Substructure in externally irradiated protoplanetary disks, I. spirals and rings in two-dimensional radiation hydrodynamics

Alexandros Ziampras; Lin Qiao; Thomas J. Haworth

arxiv: 2604.08248 · v1 · submitted 2026-04-09 · 🌌 astro-ph.EP

Substructure in externally irradiated protoplanetary disks, I. spirals and rings in two-dimensional radiation hydrodynamics

Alexandros Ziampras , Lin Qiao , Thomas J. Haworth This is my paper

Pith reviewed 2026-05-10 18:28 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords protoplanetary disksexternal irradiationspiral armsdust ringsradiation hydrodynamicstemperature asymmetrydisk substructure

0 comments

The pith

External irradiation from a nearby massive star can drive spiral arms in gas and rings and gaps in dust of a protoplanetary disk via maintained temperature asymmetry.

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

The paper investigates whether external irradiation from a massive star produces dynamical changes inside a protoplanetary disk beyond the already known mass loss and truncation. Two-dimensional radiation hydrodynamics simulations show that an asymmetric temperature distribution, sustained by the external flux, creates a shadowed region together with spiral arms in the gas and rings with gaps in the dust. These features arise through the same shadow-driven mechanism previously studied for inner-disk shadows, but here the asymmetry is imposed from outside. The result matters because it implies that external irradiation can actively shape disk substructure and therefore influence how disks evolve in regions containing massive stars.

Core claim

We find that a nearby massive star can, under certain conditions, induce significant dynamical effects on a protoplanetary disk, including a shadowed region, pronounced spiral arms in gas, and rings and gaps in dust. The dynamics are caused by the temperature asymmetry driven and maintained by external irradiation, akin to the well-established mechanism of shadow-induced spirals and rings in disks with shadowing from their inner regions. Our results show that if an external temperature asymmetry can be induced it can have a significant dynamical impact on the disk itself, possibly even driving substructure.

What carries the argument

Temperature asymmetry driven and maintained by external irradiation, modeled as a plane-parallel flux together with a simplified nonaxisymmetric heating rate from thermal re-emission in the marginally optically thick region.

If this is right

A shadowed region forms in the disk as a direct result of the imposed external heating asymmetry.
Pronounced spiral arms develop in the gas component.
Dust particles concentrate into rings separated by gaps.
These internal dynamical changes occur alongside the known mass-loss and truncation effects.
External irradiation can therefore drive substructure in the disk.

Where Pith is reading between the lines

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

External irradiation may contribute to the diversity of disk morphologies observed across different star-forming environments.
Three-dimensional simulations that include full dynamical radiative transfer would test whether the two-dimensional substructure persists at higher fidelity.
Observers interpreting disk substructure for signs of embedded planets should also consider whether external irradiation could produce similar patterns.

Load-bearing premise

External irradiation can be adequately represented by a plane-parallel flux together with a simplified nonaxisymmetric heating rate that corresponds to thermal re-emission from material in the marginally optically thick region.

What would settle it

High-resolution observations of protoplanetary disks near massive stars that show neither gas spiral arms nor dust rings and gaps, even when external irradiation is clearly present and the disk is not truncated, would falsify the claim that the temperature asymmetry produces these dynamical features.

Figures

Figures reproduced from arXiv: 2604.08248 by Alexandros Ziampras, Lin Qiao, Thomas J. Haworth.

**Figure 1.** Figure 1: Heatmaps of the perturbed gas density ∆Σg/Σg,0 (panel b), temperature T (c) and mm-grain dust density Σd (d) after 100 kyr of evolution in our model with external irradiation, showing prominent spiral structures in gas, the disk’s colder, shadowed farside, and rings in the dust distribution.. Gas density perturbations are also shown at an earlier state (10 kyr) on panel a. A black–white dotted circle marks… view at source ↗

**Figure 3.** Figure 3: Dust surface density heatmaps after 100 orbits at R0 in two additional models. Left: placing the external source at a distance of 1 pc rather than the fiducial 0.1 pc led to no noticeable substructure after 100 orbits (100 kyr). Right: a less massive, smaller disk shows substructure in the form of circular rings after 100 orbits at R0 = 40 au (25 kyr), albeit less prominent than in the fiducial model. 0.3 … view at source ↗

**Figure 4.** Figure 4: Synthetic ALMA observations at 1.3 mm of our model, loosely mimicking a source at 400 pc distance, after 10 (left) and 100 kyr (right) of evolution. Rings only become visible after ∼30 kyr for this model. served substructures in σ Orionis, we note that a more detailed exploration of the parameter space in addition to more sophisticated modeling is needed to fully understand the relevance of this mechanism… view at source ↗

read the original abstract

It is known that the external irradiation of protoplanetary disks by nearby massive stars can result in mass loss that impacts the disk evolution, however the dynamical impact of external irradiation upon the disk itself has not been explored in detail. We aim to investigate the dynamical effect of asymmetric external irradiation on the structure of such disks. We perform two-dimensional multi-fluid radiation hydrodynamical simulations of protoplanetary disks subject to external irradiation using the PLUTO code, with external irradiation modeled as a plane-parallel flux and a simplified nonaxisymmetric heating rate corresponding to the thermal reemission from hot material within the region marginally optically thick to the external irradiation. We find that a nearby massive star can, under certain conditions, induce significant dynamical effects on a protoplanetary disk, including a shadowed region, pronounced spiral arms in gas, and rings and gaps in dust. The dynamics are caused by the temperature asymmetry driven and maintained by external irradiation, akin to the well-established mechanism of shadow-induced spirals and rings in disk with shadowing from their inner regions. Our results show that if an external temperature asymmetry can be induced it can have a significant dynamical impact on the disk itself (in addition to the well-studied mass loss and truncation effects due to external irradiation), possibly even driving substructure. This prompts further investigation with detailed, dynamical radiative transfer models.

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.

Desk Editor's Note private letter to a colleague

The paper shows external irradiation can drive gas spirals and dust rings via imposed temperature asymmetry in 2D hydro runs, but the effect rests on a simplified heating prescription the authors flag as preliminary.

read the letter

The main new point is that asymmetric external irradiation from a nearby massive star can maintain a temperature gradient strong enough to produce spiral arms in the gas and rings plus gaps in the dust, on top of the usual truncation and mass loss. They run 2D multi-fluid radiation hydrodynamics with PLUTO, treating external flux as plane-parallel plus a nonaxisymmetric heating term that approximates re-emission from the marginally optically thick zone. This produces a shadowed region and the reported substructure, framed as an extension of the known inner-shadow spiral mechanism to external sources. The multi-fluid dust treatment is a reasonable step that lets them track how gas perturbations affect solids. The setup is straightforward and the outcomes are presented clearly as conditional on the irradiation geometry. The authors themselves note that full dynamical radiative transfer is needed next, which keeps the claim proportionate. The soft spot is exactly the heating model. It is prescribed rather than emerging from self-consistent radiation transport, so the persistence of the azimuthal temperature asymmetry depends on how that term is chosen. If optical depth, scattering, or vertical structure alter the reprocessing in ways not captured here, the spirals and rings could weaken or shift. Two dimensions also omits vertical flows and full 3D shadowing geometry. No resolution or parameter sweeps are highlighted in the available description, though the basic hydro approach follows standard practice. Citations track the relevant prior work on irradiated disks and shadow-driven spirals without obvious gaps. This is useful for anyone modeling disks in clustered star-forming regions or looking for additional channels that can seed substructure before planets form. A reader who wants an initial numerical exploration of external irradiation beyond mass loss will find concrete examples to build on. It deserves peer review so referees can test the heating prescription against more complete radiative transfer and check whether the reported structures survive those upgrades.

Referee Report

3 major / 2 minor

Summary. The manuscript presents 2D multi-fluid radiation hydrodynamical simulations with the PLUTO code of protoplanetary disks subject to external irradiation from a nearby massive star. External irradiation is implemented as a plane-parallel flux together with a simplified nonaxisymmetric heating rate that approximates thermal re-emission from material in the marginally optically thick region. The simulations produce a shadowed region, spiral arms in the gas, and rings/gaps in the dust, which the authors attribute to a persistent azimuthal temperature asymmetry maintained by the external irradiation. This is presented as analogous to the well-known shadow-induced substructure mechanism, with the conclusion that external irradiation can drive dynamical substructure in addition to mass loss and truncation, motivating follow-up work with self-consistent dynamical radiative transfer.

Significance. If the reported structures prove robust, the result would be significant for disk evolution in clustered star-forming regions, as it identifies an external mechanism capable of generating spirals and rings without internal shadowing or embedded planets. The multi-fluid treatment, which tracks gas and dust separately, is a methodological strength that allows clear separation of the responses. The work usefully extends the known effects of external irradiation beyond photoevaporation and truncation. However, immediate impact is reduced by the reliance on a prescribed heating term rather than emergent radiative transfer, as the authors themselves note.

major comments (3)

[Irradiation modeling section] Irradiation modeling section: The central claim that external irradiation maintains a temperature asymmetry capable of driving spirals and dust rings rests on the 'simplified nonaxisymmetric heating rate' that is imposed rather than obtained from self-consistent radiative transfer. Because the heating profile is prescribed to correspond to re-emission from the marginally optically thick zone, the temperature asymmetry is effectively built into the setup. The manuscript should supply the explicit functional form of this heating term and demonstrate, via parameter variations or comparison runs, that the reported substructures are not sensitive to the precise choice of the ad-hoc profile.
[Results section] Results section: Only qualitative descriptions of the induced features (shadowed region, spiral arms, rings and gaps) are supplied. To substantiate the claim of 'significant dynamical effects' and 'pronounced' structures, the paper must report quantitative diagnostics such as spiral arm density contrasts, pitch angles, ring/gap contrasts, and their time evolution, together with resolution and convergence tests that confirm the features are not numerical artifacts.
[Discussion section] Discussion section: The manuscript correctly notes that full dynamical radiative transfer models are ultimately required. However, it does not quantify the uncertainties introduced by the current 2D approximation, the plane-parallel flux assumption, or the decoupling of the heating rate from the evolving density and temperature fields. These limitations directly affect whether the reported asymmetry and substructure can be regarded as a generic outcome of external irradiation.

minor comments (2)

[Abstract] The abstract refers to 'certain conditions' under which the effects occur but does not specify the explored range of disk mass, irradiation flux, or optical depth; adding one sentence with these parameters would improve context.
[Figures] Figure captions should explicitly distinguish gas and dust quantities and indicate the simulation time or evolutionary stage shown, to aid readers in interpreting the substructure development.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We appreciate the recognition of the methodological strengths and potential significance of our results on external irradiation driving substructure. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Irradiation modeling section] Irradiation modeling section: The central claim that external irradiation maintains a temperature asymmetry capable of driving spirals and dust rings rests on the 'simplified nonaxisymmetric heating rate' that is imposed rather than obtained from self-consistent radiative transfer. Because the heating profile is prescribed to correspond to re-emission from the marginally optically thick zone, the temperature asymmetry is effectively built into the setup. The manuscript should supply the explicit functional form of this heating term and demonstrate, via parameter variations or comparison runs, that the reported substructures are not sensitive to the precise choice of the ad-hoc profile.

Authors: We agree that the explicit functional form should be provided for clarity and reproducibility. In the revised manuscript, we will add the mathematical expression for the simplified nonaxisymmetric heating rate in the Irradiation modeling section. To demonstrate robustness, we will include additional comparison runs with varied heating profiles (e.g., different azimuthal dependencies or amplitudes) and show that the shadowed region, spiral arms, and dust rings persist, confirming the substructures are not artifacts of the specific ad-hoc choice. revision: yes
Referee: [Results section] Results section: Only qualitative descriptions of the induced features (shadowed region, spiral arms, rings and gaps) are supplied. To substantiate the claim of 'significant dynamical effects' and 'pronounced' structures, the paper must report quantitative diagnostics such as spiral arm density contrasts, pitch angles, ring/gap contrasts, and their time evolution, together with resolution and convergence tests that confirm the features are not numerical artifacts.

Authors: We concur that quantitative measures are needed to strengthen the claims. In the revised Results section, we will report specific diagnostics including gas density contrasts in spiral arms, spiral pitch angles, dust ring/gap surface density contrasts, and their temporal evolution. We will also add resolution studies (e.g., doubling the grid resolution) and convergence tests to verify that the features are resolved and not numerical artifacts. revision: yes
Referee: [Discussion section] Discussion section: The manuscript correctly notes that full dynamical radiative transfer models are ultimately required. However, it does not quantify the uncertainties introduced by the current 2D approximation, the plane-parallel flux assumption, or the decoupling of the heating rate from the evolving density and temperature fields. These limitations directly affect whether the reported asymmetry and substructure can be regarded as a generic outcome of external irradiation.

Authors: We will expand the Discussion section to provide a more detailed assessment of these limitations, including how the 2D geometry and plane-parallel flux may affect the persistence of the temperature asymmetry and the resulting substructure. While a precise numerical quantification of all uncertainties would require new self-consistent 3D radiative transfer simulations (which we identify as necessary future work), we will discuss the expected range of validity and conditions under which the mechanism is likely to operate. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results emerge from forward hydrodynamical integration with prescribed external forcing

full rationale

The paper conducts 2D multi-fluid radiation hydrodynamical simulations in PLUTO with an imposed plane-parallel flux and a simplified nonaxisymmetric heating term. Spiral arms, rings, and gaps are outputs of integrating the governing equations under this external boundary condition. No parameters are fitted to produce the target structures, no equations are defined in terms of their own outputs, and no load-bearing premise reduces to a self-citation chain. The analogy to inner-disk shadow-induced spirals references external literature rather than prior work by these authors. The derivation is therefore self-contained as a controlled numerical experiment.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; the listed axiom captures the central modeling assumption required for the temperature asymmetry. No free parameters or invented entities are identifiable from the provided text.

axioms (1)

domain assumption External irradiation is modeled as a plane-parallel flux with a simplified nonaxisymmetric heating rate from thermal re-emission in the marginally optically thick region.
This assumption directly supplies the temperature asymmetry that drives the reported spirals and rings.

pith-pipeline@v0.9.0 · 5548 in / 1260 out tokens · 59649 ms · 2026-05-10T18:28:56.734592+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

external irradiation modeled as a plane-parallel flux and a simplified nonaxisymmetric heating rate corresponding to the thermal reemission from hot material within the region marginally optically thick
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

dynamics are caused by the temperature asymmetry driven and maintained by external irradiation, akin to the well-established mechanism of shadow-induced spirals and rings

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

C., Hollenbach, D., Laughlin, G., & Gorti, U

Adams, F. C., Hollenbach, D., Laughlin, G., & Gorti, U. 2004, ApJ, 611, 360 ALMA Partnership, Fomalont, E. B., Vlahakis, C., et al. 2015, ApJ, 808, L1 Anania, R., Winter, A. J., Rosotti, G., et al. 2025, A&A, 695, A74 Andrews, S. M., Huang, J., Pérez, L. M., et al. 2018, ApJ, 869, L41 Ansdell, M., Williams, J. P., Manara, C. F., et al. 2017, AJ, 153, 240 ...

work page 2004
[2]

2012), and the implicit drag module described in Ziampras et al

and LeV- eque (2004) Riemann solvers for the gas and dust, respectively, with a second-order Runge–Kutta time integrator and piecewise linear spatial reconstruction, the FARGO algorithm (Masset 2000; Mignone et al. 2012), and the implicit drag module described in Ziampras et al. (2025b). Our initial disk setup corresponds to a disk orbiting at Keple- rian...

work page 2004

[1] [1]

C., Hollenbach, D., Laughlin, G., & Gorti, U

Adams, F. C., Hollenbach, D., Laughlin, G., & Gorti, U. 2004, ApJ, 611, 360 ALMA Partnership, Fomalont, E. B., Vlahakis, C., et al. 2015, ApJ, 808, L1 Anania, R., Winter, A. J., Rosotti, G., et al. 2025, A&A, 695, A74 Andrews, S. M., Huang, J., Pérez, L. M., et al. 2018, ApJ, 869, L41 Ansdell, M., Williams, J. P., Manara, C. F., et al. 2017, AJ, 153, 240 ...

work page 2004

[2] [2]

2012), and the implicit drag module described in Ziampras et al

and LeV- eque (2004) Riemann solvers for the gas and dust, respectively, with a second-order Runge–Kutta time integrator and piecewise linear spatial reconstruction, the FARGO algorithm (Masset 2000; Mignone et al. 2012), and the implicit drag module described in Ziampras et al. (2025b). Our initial disk setup corresponds to a disk orbiting at Keple- rian...

work page 2004