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 100 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 100 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.

Parameterization (Condensed, as input into the code)

Acceleration Time of Jet	.02 computational units
Ambient Density	400 cm-3
Jet Density	40,000 cm-3
Ambient Temperature	1K
Jet Temperature	10K
Jet Velocity	107 cm/s
Jet Radius	1 computational unit
Torus Alpha (\alpha_{t})	.7
Torus Beta (\beta_{t})	.8
Magnetic Alpha (Rm)	.6

Scales (Computational Unit to Real Unit Conversions)

Time	8250 years/cu
Length	500 AU/cu
Density	300 (particles/cc)/cu
Temperature	10 K/cu

Hydro Runs

	Constant Ambient	Stratified Ambient	Toroidal Ambient
Clump	​movie	​movie	​movie
Jet	​movie	​movie	​movie
Diverging Winds	​movie	​movie	​movie
Spherical Winds	Status: In Progress ​movie	Status: In Progress ​movie	Status: In Progress ​movie |

MHD Runs, Beta = 1

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

MHD Runs, Beta = .5

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

HiRes LowRes Comparison

The following is a run of the Toroidal Ambient Jet in two different levels of resolution. The image on the left is run at 64 cells per jet radius and the image on the right is run at roughly 25 cells per jet radius. ​movie