Chi Yung Chim, Jaehyeok Yoo,
Xiang Zhai, Yaojun Zhang
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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?
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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.
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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:
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Ways to add masses:
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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
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Equal number of identical test masses on
each ring
Distribution of {r1, r2, …} follows the
probability distribution:
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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
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Another convenient method:
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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
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We use the same probability of the number of
masses, and put the number of test masses for
each ring according to the probability.
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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
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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:
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Point-intruder to galaxy
Galaxy to galaxy
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Phenomenon: Ring-like structure
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Simple Model Explanation:
What’s the influence of the two big nuclei on
ONE test particle ?
Force Exerted by the Intruder
Solvable Problem
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Change in velocity:
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Trajectory of the test particle:
Trajectory and Time Dependence
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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.