Applied Multi-Messenger Astronomy 1

Multi-messenger astronomy is a newly emerging field of astronomy dedicated to the understanding of the high-energy content of our universe. In contrary to classic astronomy, it is focused on neutrinos, gamma rays, and cosmic rays at energies between several MeV and EeV. In order to analyse the enormous amount of data collected from various observatories, it is common practice to apply analysis techniques from statistics, numerics, and data science. We want to broaden the students' understanding for the important results and open questions of multi-messenger astronomy and teach the ability to understand and reproduce some of the most important results of the field by applying basics tools of statistics, data analysis, and software engineering.

In the introductory module Applied Multi-Messenger Astronomy I, the main discoveries of leading experiments like Fermi-LAT, IceCube, and MAGIC are discussed. Examples are searches for and characterization of the diffuse neutrino and gamma-ray flux, (non-thermal) point sources or emissions from the Galactic plane. We will introduce basic terminology such as effective area and point-spread function. Based on this knowledge, the module will cover fundamental methods of statistics that are commonly used in those analysis, i.e. central limit theorem, Poisson statistics, likelihood ratio hypothesis tests, and Monte Carlo simulations. In parallel, important software frameworks such as Python and numerical libraries such as NumPy and SciPy are introduced with a special focus on their application in data analyses. Numerical methods discussed in this context could be splines or numerical integration and minimization algorithms.

The contents of the Lecture comprise:

• instruments for gamma-ray observations (Fermi-LAT, MAGIC, CTA)
• instruments for the observation of neutrinos (IceCube, KM3Net, GVD)
• instruments for observing cosmic rays (Auger, Telescope Array)
• the corresponding main scientific milestones.
• introduction to scientific programming with Python (Numpy, Scipy, Matplotlib)
• basics of statistical data analysis (chi2, Likelihood, p-Values, ...)
• tools for data analysis (minimizers, Markov-Chain Monte Carlo, machine learning)

After successful completion of the module the students are able to:

• understand the basic concept of multi-messenger astronomy
• iterpret the content of scientific publications in that field
• plot data in Python using Matplotlib
• solve statistical problems in Python using NumPy and SciPy
• understand and perform maximum likelihood and chi2 fits
• understand the concept of and use minimizers like Minuit
• understand the concept of and perform Markov-chain Monte Carlo sampling

No preconditions in addition to the requirements for the Master’s program in Physics.

In the lecture, the learning content is presented in three blocks. In the first block, the concept of multi-messenger astronomy is introduced and the working principals of telescopes like IceCube, Fermi-LAT, and MAGIC are explained. In the second block, basic programming concepts and the Python programing language are introduced. In the last block, basic statistical concepts are repeated and an introduction to the most important numerical tools for data analysis and model fitting is provided.

In the exercise, the students learn how to plot data and solve statistical problems in the programming language Python by working on hands-on exercises under supervision. The students are provided with a virtual Linux machine that has all the required software pre-installed.

PowerPoint presentations (recordings also available to students), live coding, text books, complementary literature

• T.K. Gaisser, R. Engel & E. Resoni: Cosmic Rays and Particle Physics, Cambridge University Press, (2016)
• M.A. Wood: Python and Matplotlib Essentials for Scientists and Engineers, Morgan & Claypool, (2015)
• G. Cowan: Statistical Data Analysis, Oxford Science Publications, (1998)

The achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using presentations independently prepared by the students. The exam of 25 minutes consists of the presentation and a subsequent discussion.

For example an assignment in the exam might be:

• Derive the energy spectrum from a given Fermi data set and fit the spectral index (using Python code).
• What is the expectation value of a Poisson distribution?
• What is the key advantage of the multi-messenger approach?
• What is an effective area and what can it be used for?

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.