Exploring Galaxy Cluster Dynamics in Phase Space

This summer, I experienced my first real taste of what scientific research is all about. Having done nothing of the sort prior to this summer, it took a while to get the wheels rolling. I was thrown into an unknown environment working with unknown tools to explore an area of science I knew nothing about. But that is exactly what research is for.

In Dr. Johnson’s lab this summer, I was tasked with exploring the dynamics of a simulated galaxy merger in an effort to understand the dynamics of large-scale structures in our universe. The simulation in question was performed in the late 2000’s by Dr. Zuhone, an Astrophysicist working for the Harvard-Smithsonian Center for Astrophysics in Massachusetts[1]. His simulations were aimed at capturing the effect that a galaxy merger would have on dark matter, which is collisionless, meaning that interactions with other particles have very little to no effect on the system as a whole. The reason that we can model galaxies in a similar way is because both dark matter and galaxies are collisionless and therefore their dynamics should be the same in the event of a merger. The data I worked with was only a small chunk of the enormous and numerous simulations performed by Dr. Zuhone. I was given the xyz-positional and velocity data of one-hundred thousand “galaxies”. My goal was to track these galaxies throughout the merger simulation and plot them in what is known as phase space. Phase space plotting is a method used to plot higher dimensional data in lower dimensions. For instance, when trying to understand the dynamics of three-dimensional space, a phase space plot can show it more plainly in two-dimensions.

My goal in research this summer was to begin to understand some of the dynamics of fourth-dimensional space using this phase space plotting method. The entirety of my work this summer has been on Python. I have been writing a program that gathers, groups, normalizes, and plots the simulation data. This process did give me an incredible opportunity to enter the research world and get a taste of what full time research would be like, at least from a computational standpoint.


Figure 1. Final working code in Python

The most important part of this research are the graphs and figures I’m able to produce. Phase plots are not as straightforward as normal plots would seem. This plotting style is particularly useful in the plotting and analysis of light curves. The process of creating the plot is somewhat confusing and unnatural. To start, it’s important to understand what the data I dealt with looked like. Of the hundred-thousand “galaxies” previously mentioned, about fifty-one percent came from one cluster while the remaining forty-nine came from the other. My goal was to see if “galaxies” from either cluster exhibited any dynamical differences. The data I received for the merger simulation stretched over seventy-one timesteps, so I had to track the “galaxies” throughout the merger. My program was designed to take an equal amount of randomly chosen “galaxies” from each cluster and gather their position and velocity data over time.

Even though seventy-one time steps is quite a lot, one issue that came up was that they were not all sequential. Some time steps data had been corrupted and therefore lost. I needed to interpolate twelve missing time steps, which was done using linear interpolation. Once all the data was compiled, interpolated, and subsequently normalized, I grouped my data by variable. Then I grouped the values into successive groups of three. These groups of three values then acted as the x, y, and z-coordinates for my phase diagram. This section from a paper by Nada Jevtic illustrates it very clearly.


I used this method of plotting with my simulation data to create plots like this. Position measurements have been normalized and are in units of cm. Velocity measurements have also been normalized and are units of cm/s.
X-Position: (two separate sets of 10 “galaxies”)


Red lines: Cluster 1

Blue lines: Cluster 2
X-Velocity: (same sets of 10 “galaxies”)


I am now at the analysis stage of my research and plan to have an in-depth analysis of all of the graphs over the coming weeks prior to our return to campus in August. Dr. Johnson has given me and the rest of the students in the lab a good bit of independence so that we develop troubleshooting and problem-solving skills on our own, instead of relying on others as a crutch. Even though the eight weeks are just about over, I’m excited to continue my research at home as well as through the upcoming school year.

But now I must talk about the only reason I chose to do research this summer. The mystical ancient art of hacky-sacking, foot-bagging, etc. There are few schools throughout not only the United States but the world that study the art. Dr. Johnson’s hack circle appears from the outsider’s perspective to be nothing more than people in a circle kicking a bag full of assorted beads. But once you enter the circle, your entire world changes for the better. You learn patience, teamwork, how to succeed with style and smack talk, and most importantly how to fail while simultaneously looking like you’ve forgotten how to use your legs.

Hacking offer’s a reprieve from the constricting world of Python(bonus pts for the pun). Hacking is a time to reflect on yourself and what you’ve done, what you still have to do and is great to refocus yourself because you just lost half an hour kicking a sack around. For me hacking has been a stress-free environment that I can use to clear my head and get revitalized for the rest of the day. As an unexpected but welcome bonus, I have also learned basic teleportation and levitation from my time studying at the Johnson School of Hacking. I have learned the proper form of arms above the shoulders and to always look for “fours” and “elevens”. Hacking is both an incredibly individual activity as well as a group activity. It has taught me that to succeed you can’t rely on one person, even if they’re as good as Dr. Kerney, and that focusing on working as a team is the best way to solve any and every problem. Working off of each other’s strengths and weaknesses to form a cohesive and functioning machine is what being a team and being a researcher is all about. I can’t, and most definitely do not, know everything there is to know about research, my field, or physics in general. But I know that to succeed it’s going to take a lot of work from me but also, a lot of faith in others.

~Hayden Hall

Really important link : https://www.youtube.com/watch?v=czTksCF6X8Y

[1] https://arxiv.org/abs/1004.3820


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