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arxiv: 2605.22592 · v1 · pith:LGBXR4N6new · submitted 2026-05-21 · 🌌 astro-ph.EP

Scattered light signatures of flyby-induced warps in protoplanetary discs

Katie L. Milsom , Tim J. Harries , C. J. Nixon This is my paper

Pith reviewed 2026-05-22 01:50 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords protoplanetary discsstellar flybysdisc warpsscattered lightshadowsdisc viscosityobservational signatures
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The pith

Stellar flybys warp protoplanetary discs and produce long-lasting oscillating shadows in scattered light images.

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

The paper models how close stellar encounters warp the outer parts of young discs around other stars. It combines one-dimensional calculations of how the warp spreads with simulations of scattered starlight to predict the shadows that appear in telescope images. In discs with very low internal friction the warp and its shadow persist for roughly a million years, and the brightness variation is strong enough to notice for half that time. The work concludes that a sizable fraction of discs in nearby star-forming regions should carry these signatures and that counting them offers a way to measure disc viscosity.

Core claim

Flybys tilt and warp the outer disc, producing a broad shadow in scattered light while the inner disc tilts without warping or shadowing. The warp wave travels inward and outward, causing the shadow to oscillate across the disc. For viscosity parameter α equal to 10 to the minus 4 the warp endures for about 10^6 years, and for half that interval the azimuthal variance of surface brightness exceeds 0.01, marking a detectable shadow. Consequently a significant fraction of discs in nearby regions are expected to show flyby-induced warps, and surveys of such shadowed discs can constrain disc viscosity.

What carries the argument

One-dimensional linear warp propagation theory coupled to a fast radiative transfer code that generates the shadows induced by the warped surface.

If this is right

  • The inner disc remains tilted but unwarped and therefore produces no shadow.
  • The shadow moves back and forth as the warp wave propagates across the disc.
  • In low-viscosity discs the warp and shadow last for most of the disc lifetime.
  • A substantial fraction of discs in nearby star-forming regions should exhibit observable flyby-induced shadows.
  • Surveys that count shadowed discs can place limits on average disc viscosity.

Where Pith is reading between the lines

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

  • The fraction of discs showing these shadows would directly indicate how often flybys occur in typical birth clusters.
  • Periodic changes in outer-disc illumination from moving shadows could affect the growth or migration of forming planets.
  • Comparing the observed lifetime of shadows across different star-forming regions could reveal regional differences in disc viscosity.
  • Time-domain imaging over several years could detect the predicted back-and-forth motion of the shadow.

Load-bearing premise

One-dimensional linear warp propagation theory accurately reproduces the warp shape and resulting shadow geometry for the chosen flyby distances, angles, and disc properties.

What would settle it

A large survey of discs in a young cluster that finds either no shadows at all or shadows whose lifetimes and oscillation periods fall well below the predicted million-year scale would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.22592 by C. J. Nixon, Katie L. Milsom, Tim J. Harries.

Figure 1
Figure 1. Figure 1: Figure showing the staggered grid set-up of our model. The blue represents the annuli which make up the disc where the solid lines show the edge of each annulus and the dotted lines show the centre of each annulus. l is defined at the full grid points (𝑅) at the centre of each annulus and G is defined on the half grid points (𝑅1 2 ) at the edge of each annulus. The subscript denotes the position on the rad… view at source ↗
Figure 2
Figure 2. Figure 2: Figure showing the parabolic orbits of the perturbers for models 1 (blue line) and 2 (orange line). The disc is shown in grey (not to scale) in the 𝑥 𝑦-plane. The unit vector of the velocity is marked at periapsis for both orbits. Model 1 has a parabolic orbit in the 𝑥𝑧-plane with periapsis at [𝑎, 0, 0] and Vˆ = [0, 0, 1] at periapsis (so the perturber is travelling in the positive 𝑧-direction). Model 2 is… view at source ↗
Figure 3
Figure 3. Figure 3: Shadows due to the warps induced by the flyby encounter from model 1. Rows 1 and 3 show face-on scattered light models produced using a fast radiative transfer code for different time periods. Each image is log scaled and normalised to the maximum surface brightness value. The image below each scattered light image shows the shaped of the warped disc where the colours show the height above (or below the mi… view at source ↗
Figure 4
Figure 4. Figure 4: Same as figure 3, but for the flyby encounter in model 2. Rows 1 and 3 show face-on scattered light models for different time steps (log scaled and normalised to the maximum surface brightness value) and the images below show the shaped of the warped disc where the colours show the height above (or below the midplane): orange is in the midplane, blue is above, and red below. These models are inclined by 70… view at source ↗
Figure 5
Figure 5. Figure 5: Figure showing the maximum tilt of the disc (red), and the azimuthal variance of the surface brightness of the scattered light image, 𝜎2 , (blue) at each time step for models 1 (left) and 2 (right). The tilt is calculated as the angle between the angular momentum vector of the disc and the 𝑧-axis for each radius of the disc and the maximum value is taken for each time step. For model 1 the disc initially i… view at source ↗
Figure 6
Figure 6. Figure 6: Same as the left of [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: The peak of 𝜎2 (after 2500 years) for model 1 with different values of 𝑉 and 𝑎 of the perturber; 𝑎 = 300, 400, 500, and 600 au (blue, orange, green, and red lines respectively. Results from our models are plotted as crosses and the lines have been interpolated. The figure shows the same models as in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Figure showing the peak of the maximum tilt for each oscillation of the warp with time. Oscillations of the maximum tilt of the disc with time are plotted (low opacity lines) for model 1 with 𝛼 = 10−4 , 10−3 , 10−2 (blue, orange, and green lines respectively). The low opacity blue line is the same as the red line in the left of [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Figure showing 𝜎2 (low opacity lines) with time for model 1 with 𝛼 = 10−4 , 10−3 , and 10−2 (blue, orange, and green lines respectively). The peak of 𝜎2 for each oscillation is plotted as solid lines. The grey dotted line marks where 𝜎2 = 0.01 where below this line shadows are no longer observable. The higher the viscosity of the disc the quicker the warp decays and the shadows become unobservable. For a … view at source ↗
Figure 12
Figure 12. Figure 12: Figure showing the percentage of time when 𝜎2 > 0.01 (after 2500 years), and so shadows are observable, for models with varying 𝑎 and 𝑉 (see legend). All models were run for 7500 years so we are calculating the percentage of time which the disc is shadowed for ∼ 1 oscillation of the warp. Solid lines show results from the models based on model 1 which are shown in 8. Dashed lines show results from models … view at source ↗
Figure 13
Figure 13. Figure 13: Scattered light images of the shadowing for model 1 for different inclinations of the disc (𝑖𝑛𝑐) and rotation angles of the disc (𝜙). Columns show different time steps and rows show the disc for different values of 𝑖𝑛𝑐 and 𝜙. We define 𝜙 to be 0◦ when the shadow is in the north of the disc at 2000 years and we rotate clockwise. An inclination of 0◦ is face-on and 90◦ edge-on. The first three rows show 𝜙 =… view at source ↗
Figure 14
Figure 14. Figure 14: Position of the centre of the flux in x (left) and y (right) with time for images inclined by 60◦ . Different colours show different values of 𝜙 (see legend). We can see that for 𝜙 = 90◦ the variation in the centre of the flux is maximum in x and minimum in y. The opposite is true for 𝜙 = 0 ◦ . 0 1000 2000 3000 4000 5000 6000 7000 Time (years) 20 10 0 10 20 X centre of flux (au) = 0 = 45 = 90 0 1000 2000 … view at source ↗
Figure 15
Figure 15. Figure 15: Left: Same as the left of [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Rate of flyby encounters, per Myr, (calculated using Equation 26) against closest approach for different cluster densities (see legend). The cluster has 𝜎d = 4 km s−1 and 𝑚c = 𝑚p = 1𝑀⊙. Values of the encounter rate are marked for 400 < 𝑎 < 500 au (grey shaded region) and 𝑎 < 1000 au for different stellar densities (shown by the colours in the legend). We can see that the encounter rate strongly depends on… view at source ↗
read the original abstract

We explore the observational signatures of flybys in scattered light images of protostellar discs. The warps are modelled using 1D warp propagation theory coupled to a fast radiative transfer code that simulates the shadows induced. We consider two scenarios, namely a flyby in a plane orthogonal to, and at an angle with, the disc plane. In both models the outer disc becomes warped (leading to a broad shadow in the outer disc) and the warp wave propagates back and forth (causing the shadow to oscillate). We find that the inner disc, although tilted, is not warped and is therefore not shadowed. For a low viscosity disc ($\alpha=10^{-4}$) the warp lasts for most of the disc's lifetime ($\tau \sim 10^6\,$years), and for $50\%$ of the time the azimuthal variance of the surface brightness from the scattered light images, $\sigma^2$, is above $0.01$, meaning that the shadow in the disc is significant. We find that a significant fraction of discs in nearby star forming regions should have undergone a flyby sufficient to induce an observable warp, and that surveys of shadowed discs could provide a valuable probe of disc viscosity.

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

1 major / 2 minor

Summary. The paper models flyby-induced warps in protoplanetary discs using 1D linear warp propagation theory coupled to a fast radiative transfer code. It examines orthogonal and inclined flyby scenarios, finding that the outer disc warps produce broad oscillating shadows while the inner disc remains unshadowed. For α=10^{-4}, the warp persists for most of the disc lifetime (∼10^6 yr) and σ² exceeds 0.01 for 50% of the time, implying observable shadows; the authors suggest this fraction of discs in nearby regions may show such signatures and that shadow surveys could constrain viscosity.

Significance. If the modeling assumptions hold, the work supplies quantitative, observationally testable predictions linking flybys to scattered-light shadows and offers a potential viscosity diagnostic via the duty cycle of high-σ² states. Credit is due for the efficient 1D-plus-RT framework that permits long-term evolution tracking and for the clear definition of the σ²>0.01 threshold as a significance metric.

major comments (1)
  1. [§2 (modeling approach)] §2 (modeling approach): the central lifetime (τ∼10^6 yr) and 50% duty-cycle claims rest on the 1D linear bending-wave equations plus post-processed RT accurately reproducing both the radial warp profile and the azimuthal surface-brightness variance. No demonstration is given that the adopted flyby inclinations and impact parameters keep tilt angles and gradients inside the small-amplitude regime assumed by the linear theory (cf. Lubow & Ogilvie 2000), nor is a comparison to 3D hydrodynamics provided to confirm that non-axisymmetric density perturbations do not alter the shadow contrast. This is load-bearing for the headline quantitative results.
minor comments (2)
  1. [Abstract and §3] Abstract and §3: the exact numerical values of the flyby inclination, impact parameter, and disc mass ratio should be stated explicitly rather than described qualitatively, to allow reproducibility of the 50% time fraction.
  2. [Figure captions] Figure captions: several panels lack labels for the time at which each snapshot is taken; adding these would clarify the oscillation period of the shadow.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the potential observational implications of our work. We address the major comment on the modeling assumptions below and have revised the manuscript to strengthen the justification for the linear theory.

read point-by-point responses

  1. Referee: [§2 (modeling approach)] §2 (modeling approach): the central lifetime (τ∼10^6 yr) and 50% duty-cycle claims rest on the 1D linear bending-wave equations plus post-processed RT accurately reproducing both the radial warp profile and the azimuthal surface-brightness variance. No demonstration is given that the adopted flyby inclinations and impact parameters keep tilt angles and gradients inside the small-amplitude regime assumed by the linear theory (cf. Lubow & Ogilvie 2000), nor is a comparison to 3D hydrodynamics provided to confirm that non-axisymmetric density perturbations do not alter the shadow contrast. This is load-bearing for the headline quantitative results.

    Authors: We appreciate the referee highlighting the importance of validating the linear regime assumptions. In the revised manuscript we have added an explicit verification in §2, based on the flyby torque and resulting warp amplitudes in our 1D models, confirming that maximum tilt angles and radial gradients remain well within the small-amplitude limit of Lubow & Ogilvie (2000). This directly supports the reliability of the reported lifetimes and duty cycles. A full side-by-side comparison with 3D hydrodynamics lies beyond the scope of the present study; however, we have expanded the discussion to explain that transient non-axisymmetric perturbations from the flyby do not substantially modify the broad, radially extended shadows that dominate the scattered-light variance metric. These additions address the core concern while preserving the efficiency of the 1D-plus-RT approach for long-term evolution. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results are forward-model outputs

full rationale

The paper models warp evolution via 1D linear bending-wave equations (standard in the literature) and couples them to radiative-transfer post-processing to generate scattered-light images. The reported τ ∼ 10^6 yr lifetime at α=10^{-4} and the 50 % duty cycle with σ² > 0.01 are direct numerical outputs of the chosen viscosity, flyby geometry, and disc parameters run through that forward model. No equation or result is defined in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing step reduces to a self-citation chain. The derivation chain is self-contained as a simulation study whose quantitative claims follow from the input setup rather than by tautology.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central results rest on the validity of linear 1D warp theory, the chosen flyby geometry and impact parameter, and the assumption that the radiative-transfer code correctly maps warp height to scattered-light shadows. No new particles or forces are introduced.

free parameters (2)
  • viscosity parameter α
    Set to 10^{-4} to obtain long-lived warps; directly controls the reported lifetime and shadow significance fraction.
  • flyby inclination and impact parameter
    Two discrete geometries are explored; results are reported only for these specific choices.
axioms (1)
  • domain assumption One-dimensional linear warp propagation theory accurately describes the warp evolution and shadow geometry after a flyby.
    Invoked in the modeling paragraph of the abstract to couple warp shape to radiative transfer.

pith-pipeline@v0.9.0 · 5756 in / 1328 out tokens · 30478 ms · 2026-05-22T01:50:22.648715+00:00 · methodology

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