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