48716 - Numerical Calculation and Statistics

Learning outcomes

At the end of the class the student will be able to numerically solve ordinary and partial derivative equations (for instance the gasdynamics equations). The student will be able to set-up and investigate astrophysical problems, like the evolution of SN remnants, AGN feedback in galaxies, and more).

Moreover, the student will learn commonly used statistical methods to analyze measured quantities and estimate uncertainties.

Course contents

Statistics:measurement concepts; measurable quantities (mass, luminosity...) and associated uncertainties. Analysis of astronomical data; comparison between distributions, likelihood tests. Determination of relations between observables (Tully-Fisher relation, Faber0Jackson relation). Signal analysis; signal-to-noise ratio for photometric and spectroscopic observations. Limiting magnitude; completeness of a sample. K-sigma clipping. Sky background determination. Masses of galaxy clusters using galactic dynamics. Galaxy luminosity functions. 

 

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.

 

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) Methods for parabolic equations: explicit and implicit schemes. Crank-Nicholson method. 6) 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...

Readings/Bibliography

Lecture slides (on Campus 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.

Numerical Recipes”, Press et al.

Teaching methods

Lectures on the theory used, using both slides and blackboard. Lab sessions.

Assessment methods

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

Office hours

See the website of Fabrizio Brighenti

See the website of Carlo Nipoti