# Milky Way 2D

## February 15, 2017

In order to simulate galaxy outflows, we need to start with reasonable approximation of a gas disk that is stable over many rotation periods. This post begins what will be a series of tests describing the setup of such a disk. For simplicity, I’ll start with a two-dimensional simulation.

**A Milky-Way-like static potential**

The static potential for my disk will be based on that of the Milky Way, with a few simplifications. (I’m ignoring a bulge compenent, and artificially increasing the halo concentration to account for adiabatic contraction of the dark matter halo.) Specifically, I’ll assume an NFW halo for the dark matter:

where and . is the halo scale length, which I get from the halo concentration, , with and kpc. The total mass of the dark matter halo is set by the viral mass minus the disk mass, , which I set to and . (Here, refers to the stellar disk mass). The potential of the disk follows a Kuzmin profile:

where kpc is the disk scale length and is the disk scale height. From these potentials, I calculate the total radial acceleration in the plane ():

From the radial acceleration, I get the circular velocity due to the combined Kuzmin disk plus NFW halo profile: . The circular velocity curves for this potential are shown below, with the disk component in blue, the halo component in green, and the total in red.

**An Exponential Gas Disk**

The potential described above gives the motion of the gas in the disk. For the disk surface density profile, I’m using an exponential, with a mass that of the stellar disk, and a scale length . The surface density profile thus goes as:

The surface density should not evolve with time.

**Results**

The total circular velocity curve given above has a value of 225 km/s at a radius of 8 kpc. I’ve run the simulation for 5 orbital periods at this radius, at resolutions of , , and . Movies showing the evolution of the surface density radial profile and circular velocity radial profile are below, as well as an image of the disk (with a dot showing the approximate location of the sun).

**L1 Errors**

For the grid, the L1 density error ranges between 1 and 3 percent, with an average of 2.3% over the 500 timesteps (where I’ve normalized by the average value of across the grid. The L1 veloctiy errors are slightly better, an average of 0.21%. While the L1 errors start out lower for the higher resolution grids, the final average values aren’t that different - 1.9% and 0.18% for the grid, and 1.5% and 0.16% for the grid.