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Investigate the unique features of ring galaxies utilizing the Cartwheel model through simulations with Aarseth's Code to understand their formation and dynamics. Experiment with varying initial conditions and mass distributions to observe the system's evolution and interactions. Discover the influence of multiple nuclei on test particles and analyze the trajectory changes. Compare simulated outcomes with existing observations and theoretical predictions. Enjoy a comprehensive study on these fascinating celestial formations with this computational approach.
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Cartwheel Galaxies Chi Yung Chim, Jaehyeok Yoo, Xiang Zhai, Yaojun Zhang
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?
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.
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:
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
Rings of equal mass • Equal number of identical test masses on each ring • Distribution of {r1, r2, …} follows the probability distribution:
How to pick the radius: • Let q = r/r0, and g(q) = q Exp(-q2/2) • We know g(q) < gmax= 0.606531 • Repeat choosing two uniformly distributed random numbers 0<X1<gmax and 0<X2<∞ ≈ 100, until X1 > g(X2) • Then q = X2
Another convenient method: • Choose random numbers 0<Xi<1 Xi
Mass Distribution Confirmation All equal mass Normalized for Md to be 0.01
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
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.
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
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
Theoretical Interpretation • Phenomenon: Ring-like structure • Simple Model Explanation: What’s the influence of the two big nuclei on ONE test particle ?
Solvable Problem • Change in velocity: • Trajectory of the test particle:
Thanks!! • We refered to: • Lynds, Roger and Toomre, Alar. On the Interpretation of Ring Galaxy. The Astrophysical Journal, 209: 382 - 388, 1976. • Toomre, Alar and Toomre, Juri. Galactic Bridges and Tails. The Astrophysical Journal, 178: 623 - 666, 1972.
