1. Chi Yung Chim, Jaehyeok Yoo, Xiang Zhai, Yaojun Zhang
Cartwheel Galaxies
Chi Yung Chim, Jaehyeok Yoo,
Xiang Zhai, Yaojun Zhang

2. Introduction System: a ring galaxy discovered in 1963 by Herzog
More detailed feature discovered by Lynds in 1976: ring + nucleus
Analysis of the spectrum reveals different velocities of ring and nucleus
Material between the ring and nucleus → Linking between the two?

3. The photo Lynds took

4. Then Lynds and Toomre proposed the Cartwheel model to explain the features.
They proposed that the intruder gives a brief inward gravitational pull that changes a typical galaxy into a ring like structure.
Simulation: only the nuclei attract significantly
Our target: to revisit this simulation using Aarseth's Code.

7. Start: Initial conditions
We want a Gaussian distribution of areal density of the disk:
To make the nuclei only the significant source of gravitation, we set mdisk:mnucleus=1:99
Kepler velocity for the masses on disk:

8. Ways to add masses:
Equal masses on the rings, with the ring separation determined by the density
Equal ring separation, with masses determined by density
Forget the rings and put equal masses throughout the whole space

9. Rings of equal mass Equal number of identical test masses on each ring
Distribution of {r1, r2, …} follows the probability distribution:

10. How to pick the radius: Let q = r/r0, and g(q) = q Exp(-q2/2)
We know g(q) < gmax=
Repeat choosing two uniformly distributed random numbers 0<X1<gmax and 0<X2<∞ ≈ 100, until X1 > g(X2)
Then q = X2

11. Another convenient method:
Choose random numbers 0<Xi<1 Xi

12. Mass Distribution Confirmation
All equal mass
Normalized for Md to be 0.01

13. Mass Distribution Confirmation
Accumulated Gaussian dist.
Equal ring mass
Equal mass particles on a ring
Normalized for Md to be 0.01
Equal ring mass
Equal separation particles on a ring

14. Let's see the outcome...

15. Rings of equal separation
We use the same probability of the number of masses, and put the number of test masses for each ring according to the probability.

16. No more rings: cloud-like distribution
Put in masses randomly using r determined by the previous rule, and θ, φ determined by setting uniform random variables X1=0.5, 0 < X2 <1

17. Put it into motion! Algorithm used: Aarseth Code η = 0.2, ε = 0.3
G = M = r0 =1
Taken initial approach speed as if released from infinity
We performed two kinds of collision:
Point-intruder to galaxy
Galaxy to galaxy

18. Single mass vs Galaxy

19. Galaxy vs Galaxy

21. Let's strike with some missing...

22. Other initial conditions works too

24. Diffused points..

25. Diffused Points..

26. Compare with the paper

27. Compare with observation

28. Theoretical Interpretation
Phenomenon: Ring-like structure
Simple Model Explanation:
What’s the influence of the two big nuclei on ONE test particle ?

29. Force Exerted by the Intruder

30. Solvable Problem
Change in velocity:
Trajectory of the test particle:

31. Trajectory and Time Dependence

33. Thanks!!
We refered to:
Lynds, Roger and Toomre, Alar. On the Interpretation of Ring Galaxy. The Astrophysical Journal, 209: , 1976.
Toomre, Alar and Toomre, Juri. Galactic Bridges and Tails. The Astrophysical Journal, 178: , 1972.

34. Enjoy!