Dr. Johnson’s Lab
Both Sabrina Marell and I are working on the understanding of galaxy cluster mergers (the combining of two galaxy clusters). Galaxy clusters are some of the largest structures in the universe and are formed through gravity acting upon galaxies, pulling them together. Now, if gravity were the only force acting upon the galaxies it would be expected that the clusters would form in spheres. In reality, the galaxies flow along filaments and, in between, there are voids of empty space, creating an almost cobweb-esque look (Figure 1). This leads scientists to believe that there is a repelling force acting upon the galaxies that we can’t see- this is what is called Dark Energy. It is believed to be the cause of the expansion of the universe. Simulations were run, such as the one below, to create data sets to work with in research, like Sabrina and I are doing. The simulations we used were run with two groups of galaxies, either each the same mass or one ten times as massive as the other. The collisions were then either head on, offset by half, or just missing each other. By using these combinations of data sets, we are able to get a good picture of what is actually happening in the universe.
Figure 1: Image of universe structure from Millennium-II simulation. The dark areas represent the voids, or empty space, and the lighter areas represent where normal matter, such as galaxies is found.
My research focuses on the methods used to measure the masses of these large galaxy clusters. The method I am most focused on is using the Virial Theorem to calculate the mass using the average velocity of the cluster. The Virial Theorem states that to keep an object in orbit its gravitational potential energy must be equal to two times its kinetic energy (this is shown through a really long proof that I’m not going to show here). This equation (in the simplest form), solved to find the mass of an object, should then read:
Where, in our case, M is the total mass of the galaxy cluster, R is the radius of the galaxy cluster, v is the mean of the velocities of all the galaxies within the cluster, and G is the gravitational constant.
Now, you would think that using this equation wouldn’t be a problem when estimating the mass of these galaxy clusters since we are able to find an average velocity for galaxy clusters. But, what I am trying to show in my research is that the velocities of these galaxy clusters are actually changing during a merger, which causes a problem when trying to use the Virial Theorem to solve for the mass. If the velocity does change during a merger of galaxy clusters, this could cause mass values to be widely over- or under-estimated depending on when the measurements are being taken.
To calculate this potential difference in velocity, or the velocity dispersion, I took data from the computer simulations depicting galaxy cluster mergers over time. Using Python to write a code to read the data in from these files and do calculations on it, I was able to create graphs of sigma over time, with error bars. There are graphs for X, Y, and Z velocities, where X and Y are the plane on the sky (so up/down and left/right) and Z is the recessional velocity, or the velocity where the galaxies are moving away or toward you. In the simulations, there are 100,000 particles to choose from each time step (the time steps are every five million years). In my code, I use around 100 to 1,000 particles, each representing a galaxy, from each galaxy cluster involved in the merger. The particles are chosen at random by my program, each time it runs through. This is referred to as “Monte Carlo sampling”. The more particles needed from each cluster, the longer my program takes to run.
Figures 2-4: The three plots above are 3D position plots at three important times. The starting position (time = 0 Myr), when the clusters first cross over each other completely (time = 65 Myr), and when they are the farthest apart until they start to move together again (time = 170 Myr).
Using the velocities of these particles, my code then takes the standard deviation of this list of either X, Y, or Z velocities. This is the velocity dispersion, or sigma (σ). By then calculating the standard error of sigma, I am able to start to graph the values in Python. For each time step, sigma and the standard deviation of sigma is calculated and graphed versus the time step (Figures 2, 3, 4). The error bars are the standard deviation of sigma. As it can be seen, the velocity does change over time during a merger. Black vertical lines indicate when the clusters are first fully over top of one another, when they have passed through each other and are the farthest apart before they move towards each other again, and then when they are once again right on top of each other. The blue and red indicate the different clusters.
Figure 5: Velocity dispersion in the X direction over time is shown here.
Figure 6: Velocity dispersion in the Y direction over time.
Figure 7: Velocity dispersion in the Z direction over time.
In the next couple weeks, I am going to work on two things. First, plotting the velocity dispersion over time for all of the simulations run and then taking that data and projecting it onto different axes to try to get a different perspective. The second project I hope to attempt is more of a visual one. I am Physics major, but I am also a Studio Art major. Dr. Johnson and I are hoping to create 3D position graphs of the simulation data that are more interesting and visually appealing. One specific graph I hope to create is actually interactive- it will be a 3D position graph, but with a slider to move the data through time and have the viewer witness they merger.
Figure 8: XY projection of velocity dispersion over time. See how it is a combined image of the X and Y graphs? That’s what it means to project onto the XY plane.
I was also lucky enough to work with Dr. Milingo, another astrophysicist in the Physics department here, for a week in Arizona. I worked alongside her, as well as Sabrina Marell and Ross Silver, in gathering data for Dr. Milingo’s research on spotted stars. Gettysburg is part of a consortium called “NURO”, or the National Undergraduate Research Observatory. With this consortium, Dr. Milingo gets allotted time to use the 31” telescope in Flagstaff. We were able to learn to work and use the programs at the telescope to help take pictures of the star cluster NGC 6811, which Dr. Milingo then uses to analyze the sun spot cycles of these stars. Out of our four allotted nights, we were able to observe for three, as it was cloudy the last night.
Figure 9: This is the NURO telescope, a 31” diameter telescope that we used to take pictures of the star cluster, NGC 6811.
Figure 10: (From left to right) Ross working on logging the images, Mikayla (myself) working on taking the images, and Sabrina working on moving the telescope and tracking our star cluster (yay Autoguider!).
Of course, we also had the chance to do a lot of fun activities while in Arizona! The four of us were able to visit Sedona, a supposed “vortex”, see a movie, and visit the Grand Canyon. It was truly an amazing trip. Here are some of the sights from the trip:
Figure 11: The sun setting behind NURO.
Figure 12: The red rock formations of Sedona.
Figure 13: The Grand Canyon.
It’s not all just work in our lab- we also do some fun activities as a lab! Every day we take a “hack break” where Sabrina, Ross, Dr. Johnson, and myself (and sometimes Julia Giannini) go outside and hacky sack all together. The point behind this is to take a break from staring at a computer screen all day and get some physical activity in. Trust me, it’s WAY more physical than you think! I once tracked my fitbit steps during an approximately 30-minute hack sesh, and it was about 1,500 steps! It’s also nice to activate a different part of your brain, and it sometimes helps me think through problems I have when trying to figure out how to code something. We also sometimes go out to the Gettysburg Observatory and take images of star stuff, like planetary nebulae. Then, we take our images and create a complete image of the object we were taking pictures of.
Figure 14: Ross, myself, and Sabrina hacking on the edge of the Grand Canyon. (Don’t worry, it was posed!)
Figure 15: Our image of the Ring Nebula, taken with a CCD at the observatory on an 8” telescope.