While the mechanism for the configuration of galactic structures has been largely attributed to dynamic effects, propagating star formation provides many of the observed properties of galaxies and may be the dominant mechanism for converting gas into stars. This model presents star formation through percolation as the main mechanism for the development of galactic structure. A region of a galaxy containing the necessary ingredients for star formation (gas, temperature), will alone form nothing. The explosion of a massive star into a supernova provides energy to compress interstellar gas into a dense molecular cloud form which stars form. Because the supernova itself is the result of earlier nearby star formation, it is a source of percolation; some of the stars formed may become supernovas themselves and repeat the process. The uncertainty and probability for star formation is contained within a single parameter p, the probability that a supernova explosion in one region gives rise to star formation in a neighboring region, which, in turn, results in the formation of another supernova. This is based on conditions such as gas density and supply, lifetime, and location relative to other stars. The effect of changes in this and other parameters will be shown using the simulation.
The galaxy is also modeled with a constant circular velocity, and therefore variable angular velocity at certain radii. The appearance of spiral arms is a s a result of this differential rotation within the galaxy. Changes in the number of rings, the circular velocity, and the probability of star formation modify the structure of the simulation showing different growth and structure within the galaxy.
The simulation operates such that star clusters placed into a small number of cells in the grid at random creates star in adjacent cells with the probability p in the next time step. The galaxy rotates and the process is repeated. The size of the star is proportional to it age, and as the supply of the necessary ingredients to star formation ins exhausted the star become inactive. This process is repeated as many times as desired to simulate the evolution of a galaxy.
Percolation involves the collective behavior of a system of particles. This system is composed of many individual constituents which, though different in nature, can exhibit common properties under certain conditions. For a galaxy, the explosion of a star into a supernova provides enough energy to trigger the propagation of star formation. Some of new stars that form from compressed molecular gases as a result of the explosion may become so massive that they too explode and repeat the star formation. This chain reaction is a process of percolation that fills the galaxy with stars.
The nature of this polar grid is such that each ring has six more cells than the previous ring. The cell denoted by a filled circle in the picture represents a region in the galaxy containing an active star. This star can cause star formation in the neighboring cells above, below, and to either side (the empty circles). A grid of a limited number of rings was suspected to produce results similar to the image below (according to Schulman and Seiden).
Here, star formation is shown for a time step of 10^7 years. This same nature can be observed by imputing a low value in the "# of rings" value field. A high number of rings will result in a more densely populated image. The pictures below are from the article "Coherent Galactic Oscillations" by Schulman and Seiden.
These pictures show proposed spiral galaxies as a result of percolation. The structure of these galaxies include ring structure, two-armed spirals, and single-armed spirals. The galaxies produced by the galaxy simulation program bear a striking resemblance to those projected by Schulman and Seiden.
PRACTICE:
This program allows you to create your very own galaxy. It is up to you to decide what your galaxy will look like by changing certain parameters. By trying different combinations of values, you can study the types of galaxies that will form. In some cases, the values you set may not prove favorable conditions for galaxy formation. Depending on the parameters, your galaxy may look very similar in structure to galaxies found everywhere in the universe. The link below provides a catalog of galaxies. Try to see how close your galaxies come to repeating the structures of real galaxies.
http://astro.princeton.edu/~frei/Gcat_htm/cat_ims.htm
You are also given the option of creating a finite or an infinite galaxy. The finite model implies the exhaustion of material within the galaxy which causes star formation. That is, once a star is formed and dies out, another star cannot be formed in its place. The galaxy will form, rotate, and die. This, of course, is over a time span of millions of years. The infinite model does not restrict star formation in that it does not exhaust materials.
This galaxy will form according to the default parameters. To change these parameters, enter new values for the number of rings, the circular velocity, and the probability p of star formation. Entering in a positive value for the velocity will make the galaxy rotate one way, while a negative velocity causes rotation in the opposite way. Large values tend to cause star formation to occur rapidly, as the active stars come in contact with more cells in a shorter period of time. The probability can be given any values between 0 and 1. It is interesting to see the effects of no percolation (p=0), but some velocity. The image below shows this very case.
The initial randomly activated stars rotate and age, but do not cause star formation. Allowing only for percolation, or no rotation (v=0), also results in an interesting simulation...
The graph button displays a histogram of the number of stars at a certain age. For a finite galaxy, the graph looks similar to graph A below. An infinite galaxy shows a graph like graph B below. The latter graph clearly shows how there can be new stars and old stars in large quantities at the same time where stars that die out are replace by new stars.
A). The graph for a finite galaxy.
B). The graph for an
infinite galaxy.
It also shows the time at every stage during the growth of the galaxy. Since the time step is 10^7 years, if you consider the time of beginning of the galaxy as the beginning of the universe (which is about 15 billion years old) it would take 1500 time steps to make a simulation of a galaxy that could be seen today. The interest of this simulation is that it is possible to see what a galaxy looks like from its beginnings, as well as what it will look millions of years into the future.
INSTRUCTIONS:
To begin the creation of your galaxy, press the Run button. To stop or pause the growth of the galaxy, push Stop. To restart once the galaxy is stopped, simply push Start. Pushing the Graph button will display a graph (as delineated above). The graph can be moved and resized with the mouse. To clear both the simulation and the graph, push Clear. Choosing either "Infinite Galaxy" or "Finite Galaxy" from the scroll-down choice box will cause the simulation to proceed as directed. Note: Once the simulation has begun, the parameters for galaxy formation cannot be changed.
WORKS CITED:
Lawrence S. Schulman and Philip E. Seiden, "Percolation and Galaxies", Science, Vol. 233, 25 July 1986, p. 425-431.
Humberto Gerola and Philip E. Seiden, "Theory of Dwarf Galaxies", The Astrophysical Journal, Vol 242, No. 2, December 1980, p. 517-527.
Philip E. Seiden, Lawrence S. Seiden and J. V. Feitzinger, "Coherent Galactic Oscillations", The Astrophysical Journal, Vol. 253, No. 1, February 1982, p.91-100.
Harvey Gould and Jan Tobochnik, An Introduction to Computer Simulation Methods: Applications to Physical Systems, Reading, Massachusets: Addison-Wesley, c. 1996, p. 663-668.
Java In A Nutshell, p. 68-70.
Dr. Wolfgang Christian, Davidson College
Dr. Laurence S. Cain, Davidson College