Dynamo Theory in Astrophysics
by ,
Sala de Juntas (Edificio A)/Salón de Actos
IAA
Magnetic fields are ubiquitous in the Universe, including the geomagnetic field, the systematic magnetic field responsible for the eleven year solar activity cycle, and the magnetic fields of planets, stars, galaxies and accretion disks. It is now generally accepted that these fields are created by the action of hydromagnetic dynamos; i.e. by the motions of conductive fluids or plasmas that sustain the field against the action of Ohmic dissipation. For all these objects there is no ab initio predictive theory for the origin of their magnetic fields. Since the 1950s, mean-field electrodynamics explains sustained large-scale astrophysical magnetic fields through systematic stretching and twisting of magnetic field lines by turbulent flows. This process is efficient when velocity and magnetic field fluctuations correlate well, so that net electromotive force is non-zero. This is possible for flows which possess a high degree of asymmetry and linkedness. Astrophysical rotating turbulence often complies with this assumption, however, high flow complexity of the flow means that analytical dynamo solutions are very challenging to derive. 3D numerical simulations became and remain the main tool of dynamo modelling.
Following the footsteps of Andrei Kolmogorov and Keith Moffatt, in this short course we aim to introduce you to the basics of turbulence and mean-field dynamo theory, as well as their link to recent numerical simulations, and the perspectives for astrophysics. The course will be delivered in English, although the discussion and questions in Spanish are welcome.
Pre-requisites:
Basics of physics and mathematics
Basics of fluid dynamics desirable (we will re-introduce the concepts on the go)
Syllabus:
Session 1: Introduction to turbulence in astrophysics Monday 9:00-12:00
Short introduction on turbulence and magnetism in astrophysics
Fluid mechanics equations:
- Without rotation or magnetic field
- With rotation and/or magnetic fields
- Dimensionless parameters
- Vorticity, helicity and the alpha tensor.
Laminar vs. turbulent flow and the energy cascade.
Examples of turbulent flows:
- Rayleigh-Bénard convection
- Circular Taylor-Couette flow and the Taylor-Proudman theorem
- Magneto-rotational instability
- Wave-induced shear flows.
Session 2: Fundamentals of dynamo theory Tuesday 9:00-12:00
Derivation and dimensionless analysis of dynamo equations.
Kinematic dynamo problem and anti-dynamo theorems.
Ponomarenko dynamo as a simple example of analytical flow.
Mean-field dynamo theory, in connection to simulations.
Dynamo nonlinearity and saturation mechanisms.
Experimental evidence and brief intro to dynamo experiments.
Where to try? Numerical software to solve the dynamo problem.
Session 3: Links with observations and new results Wednesday 9:00-12:00
Convective dynamos:
- Magnetic field of the Earth and its reversals
- Solar cycle peculiarity and its existing theories; relation to low-mass stars
Instability-driven dynamos:
- Magnetorotational instability in accretion discs
- Magnetorotational and Taylor-Spruit instability in stars
Perspectives and promising directions
Further reading:
“Magnetic Field Generation in Electrically Conducting Fluids” by K.H. Moffatt 1987, Cambridge University Press.
“Self-Exciting Fluid Dynamos”, K.H. Moffatt and E. Dormy 2019, Cambridge University Press.
“Turbulence in rotating, stratified and electrically conducting fluids” by P. Davidson, 2013, Cambridge University Press.
Short bios:
Dr. Anna Guseva is an expert in numerical and mathematical modeling of astrophysical dynamos and shear flows. After her PhD on accretion disc flows and magnetism (2018, Bremen, Germany), she conducted postdoctoral research in hydro- and magnetohydrodynamics at the Paris Observatory (France), the University of Leeds (UK), and the Polytechnic University of Madrid (Spain). Her research on hydro- and magnetohydrodynamics was funded by the German Research Foundation and ERC. She was a Marie-Curie Postdoctoral Fellow in 2020-2022 and currently holds a PSL-Paris Observatory Postdoctoral Fellowship. As a Severo Ochoa Visitor at IAA, she is excited to share her insights on dynamo theory with the astrophysics community of Granada.
Dr. Giovanni Mirouh is an Emergía fellow at the University of Granada, and an expert in stellar structure, evolution, and oscillations. He obtained his PhD in astrophysical fluid dynamics from the Université Paul Sabatier (Toulouse, France) in 2016 before postdoctoral stays at the International School of Advanced Studies (SISSA Trieste, Italy), the University of Surrey (Guildford, UK), the University of Granada (Spain) and IAA (Granada, Spain). His work now concentrates on the 1D and 2D modeling of a variety of main-sequence stars (single, binary or in clusters), with an additional focus on (rapidly-)rotating delta Scuti stars and the interaction between rotation and oscillations.
