# Where’s the Limit?

by Aarthi Koripelly

The Sloan Digital Sky Survey imaged over 600,000 galaxies using the Hubble. Our group used a data set containing 20,000 galaxies. More specifically, we took a look at the axial ratio and local density of the galaxies. The axial ratio of the galaxy is the ratio of the short radius of the galaxy to the longer radius of a galaxy. If the axial ratio of the galaxy is greater than or equal to 0.7, then the galaxy will be rounder. An axial ratio of 1 is a galaxy that is a perfect circle, meaning both the short and long radius are equal to each other. An axial ratio greater than 0.2 and less than 0.7 includes galaxies that are long or oval shaped. We filtered our data out with galaxies greater than 0.2 because when a galaxy has an axial ratio less than 0.2, the image is actually incorrect. This means that the galaxy is “edge-on” and the image was taken from a bad angle. Adding on, the local density is the number of galaxies in a galaxy cluster. Therefore, when the local density of a cluster is higher, the more galaxies would be in that cluster.

Our hypothesis stated that galaxies that are rounder (axial ratio >= 0.7) have a lower local density and galaxies that are more oval shaped (axial ratio > 0.2 & < 0.7) have a higher local density.

We came up with our hypothesis based on an analogy comparing cupcakes and brownies. Cupcakes are rounder like round galaxies, whereas brownies could be longer like oval galaxies. We first need to imagine that a brownie and a cupcake have the same volume. This way the brownie could be cut long and thin, whereas the cupcake would have a larger diameter. Therefore, we could fit more brownies side by side in a pan than cupcakes, if they are the same volume. We compared this theory to galaxies. We thought that if a rounder galaxy had a larger diameter than a longer galaxy, a rounder galaxy would take up more space in its galaxy cluster. Therefore, there would theoretically be less galaxies in a cluster with round galaxies.

My role on the team was mainly using python programming for data analysis. I used Jupyter Notebook to create most of our bar graphs. A complication  that came up was trying to graph negative values as well. Many of the local density values are negative because they are in logarithmic form. Therefore, it took some trial and error for figuring the problem out. I used python (programming language) to code. The two most prominent packages I used were Bokeh and Matplotlib. Bokeh helps with data visualization and making the graphs look pretty, whereas Matplotlib helped with actually making the graphs. I also linked our code to the Github for anyone who wants to take a look at it. (Here is the link: https://github.com/AarthiKoripelly)

Based on our analysis, we found that our data did support our hypothesis. The average local density values were all higher for long, oval galaxies compared to round, circular galaxies. The graph below shows this in more detail:

We were actually very surprised by the results. Initially, we thought maybe the data we would find would not support our hypothesis because space is infinite, so there couldn’t really be a bound to how large a galaxy cluster could be. Therefore, the axial ratios would be irrelevant to the density of the galaxy cluster. However, our hypothesis was supported. This final graph shows the average local densities all of our galaxies and also the spiral and elliptical galaxies separately. Some of the bars are upside down because they show negative values. In the future, we think it would be a great idea to research why this was the case and if our hypothesis could be supported by a larger set of data. We would also like to research is there is a limit to the size of galaxy clusters. After all, if there is a limit to how large a galaxy cluster can be, there could be a limit to the universe!