Contents
1.
2.
3.
4.
5.
PH241 Midterm
Motivation
Initial Setup
Methodology
Analysis
Conclusion
The Antennae Group
03/13/06 – pg. 1
Toomre and Toomre
•
1972 – T&T set out to model galaxies NGC-4038/9 (i.e. the antennae) and were able to
successfully produce an accurate rendering using a fourth order Runge-Kutta integration
method.
PH241 Midterm
The Antennae Group
03/13/06 – pg. 2
1972  2006
PH241 Midterm
The Antennae Group
03/13/06 – pg. 3
Kepler problem
m2
r1 
r  rˆ
m1  m2
m1
r2  
r  rˆ
m1  m2
G M 1  M 2 
vr  
sin 
Rmin 1   
G M 1  M 2 
1   cos  
v 
Rmin 1   
Rmin 1   
r   
1   cos 
PH241 Midterm
The Antennae Group
03/13/06 – pg. 4
Geometry
PH241 Midterm
The Antennae Group
03/13/06 – pg. 5
Galaxy Setup
•
We filled 12 concentric rings of radii
0.2Rmin to 0.75Rmin with a step of
0.05Rmin, with each ring having 3 more
particles than the previous
Particles given initial velocity to maintain
a circular orbit.
Softening: ε = 0.2
•
•
2
v0
GM
GMr
 2
 v0  2
2
r
r 
r  2
PH241 Midterm
The Antennae Group
03/13/06 – pg. 6
Restricted 3-Body
•
Send satellite masses to 1.0 E-9 as compared to M = 1 for the center of mass.
GMm
9
~
10
2
Rmin

Gm2
Gm2
15

~
10
r2   2
2
PH241 Midterm
The Antennae Group
03/13/06 – pg. 7
Our Results
PH241 Midterm
The Antennae Group
03/13/06 – pg. 8
Comparison
PH241 Midterm
The Antennae Group
03/13/06 – pg. 9
Orbit Plane
φ=0
φ = 2π/3
PH241 Midterm
The Antennae Group
03/13/06 – pg. 10
Tidal Forces
PH241 Midterm
The Antennae Group
03/13/06 – pg. 11