Numerical viscosity and the survival of gas giant protoplanets in disk simulations

We present three-dimensional hydrodynamic simulations of a gravitationally unstable protoplanetary disk model under the condition of local isothermality. Ordinarily, local isothermality precludes the need for an artificial viscosity (AV) scheme to mediate shocks. Without AV, the disk evolves violently, shredding into dense (although short-lived) clumps. When we introduce our AV treatment in the momentum equation, but without heating due to irreversible compression, our grid-based simulations begin to resemble smoothed particle hydrodynamics (SPH) calculations, where clumps are more likely to survive many orbits. In fact, the standard SPH viscosity appears comparable in strength to the AV that leads to clump longevity in our code. This sensitivity to one numerical parameter suggests extreme caution in interpreting simulations by any code in which long-lived gaseous protoplanetary bodies appear.