Three-Dimensional Hydrodynamics of Protostellar Disks: The Effects of Thermal Energetics

Abstract

We use a second-order three-dimensional hydrodynamics code with self-gravity to investigate the role that thermal energetics plays in the development of nonaxisymmetric instabilities in protostellar disks. The initial axisymmetric equilibrium state is a continuous, fluid star/disk system, in which the star, the disk, and the star/disk boundary are resolved in 3D in our hydrodynamics code. An adiabatic evolution is compared to two previous simulations of the same model in which either local isentropy or local isothermality is maintained in the disk throughout the calculation. In all three cases, the model is highly unstable to multiple low-order nonaxisymmetric disturbances which induce significant mass and angular momentum transport in a few dynamical times. The star and star/disk boundary are dominated by three- and four-armed disturbances, whereas the disk is susceptible to a two-armed spiral. These disturbances saturate at moderate nonlinear amplitude in the adiabatic and isentropic evolutions; the same instabilities in the isothermal evolution lead to the disruption of the disk and concentration of material into several dense, thin arcs and arclets. Figures, tables and animations are included in the CD-ROM supplement.Much numerical work has shown that protostellar objects are subject to nonaxisymmetric instabilities, generally due to a combination of rapid rotation, self-gravity, and thermal pressure. In this presentation, we investigate how different assumptions about thermal energetics affect the origin and maintenance of nonaxisymmetric structure in three dimensions.Our initial, continuous, axisymmetric equilibrium state is a cooled version of a model in the isentropic, polytropic sequence of star/disk models (the “I” models) studied in our previous work (Pickett et al. 1997, 1998; see also Imamura et al. in this volume). The equilibrium configuration represents an early stage in the axisymmetric collapse of a uniformly rotating singular isothermal sphere. The model is small in radial extent (R eq ∼ 0.10 AU), with the mass roughly evenly divided between star and rotationally supported disk. The minimum Toomre Q in the disk is 1.5. The model is shown in Figure 1; Table 1 lists physical properties.Three simulations with our 3D hydrodynamics code (Pickett et al. 1996, 1998) were conducted: 1) a locally isothermal evolution, in which the disk temperature was held at its initial, axisymmetric value; 2) a locally isentropic evolution, in which the disk entropy is held fixed; and 3) an adiabatic evolution, in which artificial viscosity was used to treat shocks. The star was treated adiabatically in all cases. Each run begins with a random density perturbation throughout the disk; grid resolution is (128,64,16) in (r,ϕ,z).Table 2 describes the simulations. We find: 1. The early growth of nonaxisymmetric modes is similar in all cases. The star and inner disk are subject to three- and four-armed Kelvin-like modes; the disk is unstable to a two-armed spiral. 2. The nonlinear development of the modes varies greatly. In the isothermal evolution, relative density amplitudes reach highly nonlinear levels (δρ/ρ ∼ 80% and above). The same instabilities in the isentropic evolution saturate at moderately nonlinear amplitudes, apparently from effective mode interaction (Laughlin & Rózyczka 1996). In the adiabatic evolution, the amplitudes fall to the percent level or less due to heating from shocks (Figure 2). 3. Copious mass and angular momentum transport occurs (Figure 3). 4. The effects of the instabilities vary drastically. The two-armed spiral in the isothermal evolution disrupts the disk, concentrating most of the material outside the star in thin, dense arms. In the isentropic and adiabatic evolutions, the disk remains, although a strong two-armed spiral is embedded inside it. Further, heating of the low density regions in the adiabatic calculation leads to their expansion (Figures 4 and 5). KeywordsArtificial ViscosityAdiabatic EvolutionDisk TemperatureAngular Momentum TransportProtostellar DiskThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.