tokens: of the system is maintained. When a dust grain is placed on a highly eccentric orbit by radiation pressure, it may create a local pressure maximum but not linger in a nearby circular orbit where it can stabilize the gas through drag backreaction. This may provide a second possible explanation for the difference between runs D and F discussed above, especially given the higher mass of dust used in run F, which may lead to drag backforces that are strong enough to destabilize gas from a circular orbit. In Figure 12 , we show the dust surface density every 50 orbits for 400 orbits. We find that the photoelectric instability sets in quickly, but has no obvious secular effect on the global structure of the disk. The behavior is dominated by transient clumps and arcs that appear and disappear on timescales of orbits to dozens of orbits. Figure 12. Dust surface density over time for run F. The photoelectric instability arises quickly and is continuously redistributing dust into nonaxisymmetric structures throughout the disk over the full course of the simulation. Though the radial distribution of the dust varies nonsecularly over time, the 2D dust structure is consistently dominated by clumps and arcs that form and dissipate on short timescales of ≈1–10 orbits. In order to confirm that the dust structures seen in run F (Figure 8 ) are conclusively attributable to the photoelectric instability, we run two additional models: one without photoelectric heating, and one with an increased dust resolution to ensure model convergence (run I). For run I, we double the number of dust superparticles while reducing the mass of each superparticle by half in order to maintain the same overall dust mass. The run without photoelectric heating shows no clumping behavior, and instead yields a smooth, structureless dust distribution, as one would expect. Run I, on the other hand, shows the same clumping behavior as seen in run F, suggesting that the resolution we use in runs A–F is sufficient. Gas and dust surface densities after 400 orbits are shown in Figure 13 . Figure 13. Gas (left panel) and dust (right panel) surface densities after 400 orbits for run I, which is a high-dust resolution (2× superparticles) duplicate of run F (). The dashed circle indicates (100 au). Doubling the number of superparticles yields substantially similar gas and dust spirals and clumps, suggesting that 800,000 superparticles are sufficient for capturing the effect of the PeI in the presence of radiation pressure (for the chosen grain size distribution). In run H, we duplicate run F (Figure 8 ) but double the birth ring width to verify that the dust clumping behavior of run F does not require a narrow birth ring. Dust and gas surface densities after 400 orbits for run H are shown in Figure 10 . We find that the enhancement in the dust-to-gas ratio produced by the photoelectric instability is weaker in run H compared with run F (see Table 1 ), but the qualitative results—nonaxisymmetric,
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