Wolfram Schmidt - A Practical Guide to Astrophysical Problem Solving

Undergraduate Lecture Notes in Physics (ULNP) publishes authoritative texts covering topics throughout pure and applied physics. Each title in the series is suitable as a basis for undergraduate instruction, typically containing practice problems, worked examples, chapter summaries, and suggestions for further reading.

ULNP titles must provide at least one of the following:

ULNP especially encourages new, original, and idiosyncratic approaches to physics teaching at the undergraduate level.

The purpose of ULNP is to provide intriguing, absorbing books that will continue to be the readers preferred reference throughout their academic career.

More information about this series at http://www.springer.com/series/8917

This Springer imprint is published by the registered company Springer Nature Switzerland AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Over the last decades the work of astronomers and astrophysicists has undergone great changes. Making observations is an essential part of astronomy, but most researchers do not operate instruments directly any longer. Most of the time they receive huge amounts of data from remote or even space-bound telescopes and make heavy use of computing power to filter, process, and analyse these data. This requires sophisticated algorithms and, these days, increasingly utilizes machine learning. On the theoretical side of astrophysics, making important discoveries just with pencil and paper belongs to the past (with the occasional exception from the rule). Scientific questions in contemporary astrophysics are often too complex to allow for analytic solutions. As a consequence, numerical computations with a great wealth of physical details play a major role in research now. Back-of-the-envelope calculations still serve their purpose to guide researchers, but at the end of the day it is hardly possible to make progress without writing and running code on computers to gain a deeper understanding of the physical processes behind observed phenomena.

In this regard, it is surprising that the education of students at the undergraduate level is still largely focused on traditional ways of problem solving. It is often argued that being able to program comes along the way, for example, when students engage with their research project for a Bachelors thesis. It is said that problems in introductory courses can be solved mostly with analytic techniques, and there is no need to bother students with programming languages. However, we are convinced that there is a great deal of computer-based problem solving that can be done right from the beginning. As a result, connections to contemporary science can be made earlier and more lively. One of the obvious merits of becoming acquainted with a programming language is that you can learn how to address a question by developing and implementing an algorithm that provides the answer.

There are two major avenues toward learning a programming language. One follows the systematic teaching model, where the language is laid out in all details and you are guided step by step through its elements and concepts. Surely, this is the preferable method if you want to master a programming language. For the beginner, however, this can become tiresome and confusing, especially since the relevance of most of the stuff you learn becomes clear only later (if at all). The alternative approach is to learn mainly from examples, to grasp the language in an intuitive way and to gradually pick up what you need to know for practical applications. We believe that Python is quite suitable for this approach. Of course, there is always a downside. This textbook is far from covering everything there is to know about Python. We focus on numerical computation and data analysis and make use of libraries geared toward these applications.

Problem solving is an art that requires a lot of practice. The worked-out examples in this book revolve around basic concepts and problems encountered in undergraduate courses introducing astronomy and astrophysics. The complete source code is provided on the web via uhh.de/phy-hs-pybook . We briefly recapitulate essential formulas and basic knowledge, but our recaps are by no means intended to replace lecture courses and textbooks on astronomy and astrophysics. This is highlighted by frequently referring to introductory textbooks for further reading. Our book is mainly intended for readers who want to learn Python from scratch. In the beginning, code examples are explained in detail, and exercises start at a rather elementary level. As topics become more advanced, you are invited to work on problems that require a certain amount of effort, time, and innovative thinking. If you have already experience with programming and know some Python, you can concentrate on topics you are interested in. Our objective is that examples as well as exercises not only help you in understanding and using Python but also offer intriguing applications in astronomy and astrophysics.