Begin with the calibrated two-dimensional fit
Open Paardekooper, Baruteau and Kley, arXiv:1007.4964v1, submitted 28 July 2010 and published in 2011. Start at section 3 to identify normalization, physical gradients and smoothing. Then read sections 4.1–4.2 and 5.5–5.7 with equations 22–23, 30–31 and 45–53 beside the code.
Before looking at a migration map, predict the weak- and strong-diffusion limits. Figures 2–3 and 6–8 compare particular formulae and numerical experiments; their agreement is conditional on the low-mass, two-dimensional setup. An evolving disk also requires equations for the changing gas response.
Reading: Paardekooper · Ogilvie & Lubow
Translate a torque map into an actual history
Next open Izidoro et al., arXiv:1703.03634v2, dated 24 May 2017. Sections 2.2–2.3 explain the adopted migration forces and maps. Check the eccentricity attenuation against Fendyke and Nelson’s original negative exponential; do not mechanically reproduce the positive sign printed in equation 9.
Read section 5.2 with figure 7 to see what happens after compact chains form, then section 6.1 with figure 14 to inspect period-ratio populations. A population comparison asks a different question from whether one specially chosen pair can enter a temporary resonance. Section 8 explicitly discusses why the modeled instability fraction may differ from the fraction required by the comparison.
Reading: Izidoro et al. · Fendyke & Nelson
Ask what changes when gas has a vertical direction
For a later, distinct test read Ziampras, Nelson and Paardekooper, arXiv:2406.08555v1, dated 12 June 2024. Sections 2.2–2.3 define radiative cooling and buoyancy; section 3 constructs cooling-time maps. Then compare the static phase in section 4.2 with the migrating phase in 4.3.
Use figure 5 to compare two-dimensional and three-dimensional migration tracks under different cooling treatments. Figures 3–4 and 6–7 connect that difference to the gas response. This is a model-specific radiation-hydrodynamic result, not a universal speedup applicable to every disk. Section 5 states the sensitivity to disk conditions.
Reading: Ziampras · Paardekooper
Use a comparison table rather than mixing prescriptions
The point is not to choose one paper as a timeless winner. Each model isolates some mechanisms and removes others. A migration-dependent response cannot be obtained merely by turning the static fit’s viscosity slider further down. Likewise, a two-dimensional picture cannot demonstrate a three-dimensional buoyancy mode.
Write down the variables evolved, the imposed background, the radiative closure and the observable being compared. Only then decide which numerical experiment would test a claim.
| Reading | Question to test | Additional calculation required |
|---|---|---|
| Paardekooper 2010v1 | Can diffusion maintain corotation torque? | Full evolving gas response |
| Izidoro 2017v2 | How do chains populate and disrupt? | A population or a four-planet birth history |
| Ziampras 2024v1 | Does radiative buoyancy change migrating torques? | Vertical radiation hydrodynamics |
Reading: Paardekooper · Izidoro et al. · Ziampras
Return to the temporary-capture counterexample
Our same-parameter twelve-thousand and fifty-thousand-period records make one limited point: extending the physical time can change the finite-window resonance diagnosis. They do not isolate the cause. To test an overstability explanation, for example, vary the damping prescription or mass ratio while monitoring eccentricities, angle amplitudes and numerical convergence.
A real test should also separate sampling effects from dynamics. Integrate finely, unwrap before downsampling, compare a second integrator and report the stopping domain. An angle that only appears bounded because phase was skipped is a numerical artifact.
Reading: REBOUND 5.2.2 and IAS15 · Izidoro et al.
Design one extension that can fail
Choose one claim and vary the ingredient needed to test it. A manageable first extension could compare the static torque fit against a frozen, documented hydrodynamic torque table in the same low-mass domain. Keep its interpolation, units and calibration separate from the gravitational integrator.
A more demanding extension could reproduce a specific radiative comparison in the 2024 paper, including the cooling prescription and appendix A’s solver tests. Merely adding decorative disk thickness would not do that. Save the time-resolved forces and trajectories so an independent reader can locate a disagreement and test its source.
Reading: Ziampras · Paardekooper