96383 - Computational Astrophysics and Statistics

Learning outcomes

The aim of the course is to provide knowledge and understanding of the fundamental numerical techniques currently employed in astrophysical simulations. The student will learn to solve ordinary and partial derivatives differential equations describing interesting astronomical problems. At the end of the course the student will be able to design and run simple numerical simulations of gasdynamical and N-body astronomical problems. A main goal of the class is to accustom the students to research fields which heavily use simulations and to understand merits and caveats of such studies.

Course contents

This course is arranged in two modules; each module includes a theory part and laboratory hours. The students will work on several astrophysical projects and will write short reports on them. Students can work in group (up to four people) or alone, but team work is encouraged.

Module 1: Computational Astrophysics.

Gasdynamics: 1) astrophysical plasma, 2) equations of gasdynamics; 3) sound waves and shock waves; 4) astrophysical applications: evolutions of supernova remnants, stellar wind bubbles, galactic winds, Bondi accretion, AGN feedback.

Numerical Astrophysics. 1) finite differences approximation; consistence, convergence and stability of a numerical scheme. 2) Conservative and transportative properties, control volume approach.. 3) Methods for hyperbolic equations: FTCS, Lax, Upwind. Von Neuman stability analysis. 4) Second order methods for hyperbolic equations: Lax-Wendroff, Upwind II order. 5) Godunov methods: I and II order. 6) Methods for parabolic equations: explicit and implicit schemes. Crank-Nicholson method. 7) Methods for Hydrodynamics: a simple 1d hydrocode. 7) Tests and applications of the hydrocode: Sod shock tube, SNRs, stellar wind bubbles, cooling flows, Bondi accretion.

Lab Projects: 1) Shock tube test; 2) Evolution of SN remnants and stellar wind bubbles; 3) AGN feedback

Module 2: Statistics.

In this module we will introduce the basic theory and methods of statistics and error analysis. Topics will include:

- Probability theory

- chi-squared model fitting

- Bayesian inference

- population statistics

- statistical estimators

Background knowledge: students must be familiar with calculus and basic computer operative systems (linux).

Most the exercises involve programming in Fortran and Python. Some introduction will be given at the beginning of the class, but some self-study might help if the student is unfamiliar with these languages.

Students are strongly encouraged to talk to the professor for every questions/problems.

Readings/Bibliography

Lecture slides (on "Virtuale" website)

Text on the fluid dynamics part: Clarke & Carswell: “Principles of Astrophysical Fluid Dynamics”

Texts on the numerical fluid dynamics part:"Numerical Methods in Astrophysics”, Bodenheimer et al.

"Computational Fluid Dynamics", John D. Anderson, McGraw-Hill

More texts and papers will be suggested in class.

Teaching methods

Teaching makes use of powerpoint presentations (always available before the lectures on the Virtuale website) and blackboard. During the Lab sessions the students will design, run and analyze numerical simulations, guided by the professor and tutor. Students can use both the PC in the Lab or her/his own laptop (some help with the software installation can be provided).

Note: to attend this class it is required by the University policy that all students take the on-line courses (modules 1 and 2) on the Safety in University Computing Lab (see: https://elearning-sicurezza.unibo.it/).

Assessment methods

For the Computational Astrophysics (CA) module the exam is structured as follow:

1) the students (or groups) must submit the written reports at least three days before the oral exam. Each report should be approximately 10 pages long, with a brief description of the project aim, the numerical methods used and results. More details will be provided in class.

2) Oral exam: it includes a discussion about the projects and questions about the theory of numerical methods. No questions will be asked about gas dynamics.

The score for the CA part is an average between the report evaluation and the oral performance.

For the Statistics module:

The students must submit reports on the assigned project, which will be graded. No oral exam for this module.

The final score for the CAS Course is a weighted average between the CA module and the Statistics one, the weight being the corresponding number of credits.

The grade scale, 0-30, can be (roughly) described as:

1) limited (though sufficient) preparation and capability to explain the numerical techniques adopted in the projects, coupled with poor responses to the theory questions: 18-22;

2) satisfactory though not complete preparation in technical and theoretical issues: 23-25;

3) good/very good capability to explain the project design and results and almost complete answers to theoretical questions: 26-28;

4) excellent/outstanding ability to discuss the topics covered in the course: 29-30. Honors are awarded by the professor to students who have shown exceptional mastery in numerical techniques.

By policy of the LM in Astrophysics and Cosmology Course, students may not decline a grade more than twice.

Students with learning disabilities or temporary or permanent disabilities: please contact the relevant University office promptly (https://site.unibo.it/studenti-con-disabilita-e-dsa/it). The office will advise students of possible adjustments, that will be submitted to the professor for approval 15 days in advance. He/she will evaluate their suitability also in relation to the academic objectives of the course.

Teaching tools

Powerpoints presentations (available before the lectures), blackboard writing, guided laboratory sessions.

Office hours

See the website of Fabrizio Brighenti

See the website of Robert Benton Metcalf