tokens: row: particles reach a quasi-steady-state scale height in which downward settling is balanced by upward turbulent diffusion: . Across the columns, we vary the nondimensional turbulent viscosity: . Simulations with radiative damping: we have simulated ZVI with the initial Run_Brunt_Step profile with vertical domains from z = −3 H to z = +3 H for 2000 orbits with nonuniform vertical cooling. The simulations were local at one radius—that is, the radial extent of the computational domain was . Because of additional damping near the vertical boundaries (for stability), the effective domain is . Thick, blue vertical dashed lines indicate simulations that did not develop ZVI, whereas thick, red vertical solid lines indicate that ZVI was triggered and developed into full zombie turbulence. The vertical extent of these lines indicates the effective size of the computational domain. Note that when no part of the computational domain or only a small part of the computational domain extends into the gray region, ZVI is not triggered, while simulations in which the stratified regions of the computational domain have significant overlap with the gray regions do develop ZVI and turbulence. 4.4. Simulations of ZVI with Radiative Damping If the photon mean free path is longer than the largest scale of interest within a flow, then all scales are optically thin and radiative transfer can be modeled with a size-scale independent Newton cooling (i.e., radiated power proportional to temperature difference with respect to some equilibrium value). On the other hand, if the photon mean free path is shorter than the smallest scale of interest within a flow, then all scales are optically thick and radiative transfer can be treated as simple diffusion. A significant challenge is the case where, at the same location in space and time in the flow, small fluctuations are optically thin and large fluctuations are optically thick; using Newton cooling will overdamp large fluctuations, while using a diffusion operator will overdamp small fluctuations. Monte Carlo techniques for radiative transfer are ideal for cases that do not fit safely within the optically thin or optically thick regimes, but these methods involve a substantial investment in additional coding and computational resources. Our goal here is more modest: we want to determine how much radiative damping baroclinic critical layers can withstand and still support the development of ZVI. In Appendix A , we report on simulations with uniform stratification that confirm that ZVI requires Newton cooling times longer than a few orbital periods. In real PPDs, gravity and stratification are not uniform. Not only that, the radiative relaxation time can vary in position within the disk and is especially sensitive to how much the dust has settled. The baroclinic critical layers are most sensitive to radiative cooling; their radial extent is much less than a gas scale height and is expected to be optically thin. Thus we
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