Planetary Nebulae Low Res Runs

Computational Setup

We would like to understand how different parameters and environments can shape planetary nebulae. In order to do this, we set up several simulations of different types of flows in various ambient media. We initialize the grid with the following environments:

• Constant Ambient: The entire grid starts with a constant density of 300 particles/cm³
• Stratified Ambient: The density decays as 1/r² radially from a central value of 300 particles/cm³
• Toroidal Ambient: The density decays smoothly from equator to pole from a seed value of 300 particles/cm³ using the function described in ​Frank & Mellema, 1994 ApJ. The two parameters used are \alpha_{t}, which determines the density contrast from the pole to equator, and \beta_{t}, which determines how elliptical or spherical the distribution is.

For each ambient, we introduce three different types of flows:

• Clump: A spherical cloud of gas with radius 500 AU travels at 200 km/s with initial density 40,000 particles/cm³.
• Jet: A jet with radius 500 AU and density 40,000 particles/cm³ injects gas into the grid from below with initial velocity 200 km/s along the y axis.
• Diverging Wind: This is the same setup as the jet, but instead of injecting gas directly along the y axis, it will sweep an arc of 10^o.

We also introduce toroidal magnetic fields in the MHD runs, which are initialized off the grid, according to the specifications in ​Lind et. al, 1989 ApJ. We choose Rm = .6Rjet, or 300 AU, based on previous papers. This parameter measures how electric current flows along the jet. To determine initial field strength, we use the magnetic \beta (not to be confused with \beta_{t} which is associated with the shape of the torus), which is the ratio of the thermal pressure to the magnetic pressure. High values of \beta will mean weak magnetic fields. For our initial runs, we chose \beta = 1.

Hydro Runs

	Constant Ambient	Stratified Ambient	Toroidal Ambient
Clump	​movie Status: Completed.	​movie Status: Completed.	​movie Status: Completed.
Jet	​movie Status: Completed.	​movie Status: Completed.	​movie Status: Completed.
Diverging Winds	​movie Status: Completed.	​movie Status: Completed.	​movie Status: Completed.

MHD Runs

	Constant Ambient	Stratified Ambient	Toroidal Ambient
Clump	Status: Implementation in Progress.	Status: Implementation in progress.	Status: Implementation in Progress.
Jet	​movie Status: Completed.	​movie Status: Completed.	​movie Status: Completed.
Diverging Winds	​movie Status: Completed.	​movie Status: Completed.	​movie Status: Completed.

Tests

Half Grid v.s Full Grid

Our simulations take advantage of the symmetry of these problems and only evolve the right half of the grid, which is then simply reflected to provide a visualization for the whole jet. We decided to run one full grid simulation to compare, just to make sure there are no boundary effects. This run is the stratified diverging wind, with the MHD equations turned on and \beta = 100000 (so essentially no magnetic fields). If we compare this to the hydro stratified diverging wind run from the previous section, we see that the symmetry of the problem is indeed preserved.

MHD Bubbles

Our initial runs show very distinct bubbles in the MHD runs that don't exist in the hydro case. While the MHD flows should be m = 0 unstable, there may be something else going on as well. The following images are from the same conditions, one purely hydro, one with MHD and \beta = .8 and the third MHD with a high \beta. As we cantsee, the bubbles are very nonexistant in the hydro case, distinct in the MHD case and mild in the high \beta case.

We have also tried running the weak magnetic field cases, with \beta = 8 and \beta = 80:

Torus

In our initial runs, the torus case seems to not be very different from the constant ambient case. We are trying different values of \alpha_{t}, the density contrast to see where there is a significant impact of the torus. So far, we have tried values of:
\alpha = .3 ​movie

\alpha = .9 ​movie

Martin, 29 July 2013. Found and fixed a bug in our module, which affected the strength of magnetic fields. Running test to see whether this gets rid of the bubble-looking features, which i think are unphysical, that we see in the mhd cases.