Tidal truncation of circumplanetary disks fails above a critical disk aspect ratio

We use numerical simulations of circumplanetary disks to determine the boundary between disks that are radially truncated by the tidal potential, and those where gas escapes the Hill sphere. We consider a model problem, in which a coplanar circumplanetary disk is resupplied with gas at an injection radius smaller than the Hill radius. We evolve the disk using the PHANTOM Smoothed Particle Hydrodynamics code until a steady-state is reached. We find that the most significant dependence of the truncation boundary is on the disk aspect ratio $H\mathrm{/}R$. Circumplanetary disks are efficiently truncated for $H\mathrm{/}R\lesssim 0.2$. For $H\mathrm{/}R\simeq 0.3$, up to about half of the injected mass, depending on the injection radius, flows outwards through the decretion disk and escapes. As expected from analytic arguments, the conditions ($H\mathrm{/}R$ and Shakura-Sunyaev $\alpha$) required for tidal truncation are independent of planet mass. A simulation with larger $\alpha =0.1$ shows stronger outflow than one with $\alpha =0.01$, but the dependence on transport efficiency is less important than variations of $H\mathrm{/}R$. Our results suggest two distinct classes of circumplanetary disks: tidally truncated thin disks with dust-poor outer regions, and thicker actively decreting disks with enhanced dust-to-gas ratios. Applying our results to the PDS 70c system, we predict a largely truncated circumplanetary disk, but it is possible that enough mass escapes to support an outward flow of dust that could explain the observed disk size.