96383 - Computational Astrophysics and Statistics

Academic Year 2023/2024

  • Moduli: Fabrizio Brighenti (Modulo 1) Robert Benton Metcalf (Modulo 2)
  • Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Astrophysics and Cosmology (cod. 5828)

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

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; 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


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

Teaching methods

Lectures and discussion on the theory, using both slides and blackboard. Lab sessions, designing and running numerical simulations.

Assessment methods

Oral exam and written report on the astrophysical project investigated during the Lab sessions.

Teaching tools

Blackboard and slides.

Office hours

See the website of Fabrizio Brighenti

See the website of Robert Benton Metcalf