AST 390: Computational Astrophysics

Michael Zingale

(Spring 2025)

This is a collection of notebooks on computational (astro)physics. Starting at the beginning, these notebooks introduce numerical methods for derivatives, integration, rooting finding, ODEs, and linear algebra and then move onto applications in astrophysics.

Course Outline

We’ll start with an An Overview of Python and Version Control with Git and then move on to core numerical methods.

You should follow the outline in the navigation panel to the left.

Note

This course assumes that you are already familiar with a programming language.

List of Astrophysical Applications

Throughout the course, we’ll see some applications to interesting problems in astrophysics. Here’s a listing to some of them:

Blackbody Radiation

An example of integrating to infinity by integrating the Planck function over wavelength.

Wien’s Law

Demonstrating root finding by numerically deriving Wien’s law.

Degeneracy

Combining integration over the Fermi-Dirac distribution and root-finding to find the electron degeneracy parameters.

Few-Body Problem

Using adaptive stepping in ODE integration to solve the few-body problem.

Polytropes

Shooting methods for two-point boundary value problelms applied to the Lane-Emden equation for polytropes.

Lorenz System Stationary States

A demonstration of using Newton’s method to find the stationary states of the Lorenz system.

Hubble’s Constant

Using linear regression to estimate \(H_0\) from Type Ia supernova.

X-ray timing

Using FFTs on time-series data to study low mass X-ray binaries.

Integrating the CNO Cycle

Using stiff-ODE solvers to integrate an CNO reaction network