My Ph.D. research looked at the key factors contributing to the duration of galaxy mergers. The merger-times of galaxies are a cornerstone in semi-analytical models of galaxy evolution and the accuracy of these merger models helps to predict key observable properties in galaxies. Below I give a brief description of a few of the key concepts involved in my work, however, for a more detailed description please contact me for a copy of my thesis.
Semi-Analytical Models (SAMs) are one of three main ways that we study galaxy evolution. SAMs work by combining several analytical prescriptions of physically important processes using the underlying cosmological structure formation as a guide. You can imagine this as 'painting' a distribution of galaxies (or black holes) onto the underlying distribution of dark matter halos and tracking key properties as they evolve according to a given analytical recipe. A key constraint is matching observed galaxy properties to the simulations at one or more times (redshifts). There is a significant amount of approximation involved, however, the advantage comes from the fact that they are computationally cheap and allow large amounts of parameter space to be studied quickly.
An important question is how to incorporate the underlying structure formation (associated with the cosmology) to the galaxies. Currently the most accurate way to characterise a cosmology's structure formation is through N-body simulations. These simulations take an initial distribution of particles (based on Cosmic Microwave Background measurements) and evolves them under the effects of gravity. This video shows the structure formation of a small volume of the universe over several billion years (although it isn't shown, the volume is also expanding under the influence of dark energy).
The next important question is how to get the key information about the structure formation so that it can be incorporated into the model. This information is best represented by a merger-tree; A merger tree essentially maps which structures are merging with each other and when. It also keeps track of the size of halos as they evolve with time. It is a very complex process, but the end result should look something like the figure below.
This shows a Milky Way sized halo as it grows over 13.5 billion years. The figure above filters out the contributions of very small halos, however, when they are included these merger-trees can be very large and complex. If you are interested to see how large they can be download this image and zoom in and out to see the halos (acroread seems to work best). Be warned that it may challenge your computers graphical processing.
Galaxy mergers are analytically described as a combination of gravitational free fall and dynamical friction. Dynamical friction is a drag force which results from the accumulated 2-body interactions as a particle travels through a sea of background particles. The presence of this drag force means that a smaller galaxy will spiral to the centre of a larger galaxy. Based on this and after a lengthy derivation, which I will not go into here, your can produce a analytical formula for predicting the time it takes two galaxies to coalesce. The resulting formula highlights four key properties; the mass ratio of the two galaxies, the dynamical timescale of the host (similar to size, but not exactly), the eccentricity of the orbit and the orbital energy.
My research has critically examined this formula in realistic situations to see whether it gives a good approximation of merger-times.
In the final year of my undergraduate degree I did a research project on Lagrange's five points of gravitational stability. These are unique points around any orbiting two body system where a dramatically lighter body will find a gravitational equilibrium. For this project I developed a software package to numerically test the dynamical stability of each Lagrange point.
While the gravitational forces (from the two massive bodies) cancel at all Lagrange points, some of them are more stable then others. The stability of the point is analogous to putting a ball in various places and seeing whether it roles in a particular direction. L4 and L5 are dynamically stable and are like putting the ball in a bowl; If you give it a push it will just role back to the centre of the bowl. Although these points are not used for any man made satellites they often collect material naturally such as dust, meteors and sometimes even moons. Conversely, the L1, L2 and L3 are only partially stable and they are like a saddle. If you put a ball in the middle of the saddle it is will roll back towards the centre if pushed directly forwards or backwards, however, if you push it to the side it will roll off.