The Frozen North



Assignment 3

deadline February 21, 2019


1. Simulation of Plummer's model


Consider Plummer's self-gravitating steady state sphere:


(a) Generate a discrete point distribution for the Plummer sphere with minimum 10**4 points. The mass of the sphere is M=2*10**11 Msolar, the radius R=1.5 kiloparsec. The radius R is related to the b parameter of Lecture 6 by the relation 3b**2=R**2.

25 points

(b) Plot the corresponding theoretical mass density distribution as a function of the radial distance from the origin and compare it with your point mass distribution.

20 points

(c) PHYSICS 241 only: Show evidence that your velocity distribution agrees with the desired theoretical distribution.

20 points

(d) PHYSICS 241 only: Simulate the orbit of a single star in the Plummer distribution. Investigate if the orbit is periodic or not.

20 points

(e) Run a simulation with your own N-body code, or the N-body Aarseth code with appropriate choice of eta and epsilon. Investigate the steady state of the distribution over your choice of a time scale which is comparable, or longer than the collapse time of the simple collapsing sphere where initially all velocities are set to zero.

100 points (141); 100 points (241) for your own C/C++ code. 40 points using the Aarseth code.

CUDA implementation is 150 points

(f) Make a movie of the two simulations.

15 points (141); 15 points (241)


2. Virial theorem


Based on the solution of Plummer's model in Lecture 6, prove Eq. (6) of the Plummer note of Lab 5 and show that Eq. (6) is equivalent to the virial theorem for the steady state Plummer's model.

30 bonus points for all


Supporting note and discussion are provided in Lab 5.