Implementing on Alar & Juri Toomres’ Model to Simulate the Formations of Galactic Bridges and Tails in Spiral Galaxies. Kyung Taek Lim and Dr. Wolfgang Christian Department of Physics, Davidson College, Davidson, NC Abstract Alar and Juri Toomres’ 1972 super computer model shows the formations of galactic bridges and tails in spiral galaxies under the assumption that they are formed by just tidal forces of close encounters of galaxies. In this model, the assumption is that each encounter is caused by only two galaxies and is roughly parabolic and the test particles or “stars” that orbit the central mass are non-interactive with each other. I have implemented this galactic model by using Easy Java Simulation and tested its accuracy by comparing my implementation against published values. I start out by creating a simplified-two dimensional model where a galaxy is fixed at the center to understand how a spiral arm or “bridge” or a long curving tail can be formed by having another galaxy simply pass by. Then I extend Toomres’ model into two galaxies moving in parabolic passages around the center and observe how the mass ratio between the two galaxies cause the formation of galactic bridges and tails. The purpose of this study is to analyze how the mass ratio between two galaxies affects the formation of spiral arms and tails to have different forms of spiral galaxies. Introduction Conclusions and References A good bridges that are reasonably dense and narrow clearly rise if the mass of companion galaxy is relatively small. A long, curving tail rise if the mass of the companion is roughly equal to the victim galaxy. Otherwise, a very thin tail or no tail is formed. Although there are many factors that affects the formation of galactic bridges and tails, we do observed that the formation can simply be form from gravitational force model. Toomre, Alar, Juri. “Galactic Bridges and Tails”. The Astrophysical Journal, 178. (December, 1972), pp Merging of galaxies are one of the most dynamic events in the universe. When two galaxies interact, tidal (or gravitational) forces dismantle the stars into classic tidal features while other materials such as dark matter is compacted causing verbose star formation. The fact that all these features are simply caused by gravitational force is rather astonishing. To create the model, Toomre used three-body code to simulate the galactic interaction. In Toomres’ model, the interaction between stars and other materials that affect the formation of peculiar galaxies are being ignored to simplify the model and just focus on the effect of tidal force. What we are interested here is the formation of spiral arms or “bridge” caused by small companion or the formation of a long and curving “tail” from far side of the encountered galaxy caused by roughly equal or heavier companion. I start out by implementing Toomres’ model in more simple way. I fixed the “victim” galaxy at the center with five discrete rings of stars orbiting the center and have the companion pass near the “victim” galaxy to observe how spiral arms or tails can be form. In this model, we will see only one spiral arm or tail because we have ignored the parabolic passage of the interacting galaxies, meaning the far-side tidal force is being ignored. Then, I further implement the model so that each galaxy is moving in a parabolic passage from the center and observe how the size of the orbit (or distance between the two galaxies) and the mass ratio between the center masses of each galaxy affect the formation of bridges and tails. Formation of a Spiral Arm & a Long, Curving Tail To create a bridge and a tail, I first need to determine the separation of the two galaxies. If the separation between two galaxies is too great, then they would barely interact but if the separation is too close, then the interaction would happen too quickly, producing a very thin tail. The center-fixed galaxy simulation Since the purpose of the center-fixed galaxy simulation is to have an idea of how a bridge or a tail forms, I will not too worry about determining the proper separation between the galaxies and just focus on the dependence of the mass ratio in this simulation but when I get into the actual simulation where two galaxies are moving in parabolic passages, then I will need to determine the proper separation. The center-fixed galaxy simulation shown below shows the evolution of the galaxy forming a bridge and a tail that depends on the mass of the companion galaxy. If the mass of the encountering galaxy is notably less than the galaxy at the center, then a spiral arm is formed. In addition, if the mass of the companion is not too far less, or greater then sometime a very thin tail is also formed. If the mass of the encountering galaxy is roughly equal, then a long, curving tail is formed. Also, due to the strong gravitational pull caused by the companion galaxy, we observed that some of the stars of the center galaxy are being captured by the companion galaxy. The galaxy at the center is being encountered by its companion galaxy Some of the outer-stars are being captured by the companion galaxy A long, curving tail is formed A spiral arm is formed and also a very thin tail is formed due to the stars pulled by the companion galaxy. Theoretical Result: Galaxies moving in a parabolic passages Before, we observed only one spiral arm because since one galaxy was fixed at the center, we ignored the tidal force caused by shifting of the center-of-mass of the “victim” galaxy due to its companion. Now, we are going to look at two galaxies moving in parabolic passages and thus include the ignored tidal force in center-fixed galaxy simulation. The figures shown below (taken from Toomres’ journal) shows what the simulation should look like in three different situations with a proper separation of two galaxies. A D irect Parabolic Passage of Equal Mass Companion A D irect Parabolic Passage of a Heavy Companion A D irect Parabolic Passage of a Small Companion