Clusters of Coded Dots

The sky is a strange place. My name is Braden Wolf, and I am working under Dr Johnson studying the dynamics of galaxy clusters. In other words, we are looking at how the motions of galaxies in clusters affects the modelling and observation of such celestial objects. Galaxy clusters typically have diameters between 1 and 5 Mpc, where 1 Mpc is 1 million parsecs, and 1 parsec is 3.24 light years. So, 1-5 Mpc is 3,240,000 ltyr to 16,200,000 ltyr, which is a quite significant distance. The speed of light is, by definition, 299,792,458 m/s, or 670,616,629 mph. A light year, by definition, is the distance that can be covered by light in one year. Therefore, if it takes light up to 16.2 million years to travel from one side of a galaxy cluster to the other, the galaxies in the back of the cluster can move quite a distance until their light catches up to the galaxies in the front, or even the middle of the cluster. The result is that observations of the cluster can cause galaxies to appear to be in a different location than they actually are relative to the other galaxies in the cluster. Cosmological simulations, on the other hand, do not take into account light travel time in their “snapshots” of galaxy clusters, and this leads to models that might not be quite representative of the observations that we are making of actual clusters.

Cosmological simulations model trillions of particles over the entire lifetime of the universe, using the computationally expensive n-body gravitation model, where each particle has a gravitational effect on every other particle in the simulation. Simulations such as these take a lot of data space, and therefore only release a certain number of snapshots from the runtime. For example, the simulation I am using right now, called Eagle, has released 28 snapshots over the entire life of the universe, with the snapshots being placed closer together in time as the age of the universe increases. For the 7 most recent snapshots, the time cadence is about 100 million years. Now, unfortunately, this is not quite short enough for what we are looking for, however, we are still using this simulation in order to develop the code used to analyze the data. The issue with such a long time cadence is the fact that light can travel through the entire cluster in 3-16 million years, much less than the resolution that we are able to track. In order to overcome this while we develop the analysis code, we adjust the speed of light to be 10% or even 1% of its normal value, to simulate a better time cadence between the simulation snapshots. While looking for simulations, we contacted 13 simulations, either by email or through direct website contact pages, looking for one that has a suitable time cadence. Most of the simulations are run a really high time cadences, sometimes even on the order of tens of millions of years, but due to data storage constraints, they only save a limited collection of snapshots. Some of the simulations had snapshots around 10 Myr apart, but most of them ranged around 80 to 100 Myr between snapshots.

So far in the summer, I have written code to adjust the galaxies’ position in a projection, using both velocity of the galaxies and the various snapshots recorded by the simulations. The code itself uses a couple of simple tricks to find the adjusted time model from the global time model that the simulation outputs. Originally, I used the velocity of a given galaxy and its distance from a given point in the cluster (either the closest galaxy to an observer or the center of the cluster) to find the new position of a galaxy. This method is good for a first approximation, and it can create pretty plots such as Figure 1, but it does have the disadvantage of not accounting for the acceleration of the galaxies diverting their paths, which limits the amount of statistical analysis we can do.

The second, more refined method we are using takes a galaxy’s distance from the center of mass of the cluster, which, because the speed of light is constant, allows us to compute the light travel time from the galaxy to the center of the cluster. For this test, we take the seven youngest snapshots from the simulations (22-28), and define snapshot 25 to be the one where the cluster center of mass is. Since we know the light travel time from each galaxy to the center of mass of the cluster and the time separation of each snapshot from snapshot 25, we can calculate which snapshot each galaxy is closest to. When we have that information, we can then take the position, velocity, and mass of the galaxy in that snapshot and add it to a collection of data, where all of the galaxies’ identifying information is stored. Figure 1 shows one example of this method, using 9 snapshots. The central snapshot in the diagram is snapshot 5. The goal is for each galaxy, to find which snapshot line it is closest too, and then obtain that galaxy’s physical information from that snapshot.

Figure 1: A diagram of how the projection method works, courtesy of David DeAngelo, ‘23

From this array, we are able to create a model of the cluster that shows both the original data (where all the galaxy position and velocity data is taken from a single snapshot) and the adjusted data (where the galaxy data is drawn from their closest snapshot). This plot for one cluster, which contains 1700 galaxies, is shown as Figure 2. This plot is derived from the velocity method.

Figure 2: Plot of a galaxy cluster, showing original and adjusted positions, using the velocity method

If we zoom into that plot far enough, you can actually see that the two points are plotted, one in green, and one in purple. The green point is the location of the original data, and the purple one is the new data.

Figure 3: Marked Galaxy pairs, zoomed in from Figure 2

Now, Figure 4 is made using the snapshot method. This is the first time we have been able use this method to develop a plot, so there are still some revisions and optimization work to do. It takes about 2.5 hours to generate this plot. This is for a different cluster, with about 5300 galaxies. One possible explanation for the odd shape of the plot is that the cluster is moving through space, and therefore, the galaxies at different times appear to be in a different location relative to the cluster center in snapshot 25.

Figure 4: The cluster with the galaxies adjusted with the snapshot method

Once the new galaxy data is collected from the snapshot method, there are two steps that will be taken on next. First, the data will be projected cleanly onto a 2D plane, so that it would mimic the appearance of a galaxy cluster as observed from earth. Once that is complete, we can begin statistical analyses of that data and compare it to the same exact equations applied to the original dataset. We will use code written by another student to compute statistical averages of both datasets and see for a collection of clusters in the simulations if the adjusted dataset has significantly different values for those measures.

Hacky sack, of course, makes up one of the most dependable rituals of the summer. Whereas last year, I was just beginning to learn, this summer, with one year more of experience under my belt, I have found a role in the circle- lunging forwards into the center of the circle to try and keep the hack alive. Additionally, now that I have pretty much mastered the basics of the game, I can also begin to experiment with more exotic moves, which would make even more fun hacks possible. Surprisingly, the most successful hacks we have are when we are not actually paying that much attention to the circle, but rather when we are in the middle of some other conversation about a complex (or otherwise involving) topic, and we are just playing unconsciously.

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