to r to the minus n, which governs the early evolution of the double-shocked bubble.

Load-bearing premise

The winds remain adiabatic with no significant radiative cooling during the interaction phase, and the surrounding medium follows a pure power-law density profile with index between 0 and 2.

What would settle it

A one-dimensional hydrodynamic simulation including radiative cooling that shows the similarity state breaks down before the overdensity reaches order unity.

Figures

Figures reproduced from arXiv: 2605.16490 by Benjamin Amend, Christopher Lagomarsino, Eric R. Coughlin, Jonathan Zrake.

Figure 1
Figure 1. Figure 1: Comparisons of our simulated fluid profiles for f = 105 to those of the interaction solutions and of the two-shock Riemann problem (RP) solutions at two dynamical times (right) and at t ≪ tdyn (left). For t ≪ tdyn, only minimal radial structure has formed in each of the shocked shells; as such, the system is well-approximated by the solution to the two-shock RP. By t ∼ tdyn, gradients have steepened in eve… view at source ↗
Figure 3
Figure 3. Figure 3: Radial fluid profiles from our simulations and the interaction solutions for f = 105 and n ∈ [0, 1 2 , 1, 3 2 , 2]. The representative time at which each snapshot was taken for any given n corresponds to the minimum relative L1 error of the forward￾shocked shell velocity between the simulation output and the interaction-phase self-similar solutions. Agreement is robust across all tested ambient medium den￾… view at source ↗
Figure 4
Figure 4. Figure 4: Relative L1 error between our hydrodynamics simulations and self-similar solutions in both interaction and energy-conserving regimes for the radial pressure profiles in the forward-shocked shell. The initial overdensity parameter f was set to 105 for each case, and n ∈ [0, 1 2 , 1, 3 2 , 2]. The change in error is plotted vs. time (top) and instantaneous overdensity f(Rc) ≡ f ·(Rw,0/Rc) 2−n (bottom). We me… view at source ↗
Figure 5
Figure 5. Figure 5: The duration t ′ ss,end of the interaction phase as a function of initial over￾density parameter f . The duration is proportional to f 1/(2−n) as predicted by Eq. 10, and is therefore extended for steeper ambient medium density profiles. For n = 2, the system is characterized by a single perpetual self-similar state, cor￾responding to tss,end → ∞. 4.2. Observational implications For a sufficiently overdens… view at source ↗
Figure 6
Figure 6. Figure 6: The positions of the reverse shock, contact discontinuity, and forward shock as a function of time for different values of n from our hydrodynamic simulations, the interaction solutions, and the energy-conserving solutions. The dotted vertical lines represent the measured timescales characterizing the transitions from the interaction to energy-conserving regime. For n = 2, these are not distinct regimes, a… view at source ↗
Figure 7
Figure 7. Figure 7: Comparisons of our simulated fluid profiles to those of the interaction and energy-conserving solutions across various epochs in the system’s evolution. The initial overdensity ratio f = 105 for this example, and the ambient medium density profile is uniform (n = 0). The snapshots here correspond to instantaneous overdensities of f(Rc) = 9.227 × 102 (left), f(Rc) = 1.109 (middle), and f(Rc) = 4.843 × 10−5 … view at source ↗
read the original abstract

Wide-angle outflows, or winds, are associated with a broad range of astrophysical systems, including protostars, massive stars, X-ray binaries, tidal disruption events (TDEs), luminous fast blue optical transients (LFBOTs), and starburst galaxies. When these winds first ``turn on," they inflate a ``bubble" into their surroundings, bounded by two shocks and a contact discontinuity, and evolve through distinct adiabatic phases prior to the onset of significant radiative cooling. For sufficiently overdense ejecta, the flow quickly relaxes into an interaction-dominated similarity state at early times and later enters an energy-conserving regime. We present a systematic study of these phases for adiabatic winds expanding into power-law density profiles $\rho \propto r^{-n}$ with $0 \leq n \leq 2$. Using analytic scalings together with one-dimensional shock-capturing hydrodynamic simulations, we quantify both the relaxation timescales and the accuracy with which the corresponding similarity solutions reproduce the fluid velocity, density, and pressure throughout the shocked bubble. We show that the interaction solutions are attained within only a few dynamical times and remain valid until the reverse-shocked shell is no longer thin relative to the forward-shocked shell, corresponding in practice to an instantaneous overdensity of order unity. For $n < 2$, the flow subsequently converges to the generalized energy-conserving scaling $R_s \propto t^{3/(5-n)}$, while the special case $n=2$ exhibits a single persistent similarity state. We discuss the durations and implications of these phases for stellar and galactic outflows, TDEs, and LFBOTs.

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 / 3 minor

Summary. The paper examines the adiabatic interaction phases of wide-angle winds and engine-driven explosions expanding into power-law density profiles ρ ∝ r^{-n} for 0 ≤ n ≤ 2. Combining analytic similarity scalings with 1D shock-capturing hydrodynamic simulations, it shows that sufficiently overdense ejecta relax rapidly (within a few dynamical times) to an interaction-dominated similarity state that accurately reproduces the velocity, density, and pressure profiles until the reverse-shocked shell ceases to be thin relative to the forward shell (corresponding to instantaneous overdensity of order unity). For n < 2 the flow then transitions to the generalized energy-conserving solution R_s ∝ t^{3/(5-n)}, while the n = 2 case remains in a single persistent similarity state. The work quantifies relaxation timescales and pointwise accuracy of the similarity solutions and discusses implications for TDEs, LFBOTs, stellar winds, and galactic outflows.

Significance. If the central claims hold, the manuscript supplies a systematic, quantitatively validated framework for the early phases of wind-driven bubbles that is directly applicable to modeling a range of high-energy transients and outflows. The explicit demonstration that interaction solutions are attained and remain accurate on short timescales, together with the clean transition criterion at overdensity ~1, strengthens the utility of similarity methods in this regime. The combination of analytic derivations and 1D simulations is a clear strength.

major comments (2)
  1. [§4] §4 (numerical methods): the manuscript states that the interaction solutions are attained within a few dynamical times and remain valid until overdensity ~1, but the quantitative error analysis (e.g., L1 or L2 norms between simulation profiles and the similarity solution for velocity, density, and pressure) is not shown in sufficient detail to confirm the claimed pointwise accuracy across the full range of n and initial overdensity.
  2. [Introduction and §5] The adiabatic assumption (no radiative cooling) is load-bearing for the reported relaxation behavior and transition criterion; however, the manuscript does not provide an estimate of the cooling time relative to the dynamical time for the parameter space of interest (e.g., for TDE or LFBOT densities), which would clarify the domain of applicability.
minor comments (3)
  1. [Abstract and §3] The abstract and §3 would benefit from an explicit statement of the initial overdensity values and ejecta mass-loading parameters used in the simulations to allow readers to assess generality of the 'few dynamical times' relaxation result.
  2. [Figures] Figure captions should specify the exact quantities plotted (e.g., normalized velocity, density, pressure) and the time snapshots shown relative to the dynamical time at the contact discontinuity.
  3. [§2] A brief comparison to existing self-similar solutions in the literature (e.g., for n=0 or n=2) would help place the new generalized n-dependent results in context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback, which has helped improve the clarity and completeness of the manuscript. We address each major comment below and have incorporated revisions to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§4] §4 (numerical methods): the manuscript states that the interaction solutions are attained within a few dynamical times and remain valid until overdensity ~1, but the quantitative error analysis (e.g., L1 or L2 norms between simulation profiles and the similarity solution for velocity, density, and pressure) is not shown in sufficient detail to confirm the claimed pointwise accuracy across the full range of n and initial overdensity.

    Authors: We appreciate this suggestion. The original manuscript relies primarily on visual profile comparisons to demonstrate agreement with the similarity solutions. We agree that explicit quantitative metrics would provide stronger support for the claimed accuracy. In the revised manuscript, we will add L1 and L2 norm calculations between the simulated and similarity profiles for velocity, density, and pressure. These will be shown as a function of time for representative values of n and initial overdensity, either in an expanded §4 or a new supplementary figure. revision: yes

  2. Referee: [Introduction and §5] The adiabatic assumption (no radiative cooling) is load-bearing for the reported relaxation behavior and transition criterion; however, the manuscript does not provide an estimate of the cooling time relative to the dynamical time for the parameter space of interest (e.g., for TDE or LFBOT densities), which would clarify the domain of applicability.

    Authors: We concur that an explicit comparison of cooling and dynamical timescales would better delineate the regime of validity for our adiabatic results. In the revised manuscript, we will add order-of-magnitude estimates of the cooling time (using standard radiative cooling functions) relative to the dynamical time for representative TDE and LFBOT densities and velocities. These estimates will be included in the Introduction and §5 to clarify the applicability of the reported relaxation behavior and transition criterion. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives interaction-dominated similarity solutions from standard hydrodynamic conservation laws and self-similar ansatzes for adiabatic winds expanding into power-law media, then validates the relaxation timescales and pointwise accuracy directly with new 1D shock-capturing simulations. No load-bearing step reduces by construction to a fitted parameter from the authors' prior work, a self-citation chain, or a redefinition of the target result; the central claims about relaxation within a few dynamical times and validity until overdensity ~1 are independently tested against the simulations under the stated assumptions of adiabatic evolution and 0 ≤ n ≤ 2.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the adiabatic assumption and power-law ambient profiles; no free parameters or invented entities are introduced in the abstract description.

axioms (2)
  • domain assumption Winds remain adiabatic with negligible radiative cooling during the interaction phase
    Invoked to justify the use of adiabatic hydrodynamic equations and similarity solutions throughout the early evolution.
  • domain assumption Ambient density follows a pure power-law rho proportional to r^{-n} for 0 <= n <= 2
    Required for the analytic similarity solutions and the distinction between n<2 and n=2 cases.

pith-pipeline@v0.9.0 · 5831 in / 1501 out tokens · 43969 ms · 2026-05-20T15:54:08.993829+00:00 · methodology

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Reference graph

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