N-Body Simulations of a Dwarf Spheroidal Galaxy Comparing
Newtonian, Modified Newtonian, and Dark Matter Models
Tristan Clark and S.G. Alexander
Miami University Physics Department
Oxford, OH
This site contains a link to animations done by Tristan Clark in his senior capstone:
N-Body Simulations of a Dwarf Spheroidal Galaxy Comparing
Newtonian, Modified Newtonian, and Dark Matter Models.
The side-by-side 3D animations show the motion of 500 stars in the galaxy for one billion years. Each
calculation has the same initial conditions:
- The baryon mass of the galaxy is 10^7 solar masses and is treated as a spherically
symmetric mass with an exponentially decaying radial density.
- The 500 stars are placed randomly in a sphere of radius 500 pc with each velocity component
chosen randomly between +15 km/s to -15 km/s.
- In the Newtonian simulation, all of the stars feel an acceleration from the baryon cloud and
each other. Standard Newtonian gravity is used.
- In the MoND simulation, the total accelerations, calculated as in the Newtonian case, are modified
according to Milgrom's scheme.
- In the Dark Matter simulation, standard Newtonian gravity is used and a spherically symmetric dark matter
cloud is included that has a total mass of 10^8 solar masses with the NFW density profile.
- Here are the density profiles for both the baryon cloud and
the dark matter cloud. For the dark matter simulation shown below, we used the density profile with the scale length a = 200pc.
Also, note that:
- Each simulation is for one billion years with frames refreshing every 500ky. The time
in millions of years is indicated in each animation.
-
The solid circle is a reference circle in the xy plane of radius
500 pc that is included to gauge where the stars are. There is also a blue rod that is along the z-axis (it's harder to see).
- The animation pans back a few times to show where the stars are, and it is rotated a few times to show that the
simulation is three dimensional.
- Also, the sizes of the stars have no physical significance; we
chose the size to make them easy to see.
Newtonian, Mondian, and Dark Matter Side-by-Side Animations
(Thanks to Ben Blankartz for his help with the animations)
(To start the animation, click on image. This is an flv file.
If it doesn't display, try the link below to the mp4 file)
Same animation in mp4 format