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# Laboratory Assignment 3

## deadline March 4, 2013

## 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 10**4 points. The mass of the sphere is M=10**11 Msolar, the radius R=1 kiloparsec. The radius R is related to the b parameter of Lecture 9 by the relation 3b**2=R**2.

(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.

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

(d) Run a simulation with 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 Plummer's sphere where initially all velocities are set to zero.

(e) Make an MPEG movie of the two simulations.

## 2. Virial theorem

### PHYSICS 241 only:

### Based on the solution of Plummer's model in Lecture 7, 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.

## Supporting note and discussion are provided in Lab 5.