9
Results

9.1      Summary

What follows is a chapter-by-chapter summary of the main results.

·         In Chapter 1, we have described thesis objectives and methodology used in the thesis.

·         In Chapter 2, we have shown that physics education is an important and crucial element for human society. Students should be more motivated by their teachers with less importance on learning and more emphasis on differentiation, individualization and self-teaching. It is for this purpose that the formation of self-teaching projects is suggested. Together with advancement in science and technology, an early connection of education and research should be made. Self-teaching educational-research projects created by specialists in their fields should be made freely available on the Internet as a service to society. A research method of education can develop student’s abilities in a complex way. Computer models and simulations of nature’s behavior are acknowledged as useful, providing connections between various fields of science education. A scheme incorporating these approaches is suggested in the “four-level educational architecture”. Surely, education is a complex system and this concept may not be valid for every student.

·         In Chapter 3, we have sketched our basic understanding of nature, laws of physics, models, simulations and confusion among them.

·         In Chapter 4, we have shown how to simulate the effect of the gravitational field and of Newton’s laws of motion to move the stars around. I described my implementation of Barnes-Hut algorithm for many-body simulation and novel geometry-based construction of the 3-dimensional Hilbert’s curve. Simulation code works in four steps. First, a tree is constructed by space decomposition from a list of bodies that form the simulated system. Space is divided utilizing Hilbert’s self-similar space-filling curve. Groups of close bodies are created. Second, centers of mass of individual nodes are computed. Third, accelerations are computed with the Barnes-Hut algorithm. Fourth, new positions and velocities are computed. Thanks to this algorithm, all simulations will be fully self-consistent, i.e. no rigid potentials will be employed.

·         In Chapter 5, we have shown how to create a computer model of a galaxy in order to study galaxy dynamics. We found that the construction of galaxy in a controllable way is difficult. Due to immense complexity, all models are very artificial in comparison to real galaxies. In spite of that, the initial density distribution function of models are in good agreement with observations of real galaxies. The galaxy models created were single or multicomponent systems in stable dynamical equilibrium.

Initial conditions were generated as follows. Specifying the mass density distribution function, we first calculate the model’s cumulative mass distribution function and corresponding gravitational potential. Then the mass density distribution function is expressed as a function of gravitational potential. The phase-space distribution function is calculated on the fly using a numerical formulation of Eddington’s formula. Once the phase-space distribution function has been calculated, one can start to randomly sample particles from the distribution function. If the use of another mass density profile is requested, all that is necessary, is to override a virtual function “rho” according to the chosen mass density profile. Through this approach, many kinds of models may be constructed. Models created in this way are quickly getting into equilibrium.

We created realizations of an elliptical galaxy from various spherical models. The spherical models were in equilibrium from the beginning. We have created disk models that showed continuous evolution. We saw that dynamically cold disk without a dark halo spontaneously formed features resembling galactic bar and spiral arms. It has been shown that a self-gravitating disk system is unstable unless a certain velocity dispersion and dark halo were included. All models were evolved for more than 1 billion years and movies from all computations were produced.

·         In Chapter 6, we have demonstrated how to study galaxy collisions and mergers with computer simulations. Interacting galaxies are very complex and highly dynamic systems. With modest computational resources, we performed computer simulations of galaxy interactions that are in excellent agreement with observations. These simulations provide an accurate and entertaining insight into galaxy collisions and mergers.

However, model results were not without their shortcomings. Our aim was not to study interactions in detail, but to show how such study can be done with all details provided. We studied the evolution of spherical galaxy interactions, minor and major mergers, and galaxy harassment.

We simulated the evolution of the Milky Way galaxy, the Large and the Small Magellanic Clouds and all 19 known satellite galaxies of the Milky Way. We have simulated the future evolution of the Local Group in the collision of two disk galaxies representing the Andromeda galaxy (M31) and the Milky Way galaxy. Models were evolved for up to 8.1 billion years and movies from all computations were produced.

·         In Chapter 7, we have shown how to prepare our simulation for the alternative gravity model. We have learned that the simulation of a galaxy in Modified Newtonian Dynamics (MOND) theory can be performed with at least the same result as the simulation in Newton’s theoretical framework. Cosmological large-scale dark matter computer simulations performed by other authors agree with the observations, while the results on galaxy scales are inconsistent. These simulations with dark matter may miss some important small scale physics of both baryonic and non-baryonic matter that is not resolved with a current resolution of cosmological simulations and computer models, while the standard model can be accurate.

One should be cautious, however, as the theory is stretched and adapted to fit the evidence, or facts are carefully selected to fit the theory. We learned from the history of physics that models of nature usually comprehended a lot of things accurately, but also usually missed important big ones. Mordehai Milgrom and others has done interesting work that healthy competes with dark matter theory. In any case, even if MOND should be revealed as an incorrect theory, it serves as a good exercise for galaxy modeling. We should keep in mind that “laws of physics” are not an accurate description of nature.

·         In Chapter 8, we have presented the main features of simulation programs and how to use them. I developed several software tools for this thesis that are available publicly to the community. GENICS (Generator of Initial Conditions) and AMON-2 (Astronomical Modeling with N-bodies) contain together over 9,000 lines of C++ source codes. DIGALEX (Digital Galaxy Explorer) contains over 5,500 lines of C++ source codes. All of the source code of software is available at http://www.kof.zcu.cz/st/dis/schwarzmeier/ or on the companion Digital Versatile Disk (DVD), and is released under the GNU General Public License (GPL).

I have created 70 animations that show simulated N-body systems described in the thesis. These animations are also available on mentioned internet website and on the companion DVD. I invite you to visit this website and explore all of these animations.

Shortened version of this thesis was presented at the conference “Moderní trendy v přípravě učitelů fyziky 3”, Srní, Czech Republic, April 2007 and was accepted for publication in conference proceedings (Rauner, 2007). Parts were presented on two monthly meetings of our department and on the annual meeting of Ph.D. students of “Theory of Education in Physics”.

9.2      Conclusions and future prospects

For the first time, a complete educational description of computer simulations of galaxy dynamics, from initial conditions generation to visualization is described in detail. It was framed into the self-teaching educational-research project. All parts of the thesis (both printed and electronic) are available for all interested on the internet website of the Department of General Physics.

The understanding of galaxy formation, evolution and interaction is obscured with complexity and uncertainty in the modeling of physical phenomena involved in galaxies. Future improvements of models should come with additional physics, and more of such self-teaching educational-research projects should be created and made publicly available.