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.
Astrophysical Applications#
Throughout the course, we’ll see some applications to interesting problems in astrophysics. Here’s a listing to some of them:
An example of using numerical differentiation to estimate the 3-\(\alpha\) reaction \(T\) sensitivity.
An example of integrating to infinity by integrating the Planck function over wavelength.
Demonstrating root finding by numerically deriving Wien’s law.
Combining integration over the Fermi-Dirac distribution and root-finding to find the electron degeneracy parameters.
Using adaptive stepping in ODE integration to solve the few-body problem.
Shooting methods for two-point boundary value problelms applied to the Lane-Emden equation for polytropes.
Investigating the longterm stability of planetary systems using symplectic integrators.
ODE integration + root finding to explore limit-cycles in a one-zone model of an X-ray burst
Using stiff-ODE solvers to integrate an CNO reaction network
A demonstration of using Newton’s method to find the stationary states of the Lorenz system.
Using linear regression to estimate \(H_0\) from Type Ia supernova.
Using FFTs on time-series data to study low mass X-ray binaries.