Rayleigh-Taylor Instability in Dusty Gas
Evolution of 2D simulations in a system with a constant vertical gravitational acceleration and a constant (initially sub-Eddington) flux incident on the lower boundary. The initial configuration corresponds to an isothermal atmosphere. Because of the optical depth is greater than one, the lowest parts of the box begin to heat up. Since the opacity is proportional to temperature squared, the opacity rises and the radiation field becomes super-Eddington, launching most of the mass in a thin shell. This shell then undergoes Rayleigh-Taylor instabilities that generate density and temperature inhomogeneities in the flow. The setup is chosen to mimic the simulation of Krumholz & Thompson, 2012. The results are discussed further in Davis et al. 2014 (ApJ, submitted).
Two simulations performed with an initial optical depth of three and initial Eddington ration of one half. The left simulation uses the flux-limited diffusion (FLD) method while the right uses our variable Eddington tensor (VET) formalism. After the Rayleigh-Taylor instability develops the density inhomogeneities allow the radiation to escape more easily through low density channels and reduce the volume averaged acceleration of matter by the radiation. In the FLD simulation this caps the acceleration from radiation and eventually most material returns to the base of the simulation. In the VET simulation the matter is (on average) still accelerated upward and the simulation is stopped when an optical depth worth of matter reaches the upper boundary, where matter is allowed to escape.
A comparison of three VET simulations with initial optical depths of one, three, and ten. The initial Eddington ratio is one half and setup is the same as the VET simulation above. The evolution of run with optical depth of ten is qualitatively similar to the case with optical depth of three, but the shell is accelerated somewhat more efficiently in this run with larger optical depth. The gas obtains a higher mean velocity and larger mass-weighted velocity dispersion. The simulation ends when gas reaches the top of the domain, doing so in about half the time it takes in the optical depth three run. In contrast, the run with optical depth of one never has a mass weighted radiation force consistently exceeding the gravitational force. The shell stalls and falls back to the bottom of the domain. It then reaches a turbulent state similar to the FLD case shown above.
Two simulations performed with an initial optical depth of three and initial Eddington ratio of one half. The left panel shows a 2D slice of density from a 3D simulation, while the right panel shows a 2D simulation. The 2D and 3D simulations were run with the same resolution, which corresponded to a factor of four less grid zones per unit length than in the simulations above. Both simulations have moderately high density matter reaching the top of the box, but the matter in the 2D calculation is somewhat concentrated near the base of the domain whereas the 3D density is more evenly distributed vertically. The density structure is filamentary in both cases, but filaments in the 2D run tend to be narrower and fewer. Therefore, the coupling between radiation and matter is stronger in the 3D simulation and the matter is more effectively accelerated by the gas.
Specific intensity from the surface of the 3D simulation with initial optical depth of three and Eddington ratio of one half. Color corresponds to the logarithm of the specific intensity computed by the code each timestep to evaluate the variable Eddington tensor. This is pseudocolor plot of the outgoing intensity on the simulation domain surface for this specific viewing angle (i.e. not a volume rendering). The domain is periodic in the horizontal directions and optically thin in the upper regions so one can perceive periodic pattern associated with the sinusoidal perturbations at early times.
Intensity from a Radiation Dominated Accretion Disk
Specific intensity from the top half of a 3D, stratified shearing box. Color corresponds to the specific intensity computed by the code each timestep to evaluate the variable Eddington tensor. This is pseudocolor plot of the outgoing intensity on the simulation domain surface for this specific viewing angle (i.e. not a volume rendering). The upper regions of the simulation are optically thin so one can perceive multiple sheared "copies" of the domain due to the shearing periodic boundary conditions on the radiation field. The dark filaments correspond to dense gas following field lines that shadow the brighter background radiation. The movie corresponds to 8 orbits. Note that the photosphere rises over the course of the movie because of density redistribution related to the dynamo that is active in these simulations. A detailed discussion of the numerical simulations and their scientific implications are presented in Jiang et al. (2013)
Scattered Light from an Irradiated Cloud
Specific intensity of scattered light from an irradiated cloud in a 3D simulation. The cold cloud is embedded in a hotter, rarefied medium, with radiation incident on one face of the 3D domain. The absorption opacity is zero and the scattering opacity is constant. Therefore the scattered light is dominated by the dense cloud, but still has a contribution from the rarefied medium. The left image shows the intensity (corresponding to the view normal) of light on the surface of the simulation domain. The right image shows a 2D slice of density and a vector plot of velocity through the center of the domain. Radiation is incident on the right side of the domain. Near the end of the simulation, time evolution is paused and the left image is rotated around the center of the domain, with the intensities always updated to correspond to the view normal. One can perceive a changes in the "sharpness" of the cloud during the rotation, owing to the variation of the change in optical depth through rarefied medium. As the cloud is pushed to the left by radiation pressure, its shape is significantly distorted due to the anisotropy of the radiation field, which is captured by Athena's VET implementation. A detailed discussion of the cloud dynamics in different regimes will be presented in Proga et al. (2014).
Radiation Flow in an Obstructed Pipe
2D flow of radiation through an obstructed pipe. The color shows the temperature of the fluid in the pipe. Radiation is only incident on the left. The obstruction prevents gas from heating immediately in obscured regions, but radiation eventually "flows" around the obstructions by heating up gas that can then radiate neighboring gas which was originally obscured. See sec. 5.2 of Jiang et al. (2012) for further discussion.