Greetings from the Astrophysics Institute of Potsdam!

By Zachary Bierstedt, Senior

Greetings from the Astrophysics Institute of Potsdam!

During my stay here in Germany, I have been fortunate enough to participate in not one, but two 1-week internships at places here in Germany. Last week I was at Rolls Royce Deutschland, and this week (Feb. 4-8) I have been at the Leipnitz Institute of Astrophysics. Many of you might remember earlier in the year I asked where you all wanted to me to focus on, fiber optics or solar. In the end, I ended up with neither.

Monday was the introduction day, where I was familiarized with the computer system. The AIP uses Unix, which is a Linux system, and I have to say that the way it is set up is weird. There are keyboard commands to get everywhere, not icons you can follow, so, for example, if you want to change the document folder you are in, you have to use cd (change directory) followed by the code of the folder you want to go to. I personally much prefer the Windows setup, but I’ve learned my way around Unix. After having a chance to get settled, I started right away with graphing the generic setup of the light cones for Einstein’s theory of special relativity. If you want an explanation of it, unfortunately I can’t give it because I don’t really understand it myself, just that it involves taking into account what position you are observing from and time dilations.

Tuesday had the potential to be a really good day, since I attended a lecture on the origins and the models of dark energy. Unfortunately, it was the last in a series designed for German university students, so I didn’t understand the language, the math, or any of the background. A couple of the models are covered in the YouTube video on dark energy, which, while far from detailed, is good for getting a basic idea of both the start of the universe and what dark energy is. The link is at the bottom.

Left is the physics building of the University of Potsdam in Golm, which is where the lecture was held. Wednesday was back at the AIP. First I was asked to program the Monte-Carlos method for determining pi. Basically, the concept is that you have a square of side length 1. Within this square, there is a quarter-circle of radius 1. Using a random number generator, the number of points that land inside the circle divided by the total number of points is about the same as the area of the quarter circle divided by the area of the square, and from this you can find pi. The more points you have placed in the square, the more accurately you’ll be able to approximate pi. Following this was a meeting on dark matter halos. From what I understood, every galaxy or galaxy cluster has a halo of dark matter surrounding it. We can’t see them, but we can observe the impact the rotation of the halo has on the motion of the galaxy, and from that we can determine the density of the halos. Determining the density of the halos helps us understand what impact they have on galaxies.

Thursday was even more programming. First was programming to find an approximation of the integral of a function using Simpson’s Rule. This was not too difficult once I figured out what to write, and then I plotted the integral approximation in a spreadsheet program. Following this was the first cosmological programming I’ve done, with 2-point correlation functions. This basically tells us how the density of galaxies within 2 spheres or circles of space are correlated. In a uniformly distributed field, the correlation function is equal to 0. However, by a complete accident the formula wasn’t explained well to me, so I got impossible answers without having an error in my program.
Friday was learning much more about the 2-point correlation equation. The function actually tells us how the density is correlated to the distances between points in a cube of space of an arbitrary size. I chose to use 50 megaparsecs for each side of the cube. Then, simulating a random distribution of 100,000 points within the cube, I wrote a program to find the distances between each point and every other point. I did get the program to work after a while. The computer just took nearly 5 minutes to run the full program. Then I moved all the points to within a circle with a radius of 10Mpcs, and ran the program again. The correlation function is, within each distance category, the number of distances of that length with the data set divided by the number of distances of the same length in the random set minus 1, or f(x)=(DD/RR)-1. There is a symbol used instead of f(x), but I don’t recall what it is. Overall, I did enjoy this internship. While I much preferred the work at Rolls Royce, the work I did at the AIP, despite it having no value to any of the projects underway at the AIP, is still very useful to know how to do before entering a career, and it involved a lot of programming, which I like to do.

Links: SciShow Dark Energy: http://www.youtube.com/watch?v=ATwVApurIQ4.

2-Point correlation functions: http://www.astro.rug.nl/~weygaert/tim1publication/lss2007/computerII.pdf

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