My REU Project
I'll admit that I didn't know anything about neutrinos or neutrino astronomy when I first arrived in Madison, and that was only part of the learning curve. I spent the first two weeks or so reading articles, searching the web, going through powerpoints and talking to my advisor trying to get some working knowledge about what IceCube was. Once I finally got a handle on that, I was given a laptop with Linux on it (something else I didn't know) so I spent some time getting used to RedHat and typing commands... Then I finally got started on the project, only to find out that everything was done in C or C++ (yet something else new to learn).
Thankfully I did have a programming background, so making the switch from Visual Basic and Java to C++ was (relatively) painless. One thing that I didn't know about but I have used extensively is ROOT. Root is, and I quote, "an object oriented framework for large scale data analysis". This functions partly as a C/C++ interpreter to programs can be written and quickly tested in an interactive envoronment. Statements can even be written inline as little code snippets and executed right away. Another aspect of Root that I utilized was some of the analysis options. Root has some built in features that allow the user to manipulate and plot data in several different formats. For the most part, I used the histogram classes to generate my plots, but looking around the Root site, there is an incredible number of features that Root offers users. This link will direct you to a code that I used to generate some plots, and it shows the implemenation of some of Root's functions
But in addition to these things, I also had a great support network here at IceCube. First, my mentor, Teresa Montaruli. Not only is she incredibly knowledgable, but she was very patient in working with me, especially at the beginning. She was able to teach me so much about the collaboration, physics in general, programming and more. Juancarlos Diaz-Velez was also a great resource, helping me to dig myself out of my programming when I was totally lost. Albrecht Karle provided me the intial code that got me started on my specific aspect of the project. Jonathan Dumm and Alessio Tamburro were also great helps when it came to aspects of the project that confused me, or were just able to answer random questions that I had. The tech crew was also very helpful getting me started and continually harassing me about using Linux. There were many others here at IceCube that I have met this summer, and for their help and hospitality, I would like to thank them.
So what can an undergrad offer a huge program like that? I was given a project called Shadow of the Moon. A telescope is only as good as how well you can see targets with it, and how accurate it is at pointing. With optical telescopes, it is fairly easy to aim your telescope toward a known celestrial object, and then, if you see it through your telescope, you know you're pointing in the right direction. Even for radio astronomy and other wavelengths, there are plenty of known sources of their respective signals. However, there is not yet a known source of continuous neutrino emission. So telescopes like AMANDA and IceCube need to callibrated some other way.
To know how well your telescope points you need a known body to look at. Luckily, we happen to have two pretty big ones right in our backyard: the Sun and the Moon. One of the sources of muons that IceCube looks for is cosmic rays. Well, the Moon and the Sun will both block some of those cosmic rays, meaning that when they finally get to Earth, there will be fewer to produce muons, and fewer for IceCube to detect. In essence what you get is a 'bald spot'. We can compare where the bald spot is in the data with where the Moon actually is, and if they coincide, then we have an accurate telescope.
The first step is to find out where the Sun and Moon are supposed to be. There are several ways to do this. One is to use a table listing the position of the bodies over various times. This type of table is know as an Ephemeris. At the NASA JPL website you can generate an ephemeris for a number of celestrial bodies. There are a number of other sites that will give you accurate positions of things like the Moon.
Another way is to write a computer algorithm that will do the calculations for you. In this way, you can have a dynamic system that can generate results based on the specific input you want it to have. You can also format the results exactly as you want them; whether that means giving coordinates in a horizonal, equatorial, eliptical or galactic system.
Several of these algorithms exist. The standard is a very long involved process first published by a French Astronomer named Jean Meeus. In his book Astronomical Algorithms, he acually gives formulae and processes for determining a number of astronomical events. This is a very complete resource, and for the most accurate results (10 arcsec in longitude, 3 arcsec in latitude, and 0.2 arcsec in HP), this method is preferred. Another algorithm was one based on code from Albrecht Karle shown here. However, in most cases this level of precision is not required, and much simpler versions can be utilized without sacrificing too much accuracy in the results.
In this project, we have opted to use an algorithm provided in SLALIB; a datbase of astronomical algorithms calculating everything from positions of planets and moons, to calculating dates, coordinate conversions and more. We are still confident that the results we gain are accurate enough, after comparing several of our results with the NASA JPD ephemerides. As quoted in SLALIB, the directional accuracy of the Sun and Moon is 5 and 30 arcseconds, respectively.
This is actually a plot comparing each of the three sources of data we used: Albrect Karle's code, SLALIB and the NASA JPL Ephemerides. This shows the absolute differences in declination values over the year 2005. Using this algorithm, we were able to generate some histograms that will allow us to predict when our greatest chances for observing the Sun and Moon's shadows will be, and how effective our process will be. I also made a plot with the declinations from all three sources laid over each other, but they lined up so well, that there was no noticeable difference. They all looked exactly like the red line in the figure below.
This graph displays the declination of the Moon and the Sun over a year. But simply knowing the position of the Moon/Sun isn't enough. In order to estimate how long it will take IceCube to see their respective shadows, we need to know how many muons we can expect, which will then allow us to calculate how many we expect to be blocked. Another criteria for the search is, under what conditions we will have the best chance of seeing the shadows. One of these is having the Moon or Sun at a declination of at least 20 degrees, or sufficiently above the horizon. The reason for this will be explained shortly. Based on my 2005, model the Sun spends much less time between the cutoff of 20 degrees and its maximum of 23 degrees (only about 17% of the time) as compared to the Moon at a maximum of 28 (about 27% of the year).
But why do they have to be above the horizon? Isn't IceCube supposed to see things coming through the Earth? Yes, but keep in mind that these are two entirely different types of events. Normally, IceCube is looking for muons that are generated close the detector from neutrinos that have travelled galactic or extra-galactic distances. In the case of the Sun or Moon's shadow, we are trying to observe atmospheric muons produced in the atmosphere from cosmic rays. Unlike neutrinos, muons interact much more, and as a consequence cannot travel as far. This first image shows the expected comic ray muon flux as a function of depth. Since the muons will have to travel through differing amounts of ice or water or rock to reach IceCube, we cannot assume a constant value. Compare the predicted muon flux with the image below. You can clearly see how sharply the muon rate drops off as the angle reaches the horizon, and how much farther the muon needs to travel before reaching the detector. This requires the muons to have more evergy, as muons lose roughly 0.2 TeV/km due to ionization. This is related to this second graph, which shows atmospheric muon flux as a function of the cosine of the zenith angle. From straight above, the muons do not need to travel as far, so the flux is obviously expected to be higher. As the zenith approaches the horizon, the flux drops off sharply. Atmospheric muons are not incredibly energitic to begin with, and as the declination decreases, fewer are likely to reach IceCube. Keep in mind that these muons are downgoing, unlike the sources that are of primary interest to IceCube, which are 'upgoing'.
From previous images we can clearly tell that the maximum declination of the Moon is about 29 degrees and the Sun is about 23.5 degrees. Also, to make sure we are recieving good signals, we want our data to be taken when they are at a declination of at least 20 degrees. In the above graphic, this corresponds roughly to the area between M4 and M6 for the Moon and M5 and M6 for the Sun. These are not especially large areas, considering the ability of IceCube to scan the entire sky. This means that the muon will have to travel between 3.8 and 5.56 km of ice before reaching the detector.
So now we have our expected muon flux, all of the information about our detector, now we can actually begin the calculations regarding how long it will take to see the Moon's shadow. The first is to choose a muon flux. Based on the criteria of 20 degrees in declination, we choose a conservative value of 8.5 x 10-9cm-2sec-1sr-1 from the above graph. From there, it turns into a fairly straightforward calculation. We decide on a search bin (3 degrees in radius, centered on the Moon) and go from there, calculating the number of expected events, then number of events in an area with 0.26 degrees (radius of Moon), the number of blocked events, the significance of such a deficit, and then we modify the results for IceCube, since all of our original calculations were based on AMANDA. The following table illustrates the results. For a detailed set of the calculations, click here. As a note, the variable p in the calculations refers to the percent of a year that the Moon or Sun will spend above 20 degrees,
One quantity you may note is anglular resolution. For this type of detector, angular resolution is defined as the angle between the true muon track and the reconstructed path. This angle give us a search bin to find potential point sources. This Paper talks about the reconstruction of tracks in AMANDA. Figure 8 show the correlation between reconstructed zenith angle and true zenith angle, and fig 9 shows the opening angle between a true and reconstructed track and finally fig 10 gives the angular resolution vs level of cut on the quality of the reconstruction (median means that is the angle that includes 50% of the events mean is the mean of the distribution sum_over_all events angles between true-reco track/total number of events. Figure 6 of this document show the angular resolution of IceCube as it depends on zenith angle. While this gets pretty technical, it is simplest to say that IceCube will have a better idea where it's pointing than AMANDA does.
This is actually an adventageous time to be looking for the Moon's shadow. If you look at the image below, you can see that maximum declination oscillates over the years. This image shows the declination of the Moon when it is above the horizon for the years 2000-2030. The red line signifies the 20 degree cutoff for data collection, and the bright yellow is roughly July 2005. We are coming up on a period of time when the Moon will be at its maximum, giving us ample data collection time. However, you will also notice that near the beginning of 2014 and lasting for about 3.5 years, the Moon will never reach the 20 degree cutoff, making observations of this sort incredibly difficult.
As mentioned at the top, I spent a large amount of time reading articles and papers to bring myself up to speed on IceCube and similar projects. Here I am going to take the opportunity to list some of them for anyone who wants to read further about neutrino astronomy and the technology behind it.
Some multimedia resources