Astrophysical Fluid Dynamics

A.Y. 2024/2025
6
Max ECTS
42
Overall hours
SSD
FIS/05
Language
Italian
Learning objectives
The course aims at providing theoretical knowledge concerning astrophysical fluid dynamics. The course will consider the fluid equations, discussing astrophysically relevant equilibrium configurations (such as polytropic spheres), wave phenomena, shocks and instabilities, such as the gravitational instability. In the second part of the course, the focus will be on accretion discs and their applications in astrophysics.
Expected learning outcomes
At the end of the course, the student will be able to: 1. Describe and solve fluid equations in specific configurations. 2. Recognize and describe hydrostatic equilibrium configurations in astrophysical contexts. 3. Derive the dispersion relation for the propagation of sound waves and dispersive waves. 4. Solve the equations describing shock waves. 5. Recognize the fluid processes at work in the dynamics of astronomical objects, such as stars, the interstellar medium and gas around compact objects. 6. Describe the Navier-Stokes equations and the role of viscosity in astrophysics and in physics, with special attention to turbulence. 6. Describe the equations that determine the evolution of accretion discs. 7. Recognize the spectrum of an accretion disc and derive its physical properties. 8. Understand the dynamics and emission from accretion discs in specific contexts, such as compact objects and young stars.
Single course

This course can be attended as a single course.

Course syllabus and organization

Single session

Responsible
Lesson period
First semester
In case of emergency, lectures will be provided synchronously through zoom and a virtual board. Lectures will be recorded and uploaded on the relevant University platforms.
Course syllabus
-) Introduction to fluid dynamics: Eulerian and Lagrangian approach.
-) Reynolds transport theorem.
-) Continuity and Euler equations. Energy equation. Barotropic fluids
-) Examples of hydrostatic balance.
-) Polytropic spheres and their applications in astrophysics. Bonnor-Ebert spheres.
-) Perturbations in a fluid. Sound waves
-) Shock waves. Rankine-Hugoniot relations.
-) Instability in a fluid: thermal, convective and gravitational instability. Rayleigh-Taylor and Kelvin-Helmoltz instabilities.
-) Viscous fluids - Navier-Stokes equations.
-) Vorticity and turbulence. Kolmogorov's theory of turbulence.
-) Spherical accretion
-) Theory of accretion discs: fundamental equations, stationary and time-dependent solutions.
-) Anomalous viscosity in accretion discs.
-) Gravitational instabilities in accretion discs.
-) Accretion discs around compact objects and young stars: SEDs, line profiles.
-) Outbursts and variability.
-) Warped accretion discs.
-) Transient phenomena and tidal disruption of stars by supermassive black holes.
Prerequisites for admission
1. Basic knowledge of mechanics (e.g., the two-body problem, Kepler's laws)
2. Calculus, especially solving one- and multi-variable differential equations, and Fourier transforms.
Teaching methods
Chalkboard lectures.
Teaching Resources
Clarke-Carswell, "Astrophysical Fluid Dynamics", Cambridge University Press.
Assessment methods and Criteria
The exam will be an oral discussion on the course topics.
FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 6
Lessons: 42 hours
Professor: Lodato Giuseppe
Professor(s)
Reception:
Monday 14.00-15.00 (upon appointment)
Teacher's office